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 |
|:--------------------|-----------------:|-----------------:|-----------------:|-----------------:|----:|-----------------:|:--------------------|-----------------:|:--------------------|------------------:|
| Children's          |      1.71734e+09 |      7.49917e+08 |      2.47696e+08 |      5.02637e+08 |   0 |      1.50025e+09 | 0.87358960917176587 |      1.54561e+09 | 0.9                 |       7.95688e+08 |
| Bexar               |      1.00166e+08 |      5.51315e+07 |      3.05519e+07 |      1.0184e+07  |   0 |      9.58673e+07 | 0.95708357053080773 |      9.01494e+07 | 0.9                 |       3.5018e+07  |
| Dallas              |      3.48025e+08 |      1.59328e+08 |      9.63172e+07 |      6.57309e+07 |   0 |      3.21376e+08 | 0.92342649888011963 |      3.13223e+08 | 0.9                 |       1.53895e+08 |
| El Paso             |      3.51136e+07 |      1.85648e+07 |      2.83702e+06 |      9.54272e+06 |   0 |      3.09446e+07 | 0.88127098828296768 |      3.16022e+07 | 0.9                 |       1.30374e+07 |
| Harris              |      5.02478e+08 |      2.57109e+08 |      8.89021e+07 |      1.08977e+08 |   0 |      4.54988e+08 | 0.90548847233504548 |      4.5223e+08  | 0.9                 |       1.95121e+08 |
| Lubbock             |      4.66376e+07 |      2.38881e+07 |      0           |      1.5792e+07  |   0 |      3.96801e+07 | 0.8508172424574002  |      4.19738e+07 | 0.90000000000000013 |       1.80858e+07 |
| Nueces              |      1.67851e+08 |      5.95591e+07 |      1.69776e+07 |      6.3383e+07  |   0 |      1.3992e+08  | 0.83359591098696639 |      1.51066e+08 | 0.89999999999999991 |       9.15066e+07 |
| Tarrant             |      3.49616e+08 |      1.27702e+08 |      1.21101e+07 |      1.46533e+08 |   0 |      2.86345e+08 | 0.81902719775487276 |      3.14654e+08 | 0.90000000000000013 |       1.86952e+08 |
| Travis              |      1.67453e+08 |      4.86353e+07 |      0           |      8.24945e+07 |   0 |      1.3113e+08  | 0.78308597489890885 |      1.50707e+08 | 0.9                 |       1.02072e+08 |
| Non-State-Owned IMD |      6.02327e+07 |      5.33981e+07 |      1.58481e+07 |      4.44242e+06 |   0 |      7.36886e+07 | 1.223398068230455   |      5.42095e+07 | 0.9                 |  811411           |
| Bexar               |      7.27522e+06 |      1.21763e+07 |      1.16793e+06 |  77597.5         |   0 |      1.34219e+07 | 1.8448729835248721  |      6.5477e+06  | 0.89999999999999991 |      -5.62863e+06 |
| Dallas              |      7.24169e+06 |      4.88278e+06 |      2.02023e+06 | 445635           |   0 |      7.34865e+06 | 1.014769757578672   |      6.51753e+06 | 0.9                 |       1.63474e+06 |
| El Paso             |      3.54143e+06 |      2.65093e+06 | 562644           | 271066           |   0 |      3.48464e+06 | 0.98396529186539594 |      3.18728e+06 | 0.9                 |  536353           |
| Harris              |      2.5388e+07  |      1.7236e+07  |      5.7341e+06  |      3.50663e+06 |   0 |      2.64767e+07 | 1.0428811952826156  |      2.28492e+07 | 0.9                 |       5.61326e+06 |
| Hidalgo             |      2.14139e+06 |      1.78129e+06 | 318367           |  22740.5         |   0 |      2.1224e+06  | 0.99112885228861003 |      1.92725e+06 | 0.9                 |  145965           |
| Lubbock             |    912.726       |   4198.2         |      0           |      0           |   0 |   4198.2         | 4.5996290213553648  |    821.453       | 0.9                 |   -3376.75        |
| MRSA Central        |      2.31387e+06 |      1.92619e+06 |      1.20885e+06 |      0           |   0 |      3.13504e+06 | 1.3548896302830737  |      2.08249e+06 | 0.9                 |  156294           |
| MRSA West           |      2.85259e+06 |      3.12614e+06 |      1.04269e+06 |      0           |   0 |      4.16882e+06 | 1.4614155147335912  |      2.56733e+06 | 0.9                 | -558802           |
| Tarrant             |      5.08125e+06 |      5.08334e+06 |      1.88194e+06 |  50718.2         |   0 |      7.01599e+06 | 1.3807603462323372  |      4.57313e+06 | 0.9                 | -510207           |
| Travis              |      4.39633e+06 |      4.53089e+06 |      1.91138e+06 |  68036.8         |   0 |      6.51031e+06 | 1.4808487217598065  |      3.9567e+06  | 0.9                 | -574185           |
| Bexar               |      3.65977e+06 |      1.54108e+06 |      1.2841e+06  | 626495           |   0 |      3.45168e+06 | 0.94313944559578233 |      3.2938e+06  | 0.9                 |       1.75272e+06 |
| Dallas              |      7.93951e+06 |      2.04302e+06 | 742417           |      3.59787e+06 |   0 |      6.38331e+06 | 0.80399290833534931 |      7.14556e+06 | 0.9                 |       5.10253e+06 |
| Harris              |      1.53824e+06 |      2.39049e+06 | 247687           |   6763.71        |   0 |      2.64494e+06 | 1.7194525646801944  |      1.38442e+06 | 0.9                 |      -1.00607e+06 |
| Hidalgo             |      8.86425e+06 |      5.48423e+06 |      0           |      2.55794e+06 |   0 |      8.04217e+06 | 0.90725835728771265 |      7.97783e+06 | 0.9                 |       2.4936e+06  |
| Jefferson           |      4.03716e+06 |      4.43607e+06 |      0           | 164396           |   0 |      4.60046e+06 | 1.1395304471073191  |      3.63344e+06 | 0.9                 | -802626           |
| Lubbock             |      8.211e+06   |      4.17844e+06 |      4.72352e+06 | 473301           |   0 |      9.37525e+06 | 1.1417919426305405  |      7.3899e+06  | 0.9                 |       3.21146e+06 |
| MRSA Central        |      1.15159e+07 |      7.69413e+06 | 982375           |      3.08436e+06 |   0 |      1.17609e+07 | 1.0212702960679261  |      1.03643e+07 | 0.89999999999999991 |       2.6702e+06  |
| MRSA Northeast      |      5.19167e+07 |      3.76467e+07 |      0           |      1.10144e+07 |   0 |      4.86611e+07 | 0.93729198078436882 |      4.67251e+07 | 0.9                 |       9.07837e+06 |
| Nueces              |      8.2054e+06  |      5.72382e+06 |      1.46767e+06 | 861619           |   0 |      8.05311e+06 | 0.98144031246300234 |      7.38486e+06 | 0.9                 |       1.66103e+06 |
| Tarrant             |      1.61445e+07 |      6.81323e+06 |      0           |      6.50791e+06 |   0 |      1.33211e+07 | 0.82512177289455924 |      1.453e+07   | 0.9                 |       7.71678e+06 |
| Travis              |      4.18283e+06 |      2.25567e+06 | 827194           | 833559           |   0 |      3.91642e+06 | 0.93630903524842013 |      3.76455e+06 | 0.9                 |       1.50888e+06 |
| State-Owned IMD     |      3.02893e+06 |      2.57785e+06 |      2.52569e+06 |   9961.93        |   0 |      5.1135e+06  | 1.6882211490914452  |      2.72604e+06 | 0.9                 |  148186           |
| Bexar               |  66404           |  98049.6         |  40867.4         |      0           |   0 | 138917           | 2.091996297558421   |  59763.6         | 0.9                 |  -38286           |
| Dallas              | 676318           | 264449           | 749221           |      0           |   0 |      1.01367e+06 | 1.498806879865225   | 608686           | 0.89999999999999991 |  344237           |
| El Paso             | 523596           | 320683           | 188209           |   9777.11        |   0 | 518670           | 0.9905925250852522  | 471236           | 0.9                 |  150553           |
| Hidalgo             |    952.087       |    437           |    258.757       |    184.826       |   0 |    880.583       | 0.92489724043054955 |    856.879       | 0.9                 |     419.879       |
| MRSA Northeast      |      0           |      0           |      0           |      0           |   0 |      0           | #DIV/0!             |      0           | #DIV/0!             |       0           |
| MRSA West           |      1.27467e+06 |      1.57827e+06 |      1.01714e+06 |      0           |   0 |      2.59541e+06 | 2.0361478816278256  |      1.1472e+06  | 0.89999999999999991 | -431070           |
| Travis              | 486994           | 315962           | 529995           |      0           |   0 | 845957           | 1.7370997378646258  | 438294           | 0.9                 |  122332           |
| State-Owned Non-IMD |      1.32677e+08 |      8.66019e+07 |      2.65822e+07 |      1.31271e+07 |   0 |      1.26311e+08 | 0.95201934013693279 |      1.19409e+08 | 0.9                 |       3.28075e+07 |
| Bexar               |      0           |   8276.6         |      0           |      0           |   0 |   8276.6         | #DIV/0!             |      0           | #DIV/0!             |   -8276.6         |
| Dallas              |      3.82116e+07 |      1.08447e+07 |      9.90033e+06 |      1.21458e+07 |   0 |      3.28908e+07 | 0.86075475016168046 |      3.43905e+07 | 0.90000000000000013 |       2.35457e+07 |
| Harris              |      9.42305e+07 |      7.54792e+07 |      1.66819e+07 | 981287           |   0 |      9.31423e+07 | 0.98845187960790237 |      8.48075e+07 | 0.9                 |       9.32831e+06 |
| MRSA Northeast      | 234977           | 269739           |      0           |      0           |   0 | 269739           | 1.147936044734986   | 211479           | 0.9                 |  -58259.3         |
| Hidalgo             |      3.86928e+08 |      1.26307e+08 |      1.25716e+08 |      9.3671e+07  |   0 |      3.45695e+08 | 0.89343366863577633 |      3.48235e+08 | 0.9                 |       2.21928e+08 |
| Jefferson           |      5.78071e+07 |      1.96895e+07 |      1.97472e+07 |      1.34759e+07 |   0 |      5.29125e+07 | 0.91532893685857453 |      5.20264e+07 | 0.9                 |       3.23369e+07 |
| MRSA Central        |      1.82394e+08 |      7.48854e+07 |      4.39944e+07 |      4.48068e+07 |   0 |      1.63687e+08 | 0.89743427902448603 |      1.64154e+08 | 0.9                 |       8.92691e+07 |
| MRSA Northeast      |      1.57196e+08 |      5.14916e+07 |      3.85771e+07 |      4.68077e+07 |   0 |      1.36876e+08 | 0.87073576446482415 |      1.41477e+08 | 0.9                 |       8.9985e+07  |
| Tarrant             |      4.57543e+08 |      1.1899e+08  |      1.09357e+08 |      1.56955e+08 |   0 |      3.85302e+08 | 0.8421114926837453  |      4.11789e+08 | 0.9                 |       2.92799e+08 |
| Travis              |      2.69775e+08 |      9.25679e+07 |      4.09251e+07 |      9.57457e+07 |   0 |      2.29239e+08 | 0.84974055625492018 |      2.42797e+08 | 0.9                 |       1.5023e+08  |



label: H=G/B
J=I/B
K=I-C-F
labeled_formulas: H=G/B
J=I/B
I=C+K
K=I-C-F
G=(C+D)+E
output: {"Arithmetic-Relationship": ["H=G/B", "J=I/B", "K=I-C-F"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_771258___xlsx_266bf9190881e3e14aeb6be9a4d97c603df77a47.xlsx___line_116