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 |
|------:|:------------------------|-----------------:|-----------------:|-----------------:|-----------------:|------------------:|------------:|
|  3607 | Alamo                   |      1.23381e+07 |      8.06348e+06 |      4.03174e+06 |      4.03174e+06 |      -4.27461e+06 | -0.346456   |
|  3539 | Alvin                   | 709307           | 451242           | 225621           | 225621           | -258066           | -0.363828   |
|  3540 | Amarillo                |      2.37855e+06 |      1.64103e+06 | 820515           | 820515           | -737515           | -0.31007    |
|  6661 | Angelina                |      1.07046e+06 | 948004           | 474002           | 474002           | -122451           | -0.114392   |
| 12015 | Austin                  |      6.90617e+06 |      5.47585e+06 |      2.73793e+06 |      2.73793e+06 |      -1.43032e+06 | -0.207107   |
|  3549 | Blinn                   |      1.94744e+06 |      1.39615e+06 | 698077           | 698077           | -551284           | -0.283082   |
|  7857 | Brazosport              | 510431           | 432309           | 216154           | 216154           |  -78122.6         | -0.153052   |
|  4003 | Central Texas           |      2.68587e+06 |      1.4346e+06  | 717302           | 717302           |      -1.25126e+06 | -0.46587    |
|  3553 | Cisco                   | 503255           | 361701           | 180851           | 180850           | -141554           | -0.281277   |
|  3554 | Clarendon               | 174919           |  74577.7         |  37288.9         |  37288.9         | -100342           | -0.573645   |
|  3546 | Coastal Bend            | 519164           | 384855           | 192428           | 192428           | -134309           | -0.258702   |
|  7096 | College of the Mainland |      1.11515e+06 | 599830           | 299915           | 299915           | -515322           | -0.462109   |
| 23614 | Collin                  |      3.49837e+06 |      2.93486e+06 |      1.46743e+06 |      1.46743e+06 | -563519           | -0.16108    |
|  9331 | Dallas                  |      1.43108e+07 |      1.11057e+07 |      5.55283e+06 |      5.55283e+06 |      -3.20512e+06 | -0.223965   |
|  3563 | Del Mar                 |      1.72116e+06 |      1.48024e+06 | 740121           | 740121           | -240921           | -0.139976   |
| 10387 | El Paso                 |      5.04662e+06 |      4.25442e+06 |      2.12721e+06 |      2.12721e+06 | -792196           | -0.156976   |
|  3568 | Frank Phillips          | 200931           | 164538           |  82268.8         |  82268.8         |  -36392.8         | -0.181122   |
|  6662 | Galveston               | 504728           | 379981           | 189991           | 189991           | -124747           | -0.247157   |
|  3570 | Grayson                 | 492621           | 527413           | 263707           | 263707           |   34792.8         |  0.0706279  |
|  3573 | Hill                    |      1.07153e+06 |      1.00074e+06 | 500370           | 500370           |  -70785.8         | -0.0660607  |
| 10633 | Houston                 |      1.14353e+07 |      1.06756e+07 |      5.33779e+06 |      5.33779e+06 | -759696           | -0.0664344  |
|  3574 | Howard                  | 547801           | 373712           | 186856           | 186856           | -174089           | -0.317796   |
|  3580 | Kilgore                 |      1.37521e+06 |      1.02118e+06 | 510591           | 510591           | -354032           | -0.257438   |
|  3582 | Laredo                  |      1.66755e+06 |      1.28119e+06 | 640595           | 640595           | -386357           | -0.231692   |
|  3583 | Lee                     | 804285           | 809208           | 404604           | 404604           |    4922.89        |  0.00612083 |
| 11145 | Lone Star               |      1.64096e+07 |      1.44858e+07 |      7.2429e+06  |      7.2429e+06  |      -1.92384e+06 | -0.117238   |
|  3590 | McLennan                |      1.62854e+06 |      1.08368e+06 | 541839           | 541839           | -544860           | -0.33457    |
|  9797 | Midland                 | 844286           | 607682           | 303841           | 303841           | -236603           | -0.280241   |
|  3593 | Navarro                 |      2.27514e+06 |      1.49772e+06 | 748858           | 748858           | -777428           | -0.341705   |
|  3558 | North Central           |      1.18826e+06 |      1.11312e+06 | 556560           | 556560           |  -75140.1         | -0.0632354  |
| 23154 | Northeast Texas         | 363061           | 335895           | 167948           | 167948           |  -27166           | -0.0748248  |
|  3596 | Odessa                  | 566168           | 600807           | 300403           | 300403           |   34638.3         |  0.0611802  |
|  3600 | Panola                  | 365998           | 402803           | 201402           | 201402           |   36805.5         |  0.100562   |
|  3601 | Paris                   |      1.23358e+06 | 541033           | 270516           | 270516           | -692550           | -0.561413   |
|  3603 | Ranger                  | 374453           | 450953           | 225477           | 225477           |   76500           |  0.204298   |
| 29137 | San Jacinto             |      3.13093e+06 |      4.43503e+06 |      2.21751e+06 |      2.21751e+06 |       1.30409e+06 |  0.416519   |
|  3611 | South Plains            |      1.59886e+06 |      1.45336e+06 | 726681           | 726681           | -145493           | -0.0909985  |
| 31034 | South Texas             |      4.71068e+06 |      4.68206e+06 |      2.34103e+06 |      2.34103e+06 |  -28625.5         | -0.00607673 |
|  3614 | Southwest Texas         |      1.21816e+06 |      1.09519e+06 | 547593           | 547593           | -122975           | -0.100952   |
|  3626 | Tarrant                 |      9.57019e+06 |      5.74814e+06 |      2.87407e+06 |      2.87407e+06 |      -3.82206e+06 | -0.399371   |
|  3627 | Temple                  |      1.01827e+06 | 797644           | 398822           | 398822           | -220629           | -0.21667    |
|  3628 | Texarkana               | 555598           | 661335           | 330667           | 330667           |  105737           |  0.190313   |
|  3643 | Texas Southmost         |      1.2333e+06  | 785639           | 392819           | 392819           | -447664           | -0.36298    |
|  3572 | Trinity Valley          |      1.02597e+06 | 988827           | 494413           | 494413           |  -37145           | -0.0362047  |
|  3648 | Tyler                   |      1.52174e+06 |      1.25036e+06 | 625180           | 625180           | -271384           | -0.178338   |
| 10060 | Vernon                  | 395604           | 310368           | 155184           | 155184           |  -85235.7         | -0.215457   |
|  3662 | Victoria                | 545770           | 432996           | 216498           | 216498           | -112774           | -0.206632   |
|  3664 | Weatherford             |      1.04729e+06 | 633166           | 316583           | 316583           | -414128           | -0.395427   |
|  9549 | Western Texas           | 205158           | 229276           | 114638           | 114638           |   24118.7         |  0.117561   |
|  3668 | Wharton                 | 578136           | 562029           | 281014           | 281014           |  -16107.3         | -0.0278608  |



label: G=D-C
labeled_formulas: G=D-C
output: {"Arithmetic-Relationship": ["G=D-C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_493119___xlsx_5812da2adb5d13054c779e053aacac78e4db38ad.xlsx___line_214