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 |
|------:|:-------------|:---------------------------|----:|-----:|----:|-----:|----:|-----:|----------:|
|   101 | Adair        | Stilwell                   |   0 |    3 |   0 |    3 |   0 |   15 |  0.2      |
|   301 | Atoka        | Atoka                      |   0 |    0 |   0 |    0 |   0 |    1 |  0        |
|   401 | Beaver       | Beaver                     |   0 |    0 |   0 |    0 |   0 |    0 |  0        |
|   502 | Beckham      | Elk City                   |   0 |    0 |   0 |    0 |   0 |    2 |  0        |
|   601 | Blaine       | Watonga                    |   0 |    0 |   0 |    0 |   0 |    1 |  0        |
|   801 | Caddo        | Anadarko                   |   0 |    0 |   0 |    0 |   0 |    1 |  0        |
|   901 | Canadian     | El Reno                    |   0 |   22 |   0 |   22 |   0 |   58 |  0.37931  |
|   902 | Canadian     | Yukon                      |   0 |    0 |   0 |    0 |   0 |  151 |  0        |
|  1001 | Carter       | Ardmore                    |   0 |    0 |   0 |    0 |   0 |   76 |  0        |
|  1002 | Carter       | Healdton                   |   0 |    0 |   0 |    0 |   0 |    7 |  0        |
|  1201 | Choctaw      | Hugo                       |   0 |    5 |   0 |    5 |   0 |    8 |  0.625    |
|  1401 | Cleveland    | Norman                     |   0 |    0 |   0 |    0 |   0 |   38 |  0        |
|  1402 | Cleveland    | Moore                      |   0 |    0 |   0 |    0 |   0 |   21 |  0        |
|  1501 | Coal         | Coalgate                   |   0 |    0 |   0 |    0 |   0 |    3 |  0        |
|  1603 | Comanche     | Fort Sill WIC              |   0 |    0 |   0 |    0 |   0 |    1 |  0        |
|  1701 | Cotton       | Walters                    |   0 |    0 |   0 |    0 |   0 |    1 |  0        |
|  1801 | Craig        | Vinita                     |   0 |    0 |   0 |    0 |   0 |   12 |  0        |
|  1901 | Creek        | Sapulpa                    |   0 |    0 |   0 |    0 |   0 |   14 |  0        |
|  1902 | Creek        | Bristow                    |   0 |    0 |   0 |    0 |   0 |    3 |  0        |
|  2001 | Custer       | Clinton                    |   0 |    0 |   0 |    0 |   0 |    0 |  0        |
|  2002 | Custer       | Weatherford                |   0 |    0 |   0 |    0 |   0 |    0 |  0        |
|  2201 | Dewey*       | Seiling Community Hospital |   0 |    0 |   0 |    0 |   0 |    0 |  0        |
|  2301 | Ellis*       | Newman Memorial Hospital   |   0 |    0 |   0 |    0 |   0 |    1 |  0        |
|  2401 | Garfield     | Enid                       |   0 |    0 |   0 |    0 |   0 |  152 |  0        |
|  2501 | Garvin       | Pauls Valley               |   0 |   25 |   0 |   25 |   0 |   32 |  0.78125  |
|  2702 | Grant        | Medford                    |   0 |    7 |   0 |    7 |   0 |    5 |  1.4      |
|  2801 | Greer        | Mangum                     |   0 |    5 |   0 |    5 |   0 |    1 |  5        |
|  2901 | Harmon       | Hollis                     |   0 |    0 |   0 |    0 |   0 |    0 |  0        |
|  3004 | Harper       | Laverne                    |   0 |    0 |   0 |    0 |   0 |    0 |  0        |
|  3401 | Jefferson    | Waurika                    |   0 |    0 |   0 |    0 |   0 |    8 |  0        |
|  3501 | Johnston     | Tishomingo                 |   0 |    0 |   0 |    0 |   0 |    0 |  0        |
|  3601 | Kay          | Ponca City                 |   0 |    0 |   0 |    0 |   0 |    1 |  0        |
|  3602 | Kay          | Blackwell                  |   0 |    0 |   0 |    0 |   0 |    0 |  0        |
|  3701 | Kingfisher   | Kingfisher                 |   0 |    0 |   0 |    0 |   0 |   37 |  0        |
|  3801 | Kiowa        | Hobart                     |   0 |    0 |   0 |    0 |   0 |    0 |  0        |
|  3901 | Latimer      | Wilburton                  |   0 |    1 |   0 |    1 |   0 |    3 |  0.333333 |
|  4001 | LeFlore      | Poteau                     |   0 |    0 |   0 |    0 |   0 |   57 |  0        |
|  4201 | Logan        | Guthrie                    |   2 |   49 |   0 |   51 |   0 |   88 |  0.579545 |
|  4301 | Love         | Marietta                   |   0 |   28 |   0 |   28 |   0 |   23 |  1.21739  |
|  4401 | McClain      | Purcell                    |   0 |    0 |   0 |    0 |   0 |   10 |  0        |
|  4402 | McClain      | Blanchard                  |   0 |    0 |   0 |    0 |   0 |   15 |  0        |
|  4501 | McCurtain    | Idabel                     |   0 |    2 |   0 |    2 |   0 |    8 |  0.25     |
|  4601 | McIntosh     | Eufaula                    |   0 |   23 |   0 |   23 |   0 |   17 |  1.35294  |
|  4602 | McIntosh     | Checotah                   |   1 |   17 |   0 |   18 |   0 |   18 |  1        |
|  4702 | Major        | Fairview                   |   0 |    0 |   0 |    0 |   0 |   19 |  0        |
|  4801 | Marshall     | Madill                     |   0 |    0 |   0 |    0 |   0 |   46 |  0        |
|  4901 | Mayes        | Pryor                      |   0 |    4 |   0 |    4 |   0 |    4 |  1        |
|  5001 | Murray       | Sulphur                    |   0 |    0 |   0 |    0 |   0 |    0 |  0        |
|  5101 | Muskogee     | Muskogee                   |   0 |   24 |   0 |   24 |   0 |   17 |  1.41176  |
|  5201 | Noble        | Perry                      |   0 |    0 |   0 |    0 |   0 |    0 |  0        |
|  5401 | Okfuskee     | Okemah                     |   0 |   29 |   0 |   29 |   0 |   28 |  1.03571  |
|  5505 | Oklahoma*    | OK.CCHD - South            |   0 |    0 |   0 |    0 |   0 |  136 |  0        |
|  5522 | Oklahoma*    | OK.CCHD - East Clinic      |   0 |   90 |   0 |   90 |   0 |  138 |  0.652174 |
|  5533 | Oklahoma*    | OK.CCHD - Fair Park        |   2 |   62 |   0 |   64 |   0 |   43 |  1.48837  |
|  5536 | Oklahoma*    | OK.CCHD - Memorial         |   2 |   68 |   0 |   70 |   0 |   91 |  0.769231 |
|  5537 | Oklahoma*    | OK.CCHD - Shepherd Mall    |   9 |  175 |   0 |  184 |   0 |  443 |  0.41535  |
|  5538 | Oklahoma*    | OK.OCHD - Northeast        |  90 |   56 |   0 |  146 |   0 |   54 |  2.7037   |
|  5540 | Oklahoma*    | OK.CCHD - West Clinic      |   0 |  224 |   0 |  224 |   0 |  256 |  0.875    |
|  5502 | Oklahoma*    | Mary Mahoney Memorial      |   3 |   52 |   0 |   55 |   0 |   67 |  0.820896 |
|  5504 | Oklahoma*    | Hope Center                |  17 |  158 |   0 |  175 |   0 |  236 |  0.741525 |
|  5512 | Oklahoma*    | NSO                        |  17 | 1219 |   0 | 1236 |   0 | 1314 |  0.940639 |
|  5510 | Oklahoma*    | Variety Care - Mid-Del     |   8 |  140 |   0 |  148 |   0 |  155 |  0.954839 |
|  5521 | Oklahoma*    | Variety Care LaFayette     |   0 |  155 |   0 |  155 |   0 |  526 |  0.294677 |
|  5526 | Oklahoma*    | Variety Care Straka        |   0 |   65 |   0 |   65 |   0 |  260 |  0.25     |
|  5541 | Oklahoma*    | Variety Care Britton       |   4 |  148 |   0 |  152 |   0 |  193 |  0.787565 |
|  5524 | Oklahoma*    | Guiding Right              |   0 |  199 |   0 |  199 |   0 |  200 |  0.995    |
|  5601 | Okmulgee     | Okmulgee                   |   4 |   43 |   0 |   47 |   0 |   11 |  4.27273  |
|  5701 | Osage        | Pawhuska                   |   0 |    0 |   0 |    0 |   0 |    6 |  0        |
|  5801 | Ottawa       | Miami                      |   0 |    0 |   0 |    0 |   0 |    0 |  0        |
|  5901 | Pawnee       | Pawnee                     |   0 |    0 |   0 |    0 |   0 |    1 |  0        |
|  5902 | Pawnee       | Cleveland                  |   0 |    0 |   0 |    0 |   0 |    3 |  0        |
|  6001 | Payne        | Stillwater                 |   0 |    0 |   0 |    0 |   0 |    7 |  0        |
|  6101 | Pittsburg    | McAlester                  |   0 |    0 |   0 |    0 |   0 |    1 |  0        |
|  6201 | Pontotoc     | Ada                        |   0 |    4 |   0 |    4 |   0 |   39 |  0.102564 |
|  6401 | Pushmataha   | Antlers                    |   0 |   16 |   0 |   16 |   0 |    1 | 16        |
|  6501 | Roger Mills* | Cheyenne - Roger Mills     |   0 |    0 |   0 |    0 |   0 |    4 |  0        |
|  6601 | Rogers       | Claremore                  |   0 |   40 |   0 |   40 |   0 |   37 |  1.08108  |
|  6702 | Seminole     | Seminole                   |   0 |    1 |   0 |    1 |   0 |   33 |  0.030303 |
|  6801 | Sequoyah     | Sallisaw                   |   2 |   39 |   0 |   41 |   0 |    5 |  8.2      |
|  6901 | Stephens     | Duncan                     |   3 |   11 |   0 |   14 |   0 |   38 |  0.368421 |
|  7001 | Texas        | Guymon                     |   0 |    0 |   0 |    0 |   0 |    3 |  0        |
|  7101 | Tillman      | Frederick                  |   0 |    0 |   0 |    0 |   0 |    0 |  0        |
|  7235 | Tulsa*       | Morton-East                |   0 |    6 |   0 |    6 |   0 |    1 |  6        |
|  7203 | Tulsa*       | TCCHD-South Tulsa WIC      |   0 |  338 |   0 |  338 |   0 |  341 |  0.991202 |
|  7205 | Tulsa*       | TCCHD-Collinsville         |   1 |   15 |   0 |   16 |   0 |   21 |  0.761905 |
|  7206 | Tulsa*       | TCCHD-Central Regional     |  15 |  256 |   0 |  271 |   0 |  299 |  0.906355 |
|  7208 | Tulsa*       | TCCHD-North Regional       |   3 |   43 |   0 |   46 |   0 |   63 |  0.730159 |
|  7209 | Tulsa*       | TCCHD-Bixby                |   6 |  103 |   0 |  109 |   0 |   97 |  1.12371  |
|  7210 | Tulsa*       | TCCHD-Sand Springs         |   6 |   49 |   0 |   55 |   0 |   67 |  0.820896 |
|  7217 | Tulsa*       | TCCHD-Mingo 21             |   3 |  240 |   0 |  243 |   0 |  297 |  0.818182 |
|  7225 | Tulsa*       | TCCHD-James O. Goodwin     |   0 |  215 |   0 |  215 |   0 |  251 |  0.856574 |
|  7232 | Tulsa*       | TCCHD-Owasso               |   1 |   97 |   0 |   98 |   0 |  107 |  0.915888 |
|  7234 | Tulsa*       | TCCHD-Broken Arrow         |   1 |  154 |   0 |  155 |   0 |  197 |  0.786802 |
|  7301 | Wagoner      | Wagoner                    |   0 |   11 |   0 |   11 |   0 |   17 |  0.647059 |
|  7302 | Wagoner      | Coweta                     |   0 |   16 |   0 |   16 |   0 |   18 |  0.888889 |
|  7401 | Washington   | Bartlesville               |   1 |   16 |   0 |   17 |   0 |   28 |  0.607143 |
|  7601 | Woods        | Alva                       |  19 |    0 |   0 |   19 |   0 |    7 |  2.71429  |
|  7701 | Woodward     | Woodward                   |   0 |    0 |   0 |    0 |   0 |    0 |  0        |
| 99372 | OSDH         | WIC State Office           |  49 | 1315 |   0 | 1364 |   0 | 1297 |  1.05166  |



labeled_formulas: H=A*F
H=D*F
H=E*F
H=F*G
F=H*I
F=H*J
H=(A*D)*F
H=(A+E)*F
H=(A*F)*G
F=(A*H)*I
F=(A*H)*J
H=(D*E)*F
G=(D+E)+H
H=(D*F)*G
F=(D*H)*I
F=(D*H)*J
F=(E-G)*H
F=(E*H)*I
F=(E*H)*J
F=(G*H)*I
F=(G*H)*J
F=(H*I)*J
G=(H+I)*J
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_620179___xlsx_7969ad18ca76260f56ce59c8438aff2740f9e4ae.xlsx___line_284