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 |
|:----------------|:-------------------------------------------|:-------|-------:|-------:|-------:|-------:|-------:|-------:|-------:|-------:|--------:|--------:|
| Alameda         | East Bay                                   | Female |  40178 |  38450 | 119918 | 136860 |  44754 | 173619 | 114339 |  78628 |  181614 |  287958 |
| Alpine          | Capital                                    | Female |      5 |     59 |    107 |    112 |     26 |     68 |     44 |     64 |     138 |     112 |
| Amador          | Middle Sierra                              | Female |    350 |    844 |   4063 |   4339 |   1866 |   1977 |   1247 |   1194 |    6205 |    3224 |
| Butte           | North State                                | Female |   3137 |   5575 |  20426 |  30707 |  10121 |  15471 |   6988 |   8712 |   40828 |   22459 |
| Calaveras       | Middle Sierra                              | Female |    644 |   1063 |   4654 |   6583 |   2510 |   2515 |    947 |   1707 |    9093 |    3462 |
| Colusa          | Capital                                    | Female |   1220 |    790 |   1774 |   1861 |    927 |    716 |    281 |   2010 |    2788 |     997 |
| Contra Costa    | East Bay                                   | Female |  24005 |  21649 |  81702 | 109575 |  40996 | 112652 |  61014 |  45654 |  150571 |  173666 |
| Del Norte       | North State                                | Female |    335 |    872 |   3250 |   2896 |   1007 |   1025 |    504 |   1207 |    3903 |    1529 |
| El Dorado       | Capital                                    | Female |   1832 |   3199 |  17385 |  21088 |   8690 |  14873 |   8015 |   5031 |   29778 |   22888 |
| Fresno          | San Joaquin Valley and Associated Counties | Female |  42890 |  33961 |  79044 |  95699 |  31686 |  47637 |  22123 |  76851 |  127385 |   69760 |
| Glenn           | Capital                                    | Female |   1199 |    852 |   2961 |   2814 |    911 |   1268 |    223 |   2051 |    3725 |    1491 |
| Humboldt        | North Coast                                | Female |   1252 |   2989 |  12211 |  17861 |   5622 |  10297 |   4919 |   4241 |   23483 |   15216 |
| Imperial        | Southern Border                            | Female |  10345 |   8493 |  13416 |  17612 |   4380 |   5952 |   2431 |  18838 |   21992 |    8383 |
| Inyo            | San Joaquin Valley and Associated Counties | Female |    289 |    432 |   2167 |   1851 |    711 |   1125 |    620 |    721 |    2562 |    1745 |
| Kern            | San Joaquin Valley and Associated Counties | Female |  35896 |  34597 |  85681 |  77311 |  23550 |  32189 |  14374 |  70493 |  100861 |   46563 |
| Kings           | San Joaquin Valley and Associated Counties | Female |   5401 |   5057 |  11610 |  13630 |   4765 |   4824 |   1982 |  10458 |   18395 |    6806 |
| Lake            | North Bay                                  | Female |   1340 |   2304 |   7667 |   7413 |   3081 |   2578 |   1284 |   3644 |   10494 |    3862 |
| Lassen          | North State                                | Female |    104 |    448 |   2254 |   2834 |   1098 |    982 |    468 |    552 |    3932 |    1450 |
| Los Angeles     | Los Angeles Basin                          | Female | 469452 | 339201 | 833130 | 905755 | 286886 | 796634 | 392694 | 808653 | 1192641 | 1189328 |
| Madera          | San Joaquin Valley and Associated Counties | Female |   8150 |   6372 |  15569 |  16176 |   5137 |   5685 |   2142 |  14522 |   21313 |    7827 |
| Marin           | North Bay                                  | Female |   3653 |   2720 |  12191 |  19665 |   7852 |  36219 |  24775 |   6373 |   27517 |   60994 |
| Mariposa        | Middle Sierra                              | Female |    176 |    388 |   1995 |   2299 |    583 |   1128 |    655 |    564 |    2882 |    1783 |
| Mendocino       | North Bay                                  | Female |   1947 |   2223 |   8321 |  11145 |   2780 |   5470 |   2863 |   4170 |   13925 |    8333 |
| Merced          | San Joaquin Valley and Associated Counties | Female |  14547 |   9558 |  22817 |  27082 |   7260 |   8773 |   4212 |  24105 |   34342 |   12985 |
| Modoc           | North State                                | Female |    233 |    245 |   1138 |   1029 |    346 |    390 |    173 |    478 |    1375 |     563 |
| Mono            | San Joaquin Valley and Associated Counties | Female |    441 |    240 |   1249 |   1496 |    334 |   1223 |    436 |    681 |    1830 |    1659 |
| Monterey        | North Central Coast                        | Female |  26297 |  12511 |  33253 |  34951 |  13249 |  22794 |  13422 |  38808 |   48200 |   36216 |
| Napa            | North Bay                                  | Female |   4844 |   2744 |  10258 |  13862 |   5528 |  12846 |   5882 |   7588 |   19390 |   18728 |
| Nevada          | North State                                | Female |    674 |   1710 |   7322 |  12647 |   4770 |   9659 |   5094 |   2384 |   17417 |   14753 |
| Orange          | Orange                                     | Female |  95436 |  82773 | 226078 | 295783 | 103789 | 302276 | 148106 | 178209 |  399572 |  450382 |
| Placer          | Capital                                    | Female |   3091 |   5061 |  28408 |  44094 |  18758 |  36782 |  16412 |   8152 |   62852 |   53194 |
| Plumas          | North State                                | Female |     42 |    302 |   1955 |   2620 |   1185 |   1022 |    708 |    344 |    3805 |    1730 |
| Riverside       | Inland Empire                              | Female |  74123 |  76385 | 246133 | 250590 |  71768 | 114804 |  62357 | 150508 |  322358 |  177161 |
| Sacramento      | Capital                                    | Female |  36261 |  34737 | 132053 | 163253 |  59710 | 112677 |  55796 |  70998 |  222963 |  168473 |
| San Benito      | North Central Coast                        | Female |   2828 |   1283 |   5633 |   6210 |   1977 |   3003 |   1117 |   4111 |    8187 |    4120 |
| San Bernardino  | Inland Empire                              | Female |  63894 |  82600 | 207886 | 216789 |  69144 | 100734 |  51771 | 146494 |  285933 |  152505 |
| San Diego       | Southern Border                            | Female |  84477 |  81134 | 244268 | 321349 | 105915 | 287251 | 161504 | 165611 |  427264 |  448755 |
| San Francisco   | Bay-Peninsula                              | Female |  29133 |  15996 |  46515 |  55393 |  19489 | 125390 |  77163 |  45129 |   74882 |  202553 |
| San Joaquin     | San Joaquin Valley and Associated Counties | Female |  26436 |  25877 |  74013 |  69510 |  25719 |  33706 |  14086 |  52313 |   95229 |   47792 |
| San Luis Obispo | South Central Coast                        | Female |   3402 |   4970 |  22063 |  36784 |  11489 |  22184 |  13095 |   8372 |   48273 |   35279 |
| San Mateo       | Bay-Peninsula                              | Female |  18350 |  13781 |  47655 |  58707 |  22741 |  90240 |  57928 |  32131 |   81448 |  148168 |
| Santa Barbara   | South Central Coast                        | Female |  16669 |  10745 |  30261 |  51260 |  13801 |  31869 |  18279 |  27414 |   65061 |   50148 |
| Santa Clara     | Bay-Peninsula                              | Female |  49929 |  39286 | 116318 | 136295 |  55259 | 199994 | 143562 |  89215 |  191554 |  343556 |
| Santa Cruz      | North Central Coast                        | Female |   8518 |   5045 |  16744 |  31516 |   9935 |  24693 |  15341 |  13563 |   41451 |   40034 |
| Shasta          | North State                                | Female |   1623 |   4328 |  17402 |  24804 |   8860 |  10266 |   5034 |   5951 |   33664 |   15300 |
| Sierra          | North State                                | Female |      8 |     45 |    174 |    547 |    176 |    160 |    103 |     53 |     723 |     263 |
| Siskiyou        | North State                                | Female |    394 |   1272 |   4030 |   5714 |   2097 |   2842 |   1198 |   1666 |    7811 |    4040 |
| Solano          | North Bay                                  | Female |   8692 |  10541 |  40387 |  50437 |  17570 |  31542 |  13119 |  19233 |   68007 |   44661 |
| Sonoma          | North Bay                                  | Female |  10698 |  10729 |  39074 |  56198 |  21063 |  44460 |  24560 |  21427 |   77261 |   69020 |
| Stanislaus      | San Joaquin Valley and Associated Counties | Female |  20534 |  18981 |  55734 |  57171 |  16356 |  22511 |   9207 |  39515 |   73527 |   31718 |
| Sutter          | Capital                                    | Female |   4165 |   3303 |   8532 |  10083 |   3994 |   3984 |   1928 |   7468 |   14077 |    5912 |
| Tehama          | North State                                | Female |   1476 |   1939 |   6839 |   8209 |   2199 |   2682 |   1062 |   3415 |   10408 |    3744 |
| Trinity         | North State                                | Female |     90 |    325 |   1595 |   1708 |    456 |    806 |    262 |    415 |    2164 |    1068 |
| Tulare          | San Joaquin Valley and Associated Counties | Female |  25031 |  17767 |  40409 |  42334 |  12700 |  14739 |   7034 |  42798 |   55034 |   21773 |
| Tuolumne        | Middle Sierra                              | Female |    307 |   1427 |   5956 |   6925 |   2567 |   2734 |   1523 |   1734 |    9492 |    4257 |
| Ventura         | Ventura                                    | Female |  27732 |  18489 |  64192 |  87025 |  32664 |  65338 |  34715 |  46221 |  119689 |  100053 |
| Yolo            | Capital                                    | Female |   4803 |   4331 |  17495 |  25349 |   5945 |  16820 |  13187 |   9134 |   31294 |   30007 |
| Yuba            | Capital                                    | Female |   1848 |   2627 |   5900 |   9253 |   2982 |   3212 |   1259 |   4475 |   12235 |    4471 |



label: K=D+E
L=G+H
M=I+J
labeled_formulas: K=D+E
L=G+H
M=I+J
output: {"Arithmetic-Relationship": ["K=D+E", "L=G+H", "M=I+J"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_581909___xlsx_d8b039093b21b77c5d1d72668b43e0140787522b.xlsx___line_602