Use rust-based formula dispersion

[domna]

This is an example for using the rust-based formula dispersion. The idea was that it would be faster but currently it is beaten by the python code with caching.

Remaining steps:

• Add caching in rust to see how it competes against python
• Check the failing tests due to divide by zero.

[domna]

Current benchmark with rust bindings:

---------------------------------------------------------------------------------------- benchmark: 6 tests ----------------------------------------------------------------------------------------
Name (time in ms)                    Min                 Max                Mean            StdDev              Median               IQR            Outliers       OPS            Rounds  Iterations
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
test_solver2x2                    4.0192 (1.0)        4.3147 (1.0)        4.1237 (1.0)      0.1047 (1.0)        4.0976 (1.0)      0.1540 (1.06)          2;0  242.4982 (1.0)          10           1
test_solver4x4_linear             4.5520 (1.13)       5.1403 (1.19)       4.7223 (1.15)     0.2002 (1.91)       4.6689 (1.14)     0.1447 (1.0)           2;2  211.7610 (0.87)         10           1
test_formula_solver2x2           34.5330 (8.59)      37.3116 (8.65)      35.0623 (8.50)     0.9151 (8.74)      34.6667 (8.46)     0.4209 (2.91)          2;2   28.5206 (0.12)         10           1
test_solver4x4_expm              97.3387 (24.22)    113.2001 (26.24)    102.1455 (24.77)    5.8321 (55.72)     99.5078 (24.28)    6.1350 (42.40)         2;0    9.7900 (0.04)         10           1
test_solver4x4_eig              116.8847 (29.08)    142.2197 (32.96)    122.6364 (29.74)    8.0648 (77.05)    119.1867 (29.09)    4.6113 (31.87)         2;2    8.1542 (0.03)         10           1
test_formula_solver4x4_expm     130.7959 (32.54)    157.7426 (36.56)    141.9801 (34.43)    7.0223 (67.09)    141.1741 (34.45)    6.8183 (47.12)         2;1    7.0432 (0.03)         10           1
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

and with the lark solution

----------------------------------------------------------------------------------------- benchmark: 6 tests -----------------------------------------------------------------------------------------
Name (time in ms)                    Min                 Max                Mean             StdDev              Median                IQR            Outliers       OPS            Rounds  Iterations
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
test_solver2x2                    3.9415 (1.0)        4.3081 (1.0)        4.0660 (1.0)       0.1016 (1.0)        4.0562 (1.0)       0.0822 (1.0)           3;1  245.9445 (1.0)          10           1
test_solver4x4_linear             4.4783 (1.14)       8.3134 (1.93)       5.0594 (1.24)      1.1572 (11.39)      4.7603 (1.17)      0.3639 (4.43)          1;1  197.6522 (0.80)         10           1
test_formula_solver2x2            6.4304 (1.63)       7.3308 (1.70)       6.8158 (1.68)      0.3166 (3.11)       6.6792 (1.65)      0.5148 (6.27)          3;0  146.7171 (0.60)         10           1
test_solver4x4_expm              96.9094 (24.59)    112.8189 (26.19)    103.5800 (25.47)     5.8240 (57.31)    103.3014 (25.47)    11.4601 (139.48)        5;0    9.6544 (0.04)         10           1
test_formula_solver4x4_expm     104.3337 (26.47)    114.8527 (26.66)    109.5190 (26.94)     3.7164 (36.57)    109.3881 (26.97)     5.3687 (65.34)         3;0    9.1308 (0.04)         10           1
test_solver4x4_eig              117.8164 (29.89)    175.5635 (40.75)    131.5376 (32.35)    19.2656 (189.56)   122.8863 (30.30)    16.9499 (206.29)        2;1    7.6024 (0.03)         10           1
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Lark w/o caching

----------------------------------------------------------------------------------------- benchmark: 6 tests -----------------------------------------------------------------------------------------
Name (time in ms)                    Min                 Max                Mean             StdDev              Median                IQR            Outliers       OPS            Rounds  Iterations
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
test_solver2x2                    4.0126 (1.0)        4.9825 (1.0)        4.2277 (1.0)       0.2915 (1.0)        4.1439 (1.0)       0.2139 (1.0)           1;1  236.5371 (1.0)          10           1
test_solver4x4_linear             4.7363 (1.18)       5.6909 (1.14)       5.1664 (1.22)      0.3476 (1.19)       5.1904 (1.25)      0.6990 (3.27)          4;0  193.5601 (0.82)         10           1
test_formula_solver2x2           14.9416 (3.72)      22.6433 (4.54)      17.9399 (4.24)      3.0592 (10.50)     17.0598 (4.12)      4.6519 (21.75)         2;0   55.7416 (0.24)         10           1
test_solver4x4_expm             112.5193 (28.04)    233.2547 (46.81)    134.6708 (31.85)    35.4077 (121.49)   123.9062 (29.90)    13.5108 (63.16)         1;1    7.4255 (0.03)         10           1
test_solver4x4_eig              124.5915 (31.05)    192.9339 (38.72)    141.7874 (33.54)    21.6871 (74.41)    130.9245 (31.59)    28.0991 (131.36)        1;0    7.0528 (0.03)         10           1
test_formula_solver4x4_expm     138.4375 (34.50)    318.3715 (63.90)    213.8903 (50.59)    62.7734 (215.38)   206.2821 (49.78)    75.0714 (350.94)        5;0    4.6753 (0.02)         10           1
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

[domna]

Benchmark with caching in rust (formula-dispersion>=0.1.1)

---------------------------------------------------------------------------------------- benchmark: 6 tests ----------------------------------------------------------------------------------------
Name (time in ms)                    Min                 Max                Mean            StdDev              Median               IQR            Outliers       OPS            Rounds  Iterations
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
test_solver2x2                    4.0317 (1.0)        4.3632 (1.0)        4.1157 (1.0)      0.0982 (1.0)        4.0971 (1.0)      0.0969 (1.0)           1;1  242.9706 (1.0)          10           1
test_solver4x4_linear             4.5299 (1.12)       5.8187 (1.33)       4.9238 (1.20)     0.4041 (4.11)       4.7483 (1.16)     0.4865 (5.02)          2;0  203.0957 (0.84)         10           1
test_formula_solver2x2            6.6203 (1.64)       8.9543 (2.05)       7.0274 (1.71)     0.7218 (7.35)       6.6708 (1.63)     0.5754 (5.94)          1;1  142.2999 (0.59)         10           1
test_solver4x4_expm              94.2108 (23.37)    109.6198 (25.12)     99.4445 (24.16)    5.1493 (52.44)     97.7993 (23.87)    7.9399 (81.96)         3;0   10.0559 (0.04)         10           1
test_formula_solver4x4_expm      98.1222 (24.34)    107.2682 (24.58)    101.2886 (24.61)    3.2138 (32.73)    100.1234 (24.44)    3.7288 (38.49)         2;0    9.8728 (0.04)         10           1
test_solver4x4_eig              117.1295 (29.05)    132.7289 (30.42)    120.4412 (29.26)    5.5503 (56.52)    117.6996 (28.73)    2.2705 (23.44)         2;2    8.3028 (0.03)         10           1
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------