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                  | 805501 | 521378 | 0.647272 | 189746 | 74594 | 0.393126  | 35911 | 20337 | 0.566317  | 82555 | 52161 | 0.631833  | 30113 | 1189 | 247369 |
| Baltimore            |  16402 |  12783 | 0.779356 |   3270 |  1903 | 0.581957  |   318 |   251 | 0.789308  |  1306 |   982 | 0.751914  |     1 | 4    |   2867 |
| Boston               |   8638 |   5639 | 0.652813 |   1602 |   556 | 0.347066  |   469 |   130 | 0.277186  |   968 |   723 | 0.746901  |     8 | 0    |   4042 |
| Buffalo              |   7432 |   4365 | 0.587325 |   3223 |  1354 | 0.420105  |   198 |    99 | 0.5       |   597 |   417 | 0.698492  |     2 | 1    |    745 |
| Cleveland            |  23615 |  15072 | 0.638238 |   5253 |  2167 | 0.412526  |   861 |   728 | 0.845528  |  3137 |  1746 | 0.556583  |     3 | 38   |   6353 |
| Detroit              |  19438 |  12494 | 0.642762 |   4273 |  1733 | 0.40557   |   363 |   258 | 0.710744  |  2570 |  1825 | 0.710117  |     2 | 37   |   5834 |
| Hartford             |   4143 |   2466 | 0.595221 |    782 |   247 | 0.315857  |   455 |   294 | 0.646154  |   355 |   251 | 0.707042  |     0 | 0    |    881 |
| Indianapolis         |  20650 |  15900 | 0.769976 |   3799 |  2246 | 0.591208  |   402 |   328 | 0.81592   |  2472 |  1877 | 0.759304  |     1 | 24   |   4291 |
| Manchester           |   2117 |   1210 | 0.571564 |    713 |   220 | 0.308555  |    98 |     4 | 0.0408163 |   207 |   144 | 0.695652  |     0 | 0    |    787 |
| New York             |  15474 |  11774 | 0.760889 |   3556 |  1485 | 0.417604  |   170 |    22 | 0.129412  |   945 |   791 | 0.837037  |     1 | 1    |   3866 |
| Newark               |   4570 |   2556 | 0.5593   |   1206 |   582 | 0.482587  |   117 |   110 | 0.940171  |   524 |   321 | 0.612595  |     0 | 1    |   1959 |
| Philadelphia VSC     |  25178 |  16453 | 0.653467 |   4419 |  2651 | 0.599909  |  2645 |  1966 | 0.743289  |  2172 |  1582 | 0.728361  | 17268 | -    |   3439 |
| Pittsburgh           |   9641 |   6541 | 0.678457 |   2962 |  1528 | 0.515868  |   343 |   240 | 0.699708  |  1309 |   867 | 0.662338  |     1 | 2    |   3043 |
| Providence           |   3409 |   1750 | 0.513347 |    730 |   187 | 0.256164  |   389 |   176 | 0.452442  |   414 |   276 | 0.666667  |     0 | 1    |   1066 |
| Togus                |   2646 |   1396 | 0.527589 |   1855 |  1007 | 0.542857  |   577 |   240 | 0.415945  |   344 |   210 | 0.610465  |     0 | 0    |    719 |
| White River Junction |   1103 |    683 | 0.61922  |    310 |   129 | 0.416129  |    57 |    12 | 0.210526  |   119 |    93 | 0.781513  |     0 | 0    |    383 |
| Wilmington           |   1305 |    720 | 0.551724 |    389 |   187 | 0.48072   |    19 |     5 | 0.263158  |   207 |   122 | 0.589372  |     0 | 1    |    504 |
| Atlanta              |  32367 |  20952 | 0.647326 |   7201 |  2501 | 0.347313  |   284 |   199 | 0.700704  |  5077 |  2854 | 0.562143  |     3 | 0    |  10217 |
| Columbia             |  21669 |  12602 | 0.581568 |   3921 |   564 | 0.143841  |   713 |    91 | 0.12763   |  1283 |   820 | 0.639127  |     2 | 5    |   4445 |
| Huntington           |   7593 |   4968 | 0.654287 |    873 |   233 | 0.266896  |   239 |   138 | 0.577406  |  1009 |   572 | 0.566898  |     2 | 3    |   2852 |
| Jackson              |  10370 |   7098 | 0.684474 |   1916 |   447 | 0.233299  |   760 |   545 | 0.717105  |   813 |   577 | 0.709717  |    19 | 23   |   3989 |
| Louisville           |  10003 |   5290 | 0.528841 |   4243 |  1555 | 0.366486  |  1435 |   827 | 0.576307  |  1078 |   643 | 0.596475  |     5 | 16   |   2563 |
| Montgomery           |  14385 |   7747 | 0.538547 |   4796 |  1498 | 0.312344  |   740 |   346 | 0.467568  |  1486 |   757 | 0.509421  |     4 | 32   |   9576 |
| Nashville            |  12735 |   5460 | 0.42874  |   3805 |   678 | 0.178187  |   642 |   207 | 0.32243   |  2037 |   842 | 0.413353  |     0 | 31   |   5713 |
| Roanoke              |  25925 |  17934 | 0.691765 |   6666 |  2761 | 0.414191  |  1128 |   233 | 0.20656   |  2010 |  1064 | 0.529353  |     3 | 5    |   6923 |
| San Juan             |   5333 |   2797 | 0.52447  |   1788 |   363 | 0.20302   |    95 |    71 | 0.747368  |   477 |   373 | 0.781971  |     2 | 2    |   4422 |
| St. Petersburg       |  47110 |  29095 | 0.617597 |   8966 |  2412 | 0.269016  |   678 |   350 | 0.516224  |  5170 |  2883 | 0.55764   |     4 | 46   |  18419 |
| Washington           |     98 |     29 | 0.295918 |     75 |    62 | 0.826667  |    37 |    35 | 0.945946  |   322 |    15 | 0.0465839 |     0 | 0    |      6 |
| Winston-Salem        |  56627 |  37351 | 0.659597 |  17262 |  8778 | 0.508516  |  4127 |  3044 | 0.737582  |  3526 |  2094 | 0.593874  |     5 | 6    |   8317 |
| Chicago              |  20932 |  16062 | 0.767342 |   3741 |  2258 | 0.603582  |   745 |   554 | 0.743624  |  2906 |  2309 | 0.794563  |     4 | 50   |   6225 |
| Des Moines           |   6989 |   3686 | 0.5274   |   2164 |   972 | 0.449168  |   196 |   145 | 0.739796  |   681 |   488 | 0.716593  |     0 | 0    |   1900 |
| Fargo                |   1400 |    570 | 0.407143 |    247 |    38 | 0.153846  |    73 |     7 | 0.0958904 |   157 |    88 | 0.56051   |     0 | 0    |    282 |
| Houston              |  35661 |  24740 | 0.693755 |  14264 |  7541 | 0.528674  |  1117 |   730 | 0.653536  |  4125 |  2637 | 0.639273  |     3 | 4    |  14142 |
| Lincoln              |   2722 |    492 | 0.180749 |    496 |    26 | 0.0524194 |   178 |    33 | 0.185393  |   429 |    81 | 0.188811  |     0 | 1    |   1569 |
| Little Rock          |   7784 |   4606 | 0.591727 |   3090 |   937 | 0.303236  |  1243 |   304 | 0.24457   |  1465 |   860 | 0.587031  |     0 | 15   |   4301 |
| Milwaukee VSC        |  11416 |   4742 | 0.415382 |   1907 |   132 | 0.0692187 |   361 |   168 | 0.465374  |   800 |   331 | 0.41375   |  8117 | 0    |   2486 |
| Muskogee             |  13779 |   7736 | 0.561434 |   3339 |   741 | 0.221923  |  1241 |   317 | 0.255439  |  1220 |   886 | 0.72623   |     8 | 5    |   3445 |
| New Orleans          |  11808 |   7047 | 0.596799 |   2886 |  1250 | 0.433125  |   355 |   204 | 0.574648  |  1472 |  1024 | 0.695652  |     2 | 28   |   5119 |
| Sioux Falls          |   1135 |    287 | 0.252863 |    294 |    27 | 0.0918367 |   312 |    18 | 0.0576923 |   189 |    76 | 0.402116  |     1 | 3    |    252 |
| St. Louis            |  17319 |  11246 | 0.649345 |   3549 |  1690 | 0.47619   |   482 |   257 | 0.533195  |  1537 |   971 | 0.63175   |     2 | 21   |   6658 |
| St. Paul VSC         |  10577 |   2606 | 0.246384 |   1756 |   178 | 0.101367  |  1302 |  1084 | 0.832565  |   563 |   284 | 0.50444   |  3818 | 0    |   1648 |
| Waco                 |  51024 |  38830 | 0.761014 |   6197 |  1242 | 0.20042   |   713 |   205 | 0.287518  |  4674 |  3171 | 0.678434  |   196 | 263  |  11611 |
| Wichita              |   4999 |   2679 | 0.535907 |   1092 |   138 | 0.126374  |    17 |     9 | 0.529412  |   522 |   325 | 0.622605  |     0 | 0    |    835 |
| Albuquerque          |   4825 |   2527 | 0.523731 |   1061 |   256 | 0.241282  |    60 |    33 | 0.55      |   521 |   307 | 0.589251  |     0 | 0    |   2150 |
| Anchorage            |   1645 |    839 | 0.51003  |   1369 |   742 | 0.542001  |   550 |   215 | 0.390909  |   310 |   218 | 0.703226  |     0 | 0    |    168 |
| Boise                |   2202 |    791 | 0.359219 |   1009 |   219 | 0.217047  |   118 |    29 | 0.245763  |   362 |   150 | 0.414365  |     0 | 0    |    858 |
| Denver               |  10551 |   5461 | 0.517581 |   2999 |   701 | 0.233745  |   399 |   103 | 0.258145  |   698 |   386 | 0.553009  |     2 | 3    |   3941 |
| Cheyenne             |   1012 |    425 | 0.41996  |    681 |   395 | 0.580029  |    31 |    16 | 0.516129  |   268 |   151 | 0.563433  |     0 | 0    |    336 |
| Fort Harrison        |   1346 |    272 | 0.20208  |    479 |    58 | 0.121086  |   144 |    11 | 0.0763889 |   213 |    47 | 0.220657  |     0 | 1    |    361 |
| Honolulu             |   5246 |   3575 | 0.681472 |    788 |   167 | 0.211929  |    85 |    38 | 0.447059  |   821 |   682 | 0.830694  |     1 | 1    |    732 |
| Los Angeles          |  22639 |  16556 | 0.731304 |   4973 |  1737 | 0.349286  |  2190 |  1417 | 0.647032  |  1687 |  1150 | 0.681683  |     0 | 1    |   6775 |
| Manila               |   3356 |   1494 | 0.445173 |   1182 |   344 | 0.291032  |   150 |    50 | 0.333333  |  1515 |   727 | 0.479868  |   254 | 42   |   2205 |
| Oakland              |  31707 |  23264 | 0.733718 |   6156 |  2823 | 0.458577  |   535 |   241 | 0.450467  |  3546 |  2809 | 0.79216   |     3 | 2    |   7117 |
| Phoenix              |  20896 |  15584 | 0.745789 |   3068 |   777 | 0.253259  |   777 |   580 | 0.746461  |  2281 |  1480 | 0.648838  |     0 | 2    |   5096 |
| Portland             |  12570 |   7622 | 0.606364 |   3743 |  2057 | 0.549559  |   964 |   293 | 0.303942  |  1522 |   825 | 0.54205   |     1 | 9    |   5078 |
| Reno                 |   7593 |   5350 | 0.704596 |   1510 |   546 | 0.361589  |    92 |    40 | 0.434783  |   798 |   570 | 0.714286  |     0 | 0    |   1026 |
| Salt Lake City       |  14365 |   6939 | 0.483049 |   5012 |  1705 | 0.340184  |  1473 |  1218 | 0.826884  |  1514 |  1027 | 0.678336  |     0 | 1    |   1966 |
| San Diego            |  29083 |  18148 | 0.624007 |   2597 |   480 | 0.184829  |   646 |   386 | 0.597523  |  1225 |   615 | 0.502041  |     0 | 0    |   4246 |
| Seattle              |  28941 |  22589 | 0.780519 |   8198 |  4374 | 0.533545  |   947 |   683 | 0.721225  |  2552 |  1744 | 0.683386  |   361 | 457  |   5957 |



label: D=C/B
J=I/H
labeled_formulas: D=C/B
J=I/H
output: {"Arithmetic-Relationship": ["D=C/B", "J=I/H"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_394786___xlsx_8f015a23c94d1101a8c8bd20fbf637648830384d.xlsx___line_375