Task: Arithmetic-Relationship (source dataset: Auto-Relate)

You are given a table with numerical values in multiple columns. Your task is to analyze the data and identify semantic relationships, expressed in arithmetic relationships, that exist between columns.

These relationships may involve any combination of the following operations: addition (+), subtraction (−), multiplication (*), and division (/). The expressions can involve two or more columns and may be nested (e.g., B = (A + C) / D).

Please only identify arithmetic relationships that hold semantically based on the data, and do not return relationships that are likely spurious, e.g., (A = B * 0), where A is an all 0 column. Please only return minimal atomic relationships, e.g., if A = B + C and D = E + F, then there is no need to return A = B + C + E + F - D.

No explanation, return all the formula(s) in JSON format: {"Arithmetic-Relationship": [<list-of-formulas>]}. If no relationship is found, return {"Arithmetic-Relationship": []}.

Input Table:
| A                    |      B |      C |         D |      E |     F |         G |     H |    I | J                     |      K |      L |        M |     N | O   |      P |
|:---------------------|-------:|-------:|----------:|-------:|------:|----------:|------:|-----:|:----------------------|-------:|-------:|---------:|------:|:----|-------:|
| USA                  | 500976 | 178171 | 0.355648  | 100610 | 23007 | 0.228675  | 18601 | 8068 | 0.43374012149884417   | 194455 | 128163 | 0.659088 | 16658 | 793 | 207389 |
| Baltimore            |  10996 |   6302 | 0.573117  |   2456 |  1111 | 0.452362  |   173 |  137 | 0.79190751445086704   |   1561 |   1082 | 0.693145 |   128 | 7   |   2628 |
| Boston               |   5775 |   2165 | 0.374892  |   1110 |   296 | 0.266667  |   573 |  349 | 0.60907504363001741   |    854 |    565 | 0.661593 |   718 | 8   |   2907 |
| Buffalo              |   5318 |   2136 | 0.401655  |   1346 |   442 | 0.32838   |   132 |   83 | 0.62878787878787878   |   1107 |    746 | 0.673893 |   301 | 11  |    789 |
| Cleveland            |  13919 |   4088 | 0.293699  |   1568 |   269 | 0.171556  |   415 |   74 | 0.1783132530120482    |   3753 |   2290 | 0.610179 |   333 | 19  |   6231 |
| Detroit              |  14507 |   7955 | 0.548356  |   1949 |   437 | 0.224218  |   181 |   98 | 0.54143646408839774   |   3397 |   1939 | 0.570798 |   386 | 26  |   4723 |
| Hartford             |   1713 |    152 | 0.0887332 |    435 |    35 | 0.0804598 |    91 |   22 | 0.24175824175824176   |    444 |    259 | 0.583333 |    48 | 3   |    878 |
| Indianapolis         |  12554 |   5539 | 0.441214  |   1662 |   313 | 0.188327  |   257 |  170 | 0.66147859922178986   |   2788 |   1740 | 0.624103 |   370 | 12  |   4012 |
| Manchester           |   1599 |    585 | 0.365854  |    403 |    59 | 0.146402  |    44 |   17 | 0.38636363636363635   |    313 |    173 | 0.552716 |    86 | 4   |    679 |
| New York             |   9907 |   4700 | 0.474412  |   1836 |   397 | 0.216231  |   243 |  150 | 0.61728395061728392   |   1929 |   1470 | 0.762053 |   402 | 20  |   3181 |
| Newark               |   3670 |   1033 | 0.281471  |    612 |   119 | 0.194444  |    79 |   54 | 0.68354430379746833   |    998 |    529 | 0.53006  |   136 | 9   |   1562 |
| Philadelphia VSC     |  12218 |   4931 | 0.403585  |   1593 |   303 | 0.190207  |  1906 |  399 | 0.20933892969569778   |   6999 |   3746 | 0.535219 |   327 | -   |   3417 |
| Pittsburgh           |   5441 |   2334 | 0.428965  |   2244 |  1496 | 0.666667  |   591 |  485 | 0.82064297800338415   |   1614 |   1002 | 0.620818 |   624 | 17  |   2173 |
| Providence           |   1907 |    349 | 0.18301   |    257 |    21 | 0.0817121 |    79 |    5 | 6.3291139240506333E-2 |    435 |    256 | 0.588506 |    66 | 2   |   1266 |
| Togus                |   3107 |    960 | 0.30898   |    881 |   211 | 0.239501  |   290 |   87 | 0.3                   |   7560 |   6441 | 0.851984 |   277 | 0   |    659 |
| White River Junction |    930 |    489 | 0.525806  |    175 |    58 | 0.331429  |    15 |   14 | 0.93333333333333335   |    150 |     94 | 0.626667 |    39 | 1   |    299 |
| Wilmington           |   1003 |    271 | 0.270189  |    263 |    69 | 0.262357  |    33 |   13 | 0.39393939393939392   |    217 |    103 | 0.474654 |    43 | 0   |    428 |
| Atlanta              |  22878 |   8815 | 0.385305  |   3146 |   575 | 0.182772  |   484 |  301 | 0.62190082644628097   |   5379 |   3290 | 0.611638 |   258 | 33  |   7894 |
| Columbia             |  12975 |   4030 | 0.310597  |   1997 |   303 | 0.151728  |   310 |  181 | 0.58387096774193548   |   6520 |   5105 | 0.782975 |   232 | 33  |   4144 |
| Huntington           |   4030 |    817 | 0.20273   |    967 |   210 | 0.217166  |   150 |   71 | 0.47333333333333333   |   7612 |   6455 | 0.848003 |   212 | 9   |   2241 |
| Jackson              |   7430 |   3282 | 0.441723  |   1692 |   350 | 0.206856  |   755 |  576 | 0.76291390728476827   |   1213 |    770 | 0.63479  |   444 | 15  |   3212 |
| Louisville           |   5137 |   1057 | 0.205762  |   1814 |   227 | 0.125138  |   570 |  281 | 0.49298245614035086   |   1310 |    817 | 0.623664 |   393 | 6   |   1544 |
| Montgomery           |  11934 |   4900 | 0.410592  |   3651 |   816 | 0.2235    |  1608 | 1143 | 0.71082089552238803   |   2894 |   1851 | 0.639599 |   599 | 33  |   8873 |
| Nashville            |   8108 |   1374 | 0.169462  |   1274 |    54 | 0.0423862 |   216 |   86 | 0.39814814814814814   |   2925 |   1791 | 0.612308 |   190 | 12  |   4466 |
| Roanoke              |  15204 |   4457 | 0.293147  |   2510 |   165 | 0.0657371 |   547 |   94 | 0.17184643510054845   |   5473 |   4386 | 0.801389 |   202 | 29  |   5793 |
| San Juan             |   4496 |   1795 | 0.399244  |    953 |   117 | 0.12277   |    49 |   33 | 0.67346938775510201   |    813 |    445 | 0.547355 |   325 | 19  |   3819 |
| St. Petersburg       |  32052 |   9919 | 0.309466  |   6206 |  1021 | 0.164518  |  1227 |  787 | 0.64140179299103506   |  16934 |  12256 | 0.723751 |  1102 | 74  |  12309 |
| Washington           |     41 |     10 | 0.243902  |     18 |     3 | 0.166667  |     2 |    2 | 1                     |     22 |     22 | 1        |    13 | 0   |     11 |
| Winston-Salem        |  38062 |  14941 | 0.392544  |   8981 |  2347 | 0.261329  |   185 |   53 | 0.2864864864864865    |   4265 |   2160 | 0.506448 |   434 | 20  |   6191 |
| Chicago              |  11997 |   4929 | 0.410853  |   1746 |   371 | 0.212486  |   645 |  276 | 0.42790697674418604   |   3118 |   2200 | 0.705581 |   390 | 16  |   6235 |
| Des Moines           |   3773 |   1075 | 0.284919  |    624 |    84 | 0.134615  |   102 |   27 | 0.26470588235294118   |   1013 |    563 | 0.555775 |    54 | 10  |   1652 |
| Fargo                |   1075 |    144 | 0.133953  |    196 |    14 | 0.0714286 |    53 |    3 | 5.6603773584905662E-2 |    520 |    386 | 0.742308 |    45 | 1   |    317 |
| Houston              |  24792 |  11784 | 0.475315  |   7251 |  1784 | 0.246035  |   335 |  222 | 0.66268656716417906   |   7745 |   5831 | 0.752873 |   539 | 21  |  12309 |
| Lincoln              |   2967 |    339 | 0.114257  |    499 |    16 | 0.0320641 |    90 |    7 | 7.7777777777777779E-2 |   6436 |   5218 | 0.810752 |    56 | 22  |   1303 |
| Little Rock          |   6025 |   1550 | 0.257261  |   1471 |   257 | 0.174711  |   269 |  142 | 0.52788104089219334   |   1735 |   1095 | 0.631124 |   259 | 8   |   2894 |
| Milwaukee VSC        |   9142 |   3388 | 0.370597  |   1055 |    63 | 0.0597156 |   130 |   32 | 0.24615384615384617   |   3282 |   2226 | 0.678245 |  2241 | 0   |   2012 |
| Muskogee             |   8919 |   2274 | 0.254961  |   1469 |    94 | 0.0639891 |   573 |   75 | 0.13089005235602094   |   7663 |   6257 | 0.816521 |    30 | 12  |   3120 |
| New Orleans          |   6732 |   1481 | 0.219994  |   1107 |   102 | 0.0921409 |    93 |    7 | 7.5268817204301078E-2 |   1391 |    887 | 0.637671 |   194 | 5   |   3582 |
| Sioux Falls          |    945 |    124 | 0.131217  |    250 |    32 | 0.128     |   145 |   25 | 0.17241379310344829   |    375 |    218 | 0.581333 |    33 | 1   |    228 |
| St. Louis            |   9477 |   2234 | 0.235729  |   1961 |   438 | 0.223355  |   293 |  124 | 0.42320819112627989   |   5288 |   4242 | 0.802194 |   445 | 24  |   4547 |
| St. Paul VSC         |   7190 |   1287 | 0.178999  |   1081 |    78 | 0.0721554 |    85 |   54 | 0.63529411764705879   |   3376 |   2727 | 0.807761 |   124 | 0   |   1191 |
| Waco                 |  23094 |   7943 | 0.343942  |   3458 |   239 | 0.0691151 |   481 |   40 | 8.3160083160083165E-2 |  15019 |   6368 | 0.423996 |   633 | 27  |   9773 |
| Wichita              |   3941 |   1580 | 0.400913  |    533 |    63 | 0.118199  |    87 |   71 | 0.81609195402298851   |    868 |    559 | 0.644009 |     8 | 1   |    806 |
| Albuquerque          |   3656 |   1219 | 0.333425  |    472 |    38 | 0.0805085 |   120 |   61 | 0.5083333333333333    |    390 |    421 | 1.07949  |   137 | 2   |   1994 |
| Anchorage            |   1112 |    339 | 0.304856  |    280 |    43 | 0.153571  |    56 |   18 | 0.32142857142857145   |    140 |    169 | 1.20714  |    30 | 2   |    213 |
| Boise                |   1706 |    223 | 0.130715  |    541 |    39 | 0.0720887 |    93 |   19 | 0.20430107526881722   |    145 |    252 | 1.73793  |    69 | 5   |    640 |
| Denver               |   7369 |   1690 | 0.229339  |   1753 |   220 | 0.125499  |   312 |  135 | 0.43269230769230771   |   1362 |    724 | 0.531571 |   256 | 12  |   3164 |
| Cheyenne             |    877 |    254 | 0.289624  |    235 |    68 | 0.289362  |    87 |   79 | 0.90804597701149425   |    266 |    127 | 0.477444 |    54 | 4   |    185 |
| Fort Harrison        |   1367 |    146 | 0.106803  |    329 |    11 | 0.0334347 |    69 |    9 | 0.13043478260869565   |    502 |    231 | 0.460159 |    52 | 11  |    260 |
| Honolulu             |   4043 |   1980 | 0.489735  |    421 |    60 | 0.142518  |    88 |   47 | 0.53409090909090906   |    799 |    593 | 0.742178 |    60 | 2   |    676 |
| Los Angeles          |  11754 |   4654 | 0.39595   |   2605 |   809 | 0.310557  |    78 |   73 | 0.9358974358974359    |   1867 |   1254 | 0.671666 |   226 | 16  |   6333 |
| Manila               |   1412 |    345 | 0.244334  |   3160 |  2016 | 0.637975  |    49 |   38 | 0.77551020408163263   |    660 |    318 | 0.481818 |   306 | 71  |   2377 |
| Oakland              |  17056 |   6999 | 0.410354  |   3024 |   851 | 0.281415  |   726 |  196 | 0.26997245179063362   |   3036 |   1908 | 0.628458 |   424 | 21  |   5825 |
| Phoenix              |  11028 |   3522 | 0.319369  |   1217 |    54 | 0.0443714 |   276 |   45 | 0.16304347826086957   |   6905 |   5766 | 0.835047 |   191 | 8   |   3560 |
| Portland             |   7482 |   1858 | 0.248329  |   2106 |   533 | 0.253086  |   551 |   92 | 0.16696914700544466   |   1691 |    943 | 0.557658 |   209 | 20  |   4197 |
| Reno                 |   5437 |   2404 | 0.442156  |    895 |   137 | 0.153073  |   122 |   60 | 0.49180327868852458   |    735 |    420 | 0.571429 |    82 | 8   |   1013 |
| Salt Lake City       |   7109 |    934 | 0.131383  |   1539 |   153 | 0.0994152 |   375 |    5 | 1.3333333333333334E-2 |   1077 |    395 | 0.36676  |    61 | 1   |   1704 |
| San Diego            |  20085 |   6638 | 0.330495  |   1668 |   154 | 0.0923261 |   637 |  147 | 0.23076923076923078   |   6405 |   5293 | 0.826386 |   109 | 8   |   3322 |
| Seattle              |  12502 |   5448 | 0.43577   |   5644 |  2358 | 0.417789  |   376 |  174 | 0.46276595744680848   |  20402 |   8768 | 0.429762 |   651 | 27  |   4658 |
| Other                |      1 |      0 | 0         |     21 |     4 | 0.190476  |     0 |    0 | #DIV/0!               |    765 |     21 | 0.027451 |     2 | 5   |  20970 |



label: D=C/B
G=F/E
J=I/H
M=L/K
labeled_formulas: D=C/B
G=F/E
J=I/H
M=L/K
output: {"Arithmetic-Relationship": ["D=C/B", "G=F/E", "J=I/H", "M=L/K"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_782667___xlsx_f88e13f64d11910f8d263e803b95c902a6b5bf58.xlsx___line_874