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 |
|:----------------|-----------------:|------------------:|-----------------:|-----------------:|-----------------:|--------:|-------:|------------:|-----------------:|------------:|
| 11 Alachua      |      1.32114e+07 |      -3.37184e+06 |      9.97388e+06 |      1.98135e+07 |      0           |     0   |      0 | 9.83959e+06 |      9.97388e+06 | 1.98135e+07 |
| 13 Bay          |      1.64573e+07 |       0           |      1.12056e+07 |      2.76629e+07 |      0           |     0   |      0 | 1.64573e+07 |      1.12056e+07 | 2.76629e+07 |
| 14 Bradford     |      1.55583e+06 |       0           | 479949           |      2.03578e+06 | 866571           | 56970.1 | 627869 | 3.10724e+06 | 479949           | 3.58719e+06 |
| 15 Brevard      |      2.88128e+07 |      -7.08459e+06 |      2.28398e+07 |      4.4568e+07  |      0           |     0   |      0 | 2.17283e+07 |      2.28398e+07 | 4.4568e+07  |
| 16 Broward      |      8.30632e+07 |       0           |      1.23118e+08 |      2.06181e+08 |      0           |     0   |      0 | 8.30632e+07 |      1.23118e+08 | 2.06181e+08 |
| 17 Calhoun      | 361145           |       0           |  90232.8         | 451377           | 720138           | 20951.6 | 663004 | 1.76524e+06 |  90232.8         | 1.85547e+06 |
| 18 Charlotte    |      1.6306e+07  |       0           |      1.86832e+06 |      1.81743e+07 |      0           |     0   |      0 | 1.6306e+07  |      1.86832e+06 | 1.81743e+07 |
| 19 Citrus       |      1.02116e+07 |      -2.22636e+06 | 765471           |      8.7507e+06  |      0           |     0   |      0 | 7.98522e+06 | 765471           | 8.7507e+06  |
| 20 Clay         |      1.28803e+07 |      -2.54744e+06 |      1.15182e+06 |      1.14847e+07 |      0           |     0   |      0 | 1.03329e+07 |      1.15182e+06 | 1.14847e+07 |
| 21 Collier      |      5.04804e+07 |       0           |      5.37306e+06 |      5.58534e+07 |      0           |     0   |      0 | 5.04804e+07 |      5.37306e+06 | 5.58534e+07 |
| 23 Miami-Dade   |      1.62294e+08 |       0           |      1.14068e+08 |      2.76361e+08 |      0           |     0   |      0 | 1.62294e+08 |      1.14068e+08 | 2.76361e+08 |
| 25 Dixie        | 430491           |       0           |  55654.3         | 486146           | 889712           | 24515   | 667454 | 2.01217e+06 |  55654.3         | 2.06783e+06 |
| 26 Duval        |      1.07213e+08 |       0           |      5.16207e+06 |      1.12375e+08 |      0           |     0   |      0 | 1.07213e+08 |      5.16207e+06 | 1.12375e+08 |
| 27 Escambia     |      3.01872e+07 |       0           |      5.72148e+06 |      3.59087e+07 |      0           |     0   |      0 | 3.01872e+07 |      5.72148e+06 | 3.59087e+07 |
| 28 Flagler      |      3.15322e+06 |       0           |      3.80388e+06 |      6.9571e+06  |      0           |     0   |      0 | 3.15322e+06 |      3.80388e+06 | 6.9571e+06  |
| 30 Gadsden      |      1.67767e+06 |       0           | 760784           |      2.43845e+06 |      2.11387e+06 |     0   | 618792 | 4.41033e+06 | 760784           | 5.17112e+06 |
| 31 Gilchrist    | 545962           |       0           |  99141.8         | 645104           |      1.04475e+06 |     0   | 645205 | 2.23592e+06 |  99141.8         | 2.33506e+06 |
| 32 Glades       | 292869           |       0           |  44469.4         | 337338           | 710358           | 14120.5 | 406555 | 1.4239e+06  |  44469.4         | 1.46837e+06 |
| 34 Hamilton     | 445515           |       0           | 134182           | 579696           | 593304           | 37245.6 | 444969 | 1.52103e+06 | 134182           | 1.65522e+06 |
| 35 Hardee       | 785073           |       0           | 344335           |      1.12941e+06 |      1.47829e+06 |     0   | 400027 | 2.66339e+06 | 344335           | 3.00773e+06 |
| 36 Hendry       |      1.74979e+06 |       0           | 640850           |      2.39065e+06 |      1.85656e+06 |     0   | 352914 | 3.95927e+06 | 640850           | 4.60012e+06 |
| 37 Hernando     |      1.15283e+07 |       0           | 537988           |      1.20663e+07 |      0           |     0   |      0 | 1.15283e+07 | 537988           | 1.20663e+07 |
| 38 Highlands    |      5.6182e+06  |       0           |      1.48417e+06 |      7.10237e+06 |      0           |     0   | 380449 | 5.99865e+06 |      1.48417e+06 | 7.48282e+06 |
| 39 Hillsborough |      1.19374e+08 |       0           |      4.2099e+07  |      1.61473e+08 |      0           |     0   |      0 | 1.19374e+08 |      4.2099e+07  | 1.61473e+08 |
| 40 Holmes       | 503265           |       0           | 123984           | 627249           |      1.09107e+06 | 21114.2 | 756074 | 2.37152e+06 | 123984           | 2.49551e+06 |
| 41 Indian River |      1.13324e+07 |      -1.80087e+06 |      4.30197e+06 |      1.38335e+07 |      0           |     0   |      0 | 9.53157e+06 |      4.30197e+06 | 1.38335e+07 |
| 42 Jackson      |      2.24756e+06 |       0           | 850303           |      3.09786e+06 |      1.2509e+06  | 86911.6 | 571714 | 4.15709e+06 | 850303           | 5.00739e+06 |
| 44 Lafayette    | 179039           |       0           |  31814.5         | 210853           | 459449           | 17609.9 | 654105 | 1.3102e+06  |  31814.5         | 1.34202e+06 |
| 45 Lake         |      1.87754e+07 |       0           |      1.22851e+07 |      3.10605e+07 |      0           |     0   |      0 | 1.87754e+07 |      1.22851e+07 | 3.10605e+07 |
| 46 Lee          |      5.56304e+07 |       0           |      3.39515e+07 |      8.95819e+07 |      0           |     0   |      0 | 5.56304e+07 |      3.39515e+07 | 8.95819e+07 |
| 47 Leon         |      1.31846e+07 |       0           |      1.11202e+07 |      2.43047e+07 |      0           |     0   |      0 | 1.31846e+07 |      1.11202e+07 | 2.43047e+07 |
| 50 Madison      | 503891           |       0           | 125427           | 629319           |      1.06749e+06 | 23805.2 | 667454 | 2.26264e+06 | 125427           | 2.38807e+06 |
| 51 Manatee      |      3.05051e+07 |       0           |      6.74313e+06 |      3.72482e+07 |      0           |     0   |      0 | 3.05051e+07 |      6.74313e+06 | 3.72482e+07 |
| 52 Marion       |      2.75769e+07 |       0           |      5.76886e+06 |      3.33458e+07 |      0           |     0   |      0 | 2.75769e+07 |      5.76886e+06 | 3.33458e+07 |
| 53 Martin       |      1.80434e+07 |       0           |      3.23557e+06 |      2.12789e+07 |      0           |     0   |      0 | 1.80434e+07 |      3.23557e+06 | 2.12789e+07 |
| 54 Monroe       |      1.26025e+07 | -650950           |      8.23997e+06 |      2.01915e+07 |      0           |     0   |      0 | 1.19515e+07 |      8.23997e+06 | 2.01915e+07 |
| 55 Nassau       |      5.56808e+06 |       0           |      1.21647e+06 |      6.78455e+06 |      0           |     0   |      0 | 5.56808e+06 |      1.21647e+06 | 6.78455e+06 |
| 56 Okaloosa     |      1.95124e+07 |       0           |      9.78435e+06 |      2.92967e+07 |      0           |     0   |      0 | 1.95124e+07 |      9.78435e+06 | 2.92967e+07 |
| 57 Okeechobee   |      2.80174e+06 |       0           | 419275           |      3.22101e+06 |      0           |     0   | 355975 | 3.15771e+06 | 419275           | 3.57699e+06 |
| 58 Orange       |      1.44793e+08 |       0           |      6.06637e+07 |      2.05457e+08 |      0           |     0   |      0 | 1.44793e+08 |      6.06637e+07 | 2.05457e+08 |
| 59 Osceola      |      2.04163e+07 |       0           |      7.63639e+06 |      2.80527e+07 |      0           |     0   |      0 | 2.04163e+07 |      7.63639e+06 | 2.80527e+07 |
| 60 Palm Beach   |      9.40906e+07 |       0           |      6.53756e+07 |      1.59466e+08 |      0           |     0   |      0 | 9.40906e+07 |      6.53756e+07 | 1.59466e+08 |
| 61 Pasco        |      3.82469e+07 |      -7.55106e+06 |      3.40343e+06 |      3.40993e+07 |      0           |     0   |      0 | 3.06959e+07 |      3.40343e+06 | 3.40993e+07 |
| 62 Pinellas     |      5.00411e+07 |      -1.1598e+07  |      4.70988e+07 |      8.5542e+07  |      0           |     0   |      0 | 3.84431e+07 |      4.70988e+07 | 8.5542e+07  |
| 63 Polk         |      4.22544e+07 |       0           |      1.88549e+07 |      6.11093e+07 |      0           |     0   |      0 | 4.22544e+07 |      1.88549e+07 | 6.11093e+07 |
| 64 Putnam       |      3.67662e+06 |       0           | 827397           |      4.50402e+06 |      0           |     0   | 426930 | 4.10355e+06 | 827397           | 4.93095e+06 |
| 65 St. Johns    |      2.23375e+07 |       0           |      1.94932e+06 |      2.42868e+07 |      0           |     0   |      0 | 2.23375e+07 |      1.94932e+06 | 2.42868e+07 |
| 66 St. Lucie    |      1.16673e+07 |       0           |      1.19398e+07 |      2.36071e+07 |      0           |     0   |      0 | 1.16673e+07 |      1.19398e+07 | 2.36071e+07 |
| 67 Santa Rosa   |      1.05143e+07 |       0           |      1.05187e+06 |      1.15662e+07 |      0           |     0   |      0 | 1.05143e+07 |      1.05187e+06 | 1.15662e+07 |
| 68 Sarasota     |      3.6109e+07  |       0           |      1.52695e+07 |      5.13785e+07 |      0           |     0   |      0 | 3.6109e+07  |      1.52695e+07 | 5.13785e+07 |
| 69 Seminole     |      2.64809e+07 |       0           |      1.68408e+07 |      4.33217e+07 |      0           |     0   |      0 | 2.64809e+07 |      1.68408e+07 | 4.33217e+07 |
| 70 Sumter       |      8.22714e+06 | -887271           |      1.23861e+06 |      8.57848e+06 |      0           |     0   |      0 | 7.33987e+06 |      1.23861e+06 | 8.57848e+06 |
| 71 Suwannee     |      2.1989e+06  |       0           | 411149           |      2.61005e+06 |      1.66821e+06 |     0   | 622957 | 4.49007e+06 | 411149           | 4.90121e+06 |
| 72 Taylor       |      1.24329e+06 |       0           | 489668           |      1.73295e+06 | 522374           | 32854.2 | 322273 | 2.12079e+06 | 489668           | 2.61046e+06 |
| 73 Union        | 324353           |       0           |  79248           | 403601           | 598029           | 72096   | 778696 | 1.77317e+06 |  79248           | 1.85242e+06 |
| 74 Volusia      |      2.3902e+07  |       0           |      2.53447e+07 |      4.92467e+07 |      0           |     0   |      0 | 2.3902e+07  |      2.53447e+07 | 4.92467e+07 |
| 75 Wakulla      |      1.44207e+06 |       0           |  40927.8         |      1.48299e+06 |      1.27036e+06 | 45777.2 | 578460 | 3.33666e+06 |  40927.8         | 3.37759e+06 |
| 76 Walton       |      1.45738e+07 |       0           |      2.34386e+06 |      1.69176e+07 |      0           |     0   |      0 | 1.45738e+07 |      2.34386e+06 | 1.69176e+07 |



labeled_formulas: J=(C*F)+D
J=(C*G)+D
J=(C*H)+D
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_177197___xlsx_7cd09bf9d1a069ac4ce8cc5f90184a7b15853a58.xlsx___line_437