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:
|     B |     C |     D |     E |     F |           G |     H |      I |       J |       K |
|------:|------:|------:|------:|------:|------------:|------:|-------:|--------:|--------:|
| 42570 | 47.71 | 47.96 | 46.68 | 47.85 | 4.5566e+06  | 47.85 | -17.71 | 7.90266 | 8.29593 |
| 42569 | 47.58 | 48.02 | 47.13 | 47.71 | 3.6899e+06  | 47.71 | -17.71 | 7.90266 | 8.27822 |
| 42566 | 47.51 | 47.76 | 46.92 | 47.43 | 5.1741e+06  | 47.43 | -17.71 | 7.90266 | 8.24279 |
| 42565 | 46.73 | 47.94 | 46.42 | 47.85 | 7.6952e+06  | 47.85 | -17.71 | 7.90266 | 8.29593 |
| 42564 | 46.55 | 46.73 | 45.42 | 45.86 | 5.4901e+06  | 45.86 | -17.71 | 7.90266 | 8.04412 |
| 42563 | 44.19 | 46.36 | 44.19 | 46.16 | 9.7786e+06  | 46.16 | -17.71 | 7.90266 | 8.08208 |
| 42562 | 41.88 | 42.74 | 41.72 | 42.41 | 4.659e+06   | 42.41 | -17.71 | 7.90266 | 7.60756 |
| 42559 | 40.7  | 41.73 | 40.7  | 41.48 | 5.1506e+06  | 41.48 | -17.71 | 7.90266 | 7.48988 |
| 42558 | 39.32 | 40.41 | 39.31 | 40.09 | 4.6032e+06  | 40.09 | -17.71 | 7.90266 | 7.31399 |
| 42557 | 39.14 | 39.41 | 37.64 | 39.31 | 8.2072e+06  | 39.31 | -17.71 | 7.90266 | 7.21529 |
| 42556 | 40.8  | 40.92 | 39.41 | 40.29 | 5.2029e+06  | 40.29 | -17.71 | 7.90266 | 7.33929 |
| 42552 | 41.02 | 41.8  | 40.83 | 41.37 | 5.0878e+06  | 41.37 | -17.71 | 7.90266 | 7.47596 |
| 42551 | 40.72 | 41.04 | 40.2  | 41.04 | 6.0278e+06  | 41.04 | -17.71 | 7.90266 | 7.4342  |
| 42550 | 39.19 | 40.92 | 39.15 | 40.57 | 7.3569e+06  | 40.57 | -17.71 | 7.90266 | 7.37473 |
| 42549 | 38.82 | 39.06 | 38.01 | 38.95 | 7.7896e+06  | 38.95 | -17.71 | 7.90266 | 7.16973 |
| 42548 | 40.64 | 40.69 | 37.41 | 37.75 | 1.29088e+07 | 37.75 | -17.71 | 7.90266 | 7.01788 |
| 42545 | 42.67 | 43.22 | 41.04 | 41.06 | 1.18618e+07 | 41.06 | -17.71 | 7.90266 | 7.43673 |
| 42544 | 45.75 | 45.92 | 44.46 | 45.17 | 4.905e+06   | 45.17 | -17.71 | 7.90266 | 7.95681 |
| 42543 | 45    | 45.64 | 44.94 | 45.09 | 4.8147e+06  | 45.09 | -17.71 | 7.90266 | 7.94668 |
| 42542 | 45.01 | 45.59 | 44.4  | 44.86 | 7.696e+06   | 44.86 | -17.71 | 7.90266 | 7.91758 |
| 42541 | 43.07 | 44.03 | 43    | 43.4  | 4.4278e+06  | 43.4  | -17.71 | 7.90266 | 7.73283 |
| 42538 | 41.9  | 43.07 | 41.5  | 42.62 | 8.115e+06   | 42.62 | -17.71 | 7.90266 | 7.63413 |
| 42537 | 42.23 | 42.9  | 41.68 | 41.83 | 7.6615e+06  | 41.83 | -17.71 | 7.90266 | 7.53417 |
| 42536 | 42.55 | 43.72 | 42.51 | 42.89 | 6.3317e+06  | 42.89 | -17.71 | 7.90266 | 7.6683  |
| 42535 | 43.98 | 44.3  | 41.46 | 42.09 | 8.16e+06    | 42.09 | -17.71 | 7.90266 | 7.56707 |
| 42534 | 45.59 | 45.88 | 43.64 | 44.06 | 7.1237e+06  | 44.06 | -17.71 | 7.90266 | 7.81635 |
| 42531 | 46.09 | 46.69 | 45.63 | 46.08 | 4.2005e+06  | 46.08 | -17.71 | 7.90266 | 8.07196 |
| 42530 | 45.59 | 46.91 | 45.44 | 46.7  | 4.6488e+06  | 46.7  | -17.71 | 7.90266 | 8.15041 |
| 42529 | 45.94 | 46.53 | 45.29 | 45.69 | 4.8735e+06  | 45.69 | -17.71 | 7.90266 | 8.02261 |
| 42528 | 44.5  | 46.46 | 44.01 | 45.81 | 5.8607e+06  | 45.81 | -17.71 | 7.90266 | 8.03779 |
| 42527 | 44.2  | 44.54 | 43.53 | 44.53 | 5.2491e+06  | 44.53 | -17.71 | 7.90266 | 7.87582 |
| 42524 | 45.01 | 45.16 | 43.6  | 44.3  | 5.6394e+06  | 44.3  | -17.71 | 7.90266 | 7.84672 |
| 42523 | 44.92 | 45.59 | 44.86 | 45.17 | 3.3553e+06  | 45.17 | -17.71 | 7.90266 | 7.95681 |
| 42522 | 45.09 | 45.46 | 44.7  | 45.25 | 3.9823e+06  | 45.25 | -17.71 | 7.90266 | 7.96693 |
| 42521 | 45.13 | 45.3  | 44.3  | 45.09 | 5.6252e+06  | 45.09 | -17.71 | 7.90266 | 7.94668 |
| 42517 | 44.56 | 45.46 | 44.53 | 45.18 | 3.6183e+06  | 45.18 | -17.71 | 7.90266 | 7.95807 |
| 42516 | 45.2  | 45.33 | 44.14 | 44.5  | 4.8833e+06  | 44.5  | -17.71 | 7.90266 | 7.87203 |
| 42515 | 45.12 | 45.94 | 45.07 | 45.13 | 3.6503e+06  | 45.13 | -17.71 | 7.90266 | 7.95175 |
| 42514 | 44.46 | 45.08 | 44.39 | 44.99 | 3.702e+06   | 44.99 | -17.71 | 7.90266 | 7.93403 |
| 42513 | 44.54 | 45    | 44.15 | 44.2  | 3.6918e+06  | 44.2  | -17.71 | 7.90266 | 7.83406 |
| 42510 | 44.39 | 45.29 | 44.22 | 44.49 | 3.2815e+06  | 44.49 | -17.71 | 7.90266 | 7.87076 |
| 42509 | 44.73 | 45.29 | 43.65 | 44.01 | 5.5528e+06  | 44.01 | -17.71 | 7.90266 | 7.81002 |
| 42508 | 44.91 | 46.28 | 44.83 | 45.27 | 4.4781e+06  | 45.27 | -17.71 | 7.90266 | 7.96946 |
| 42507 | 44.35 | 46.08 | 44.32 | 45.05 | 5.9154e+06  | 45.05 | -17.71 | 7.90266 | 7.94162 |
| 42506 | 44.32 | 44.87 | 43.51 | 44.59 | 6.0752e+06  | 44.59 | -17.71 | 7.90266 | 7.88342 |
| 42503 | 43.7  | 44.94 | 43.62 | 43.84 | 5.7611e+06  | 43.84 | -17.71 | 7.90266 | 7.78851 |
| 42502 | 46.03 | 46.03 | 43.33 | 43.78 | 7.9095e+06  | 43.78 | -17.71 | 7.90266 | 7.78092 |
| 42501 | 46.73 | 47.4  | 45.79 | 45.8  | 5.0509e+06  | 45.8  | -17.71 | 7.90266 | 8.03653 |
| 42500 | 46.07 | 47.12 | 45.79 | 47    | 4.7968e+06  | 47    | -17.71 | 7.90266 | 8.18838 |
| 42499 | 45.88 | 46.81 | 45.68 | 45.71 | 4.6035e+06  | 45.71 | -17.71 | 7.90266 | 8.02514 |
| 42496 | 44.8  | 45.73 | 44.01 | 45.7  | 9.2457e+06  | 45.7  | -17.71 | 7.90266 | 8.02387 |
| 42495 | 45.6  | 46.07 | 44.96 | 44.99 | 6.0346e+06  | 44.99 | -17.71 | 7.90266 | 7.93403 |
| 42494 | 46.71 | 46.76 | 45.15 | 45.55 | 6.7327e+06  | 45.55 | -17.71 | 7.90266 | 8.00489 |
| 42493 | 47    | 47.54 | 46.15 | 47.13 | 6.7145e+06  | 47.13 | -17.71 | 7.90266 | 8.20483 |
| 42492 | 46.61 | 46.81 | 45.81 | 46.66 | 6.6246e+06  | 46.66 | -17.71 | 7.90266 | 8.14535 |
| 42489 | 47.89 | 47.93 | 45.58 | 45.81 | 1.02332e+07 | 45.81 | -17.71 | 7.90266 | 8.03779 |
| 42488 | 48.84 | 49.21 | 47.9  | 48.06 | 5.6452e+06  | 48.06 | -17.71 | 7.90266 | 8.32251 |
| 42487 | 49.05 | 49.7  | 48.7  | 48.94 | 5.2013e+06  | 48.94 | -17.71 | 7.90266 | 8.43386 |
| 42486 | 49.75 | 50.06 | 48.05 | 49.14 | 7.5415e+06  | 49.14 | -17.71 | 7.90266 | 8.45917 |
| 42485 | 51.06 | 51.45 | 49.3  | 49.37 | 6.859e+06   | 49.37 | -17.71 | 7.90266 | 8.48827 |
| 42482 | 51.2  | 51.59 | 50.2  | 50.74 | 1.13408e+07 | 50.74 | -17.71 | 7.90266 | 8.66163 |



label: K=(H-I)/J
labeled_formulas: K=(H-I)/J
output: {"Arithmetic-Relationship": ["K=(H-I)/J"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_655484___xlsx_798d87861c750f10818f15c27263a4f1f6443212.xlsx___line_569