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 |
|----:|:-------------------------------------|--------:|--------:|--------:|--------:|--------:|--------:|--------:|--------:|--------:|--------:|
| 151 | COCOA                                |    9351 |     348 |    9699 |       0 |       0 |       0 |    9351 |     348 |    9699 |    7386 |
| 152 | VENILA                               |       0 |       3 |       3 |       0 |       0 |       0 |       0 |       3 |       3 |     114 |
| 153 | EUCALYPTUS                           |       0 |     365 |     365 |       0 |       0 |       0 |       0 |     365 |     365 |      60 |
| 154 | PALMYRA                              |       0 |    3136 |    3136 |       0 |       0 |       0 |       0 |    3136 |    3136 |    3546 |
| 155 | SOAPNUTS                             |       0 |     201 |     201 |       0 |       0 |       0 |       0 |     201 |     201 |     194 |
| 156 | BETEL LEAVES                         |    2842 |      64 |    2906 |       0 |       0 |       0 |    2842 |      64 |    2906 |    3129 |
| 157 | RUBBER                               |       0 |    1309 |    1309 |       0 |       0 |       0 |       0 |    1309 |    1309 |    1309 |
| 158 | COFFEE                               |       0 |    5149 |    5149 |       0 |       0 |       0 |       0 |    5149 |    5149 |    5112 |
| 159 | SIMHA ROOBA                          |      18 |       0 |      18 |       0 |       0 |       0 |      18 |       0 |      18 |      18 |
| 160 | ACACIACONCINNA(SEEKAKAYA)            |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       8 |
| 161 | PIPPALI                              |       0 |     411 |     411 |       0 |       0 |       0 |       0 |     411 |     411 |     337 |
| 162 | TOTAL DRUGS,NARCOTICS AND PLANTATION |   12389 |   15145 |   27534 |   28778 |   44482 |   73260 |   41167 |   59627 |  100794 |  148344 |
| 163 | FODDER JOWAR                         |    1320 |   18909 |   20229 |    3444 |   14810 |   18254 |    4764 |   33719 |   38483 |   38377 |
| 164 | FODDER MAIZE                         |     551 |    1110 |    1661 |    1581 |     460 |    2041 |    2132 |    1570 |    3702 |    3689 |
| 165 | SUBABUL                              |     364 |     148 |     512 |      79 |      24 |     103 |     443 |     172 |     615 |     253 |
| 166 | STYLOHMATA                           |       0 |      48 |      48 |      85 |       0 |      85 |      85 |      48 |     133 |      30 |
| 167 | CASURINA                             |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |      74 |
| 168 | NAPIER, PARAGRASS                    |    5759 |     175 |    5934 |     760 |     364 |    1124 |    6519 |     539 |    7058 |    7433 |
| 169 | JUTE FOR FODDER                      |       0 |    1278 |    1278 |      21 |     246 |     267 |      21 |    1524 |    1545 |    1861 |
| 170 | PILLIPESARA FOR FODDER               |      13 |     846 |     859 |      98 |    4648 |    4746 |     111 |    5494 |    5605 |   11758 |
| 171 | COW GRAM FOR FODDER                  |       0 |      18 |      18 |       0 |       0 |       0 |       0 |      18 |      18 |     215 |
| 172 | LINSEED FOR FODDER                   |       8 |       0 |       8 |       0 |       0 |       0 |       8 |       0 |       8 |       0 |
| 173 | TOTAL FODDER CROPS                   |    8015 |   22532 |   30547 |    6068 |   20552 |   26620 |   14083 |   43084 |   57167 |   63690 |
| 174 | SUNHEMP FOR MANURE                   |       0 |     796 |     796 |       0 |    1038 |    1038 |       0 |    1834 |    1834 |    2331 |
| 175 | PILLIPESARA FOR MANURE               |       0 |    1152 |    1152 |       0 |    4480 |    4480 |       0 |    5632 |    5632 |    4783 |
| 176 | INDIGO FOR MANURE                    |       0 |    1410 |    1410 |       0 |       0 |       0 |       0 |    1410 |    1410 |     449 |
| 177 | DHAINCHA FOR MANURE                  |     190 |    1829 |    2019 |       1 |     671 |     672 |     191 |    2500 |    2691 |    2809 |
| 178 | TOTAL GREEN MANURE CROP              |     190 |    5187 |    5377 |       1 |    6189 |    6190 |     191 |   11376 |   11567 |   10372 |
| 179 | CITRONELLA (KAMASHIKASULA)           |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |      45 |
| 180 | ANNATO (JAFRA)                       |       0 |      16 |      16 |       0 |       0 |       0 |       0 |      16 |      16 |      24 |
| 181 | LEMON GRASS (NIMMAGADDI)             |     322 |       6 |     328 |       1 |       0 |       1 |     323 |       6 |     329 |     171 |
| 182 | COLIUS                               |       1 |       0 |       1 |       0 |       0 |       0 |       1 |       0 |       1 |      30 |
| 183 | BILLA GANNERU                        |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |
| 184 | KALABANDA                            |       3 |      22 |      25 |       0 |       0 |       0 |       3 |      22 |      25 |      29 |
| 185 | ASWAGANDHI                           |      21 |    2374 |    2395 |       4 |       0 |       4 |      25 |    2374 |    2399 |     630 |
| 186 | PALMA ROSA                           |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |
| 187 | THULASI                              |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       3 |
| 188 | GAYLE                                |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |      10 |
| 189 | CUCUMBER/GHERKIN                     |     216 |       0 |     216 |      60 |       0 |      60 |     276 |       0 |     276 |      29 |
| 190 | TOTAL AEROMATIC PLANTS               |     563 |    2418 |    2981 |      65 |       0 |      65 |     628 |    2418 |    3046 |     971 |
| 191 | ROSE                                 |     362 |       0 |     362 |      44 |       0 |      44 |     406 |       0 |     406 |     574 |
| 192 | JASMINE (MALLI)                      |    2050 |       0 |    2050 |     313 |       0 |     313 |    2363 |       0 |    2363 |    2328 |
| 193 | SAMPANGI                             |     207 |       0 |     207 |       3 |       0 |       3 |     210 |       0 |     210 |     394 |
| 194 | MARIGOLD (BANTHI)                    |    1468 |      72 |    1540 |    1019 |       0 |    1019 |    2487 |      72 |    2559 |    2390 |
| 195 | CHRYSANTHAMUM (CHAMANTHI)            |    2031 |       0 |    2031 |     384 |       0 |     384 |    2415 |       0 |    2415 |    1934 |
| 196 | CROSSANDRA (KANAKAMBARAM)            |     860 |       0 |     860 |     204 |       0 |     204 |    1064 |       0 |    1064 |    1253 |
| 197 | LILLY                                |     681 |       0 |     681 |     135 |       0 |     135 |     816 |       0 |     816 |     675 |
| 198 | KAGADA                               |     142 |       0 |     142 |      20 |       0 |      20 |     162 |       0 |     162 |     171 |
| 199 | CHANDINI                             |       1 |       0 |       1 |       0 |       0 |       0 |       1 |       0 |       1 |      27 |
| 200 | ASTER                                |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |
| 201 | MARUVAM/DAVANAM                      |      11 |       0 |      11 |      34 |       0 |      34 |      45 |       0 |      45 |      21 |
| 202 | THULASI                              |       2 |       0 |       2 |       0 |       0 |       0 |       2 |       0 |       2 |       3 |
| 203 | TOTAL FLOWERS                        |    7815 |      72 |    7887 |    2156 |       0 |    2156 |    9971 |      72 |   10043 |    9770 |
| 204 | TOTAL AROMATIC PLANTS,FLOWERS        |    8378 |    2490 |   10868 |    2221 |       0 |    2221 |   10599 |    2490 |   13089 |   10741 |
| 205 | MULBERRY TREES                       |   10946 |     131 |   11077 |      55 |       0 |      55 |   11001 |     131 |   11132 |    8254 |
| 206 | GUARGUM (JIGURU GORUCHIKKUDU)        |       0 |       0 |       0 |       0 |      42 |      42 |       0 |      42 |      42 |    1167 |
| 207 | MISCELLANEOUS NON FOOD CROPS         |      34 |       4 |      38 |       0 |       1 |       1 |      34 |       5 |      39 |     373 |
| 208 | TOTAL NON FOOD CROPS                 |  318639 | 1653075 | 1971714 |  141999 |  109014 |  251013 |  460638 | 1762089 | 2222727 | 2500631 |
| 209 | GROSS AREA SOWN                      | 2388689 | 2724531 | 5113220 | 1193588 | 1111249 | 2304837 | 3582277 | 3835780 | 7418057 | 7893437 |
| 210 | AREA SMTO (A1-I)                     |   23513 |   27485 |   50998 |  839922 |  589467 | 1429389 |  863435 |  616952 | 1480387 | 1587760 |
| 213 | NET AREA SOWN                        | 2365176 | 2697046 | 5062222 |  353666 |  521782 |  875448 | 2718842 | 3218828 | 5937670 | 6305677 |



label: I=C+F
J=D+G
K=E+H
labeled_formulas: I=C+F
J=D+G
K=E+H
output: {"Arithmetic-Relationship": ["I=C+F", "J=D+G", "K=E+H"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_394054___xlsx_caed3faca2c8877b51ffe4c5146f7428eaec7ced.xlsx___line_723