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 |
|------:|--------:|-----:|-----:|-----:|-----:|-----:|--------:|-----:|--------:|
| 44368 | 110.541 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 29.6356 | 4.21 | 26.2568 |
| 44369 | 111.418 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 29.8707 | 4.21 | 26.465  |
| 44370 | 111.129 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 29.7932 | 4.21 | 26.3964 |
| 44371 | 111.557 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 29.908  | 4.21 | 26.4981 |
| 44372 | 112.603 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 30.1885 | 4.21 | 26.7465 |
| 44375 | 111.806 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 29.9748 | 4.21 | 26.5573 |
| 44376 | 111.836 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 29.9828 | 4.21 | 26.5644 |
| 44377 | 111.378 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 29.86   | 4.21 | 26.4555 |
| 44378 | 112.972 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 30.2873 | 4.21 | 26.8341 |
| 44379 | 114.525 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 30.7039 | 4.21 | 27.2032 |
| 44383 | 115.283 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 30.9069 | 4.21 | 27.383  |
| 44384 | 116.687 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 31.2834 | 4.21 | 27.7166 |
| 44385 | 115.542 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 30.9763 | 4.21 | 27.4445 |
| 44386 | 117.016 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 31.3715 | 4.21 | 27.7947 |
| 44389 | 118.002 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 31.6359 | 4.21 | 28.029  |
| 44390 | 119.088 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 31.927  | 4.21 | 28.2869 |
| 44391 | 119.337 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 31.9938 | 4.21 | 28.346  |
| 44392 | 118.51  | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 31.7721 | 4.21 | 28.1496 |
| 44393 | 118.271 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 31.708  | 4.21 | 28.0929 |
| 44396 | 114.874 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 30.7974 | 4.21 | 27.286  |
| 44397 | 116.966 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 31.3582 | 4.21 | 27.7829 |
| 44398 | 118.809 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 31.8522 | 4.21 | 28.2206 |
| 44399 | 122.156 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 32.7496 | 4.21 | 29.0156 |
| 44400 | 125.483 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 33.6415 | 4.21 | 29.8059 |
| 44403 | 125.573 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 33.6656 | 4.21 | 29.8272 |
| 44404 | 125.543 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 33.6576 | 4.21 | 29.8201 |
| 44405 | 121.937 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 32.6908 | 4.21 | 28.9636 |
| 44406 | 121.907 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 32.6828 | 4.21 | 28.9565 |
| 44407 | 120.961 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 32.4291 | 4.21 | 28.7317 |
| 44410 | 119.905 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 32.146  | 4.21 | 28.4809 |
| 44411 | 118.669 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 31.8149 | 4.21 | 28.1875 |
| 44412 | 117.793 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 31.5798 | 4.21 | 27.9793 |
| 44413 | 118.57  | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 31.7881 | 4.21 | 28.1638 |
| 44414 | 118.59  | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 31.7935 | 4.21 | 28.1686 |
| 44417 | 117.484 | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 31.4971 | 4.21 | 27.9059 |
| 44418 | 115.94  | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 31.0831 | 4.21 | 27.5392 |
| 44419 | 116.5   | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 31.2332 | 4.21 | 27.6722 |
| 44420 | 115.75  | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 31.0322 | 4.21 | 27.4941 |
| 44421 | 116.76  | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 31.3029 | 4.21 | 27.734  |
| 44424 | 117.54  | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 31.5121 | 4.21 | 27.9192 |
| 44425 | 116.57  | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 31.252  | 4.21 | 27.6888 |
| 44426 | 115.68  | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 31.0134 | 4.21 | 27.4774 |
| 44427 | 114.32  | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 30.6488 | 4.21 | 27.1544 |
| 44428 | 114.63  | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 30.7319 | 4.21 | 27.228  |
| 44431 | 115.15  | 1.01 | 0.89 | 0.8  | 1.03 | 3.73 | 30.8713 | 4.21 | 27.3515 |
| 44432 | 115.08  | 1.01 | 0.88 | 0.8  | 1.03 | 3.72 | 30.9355 | 4.21 | 27.3349 |
| 44433 | 115.57  | 1.01 | 0.88 | 0.8  | 1.03 | 3.72 | 31.0672 | 4.21 | 27.4513 |
| 44434 | 114.32  | 1.01 | 0.88 | 0.8  | 1.03 | 3.72 | 30.7312 | 4.21 | 27.1544 |
| 44435 | 115.12  | 1.01 | 0.88 | 0.8  | 1.03 | 3.72 | 30.9462 | 4.21 | 27.3444 |
| 44438 | 115.61  | 1.01 | 0.88 | 0.8  | 1.03 | 3.72 | 31.078  | 4.21 | 27.4608 |
| 44439 | 117.49  | 1.01 | 0.88 | 0.8  | 1.03 | 3.72 | 31.5833 | 4.21 | 27.9074 |
| 44440 | 117.45  | 1.01 | 0.88 | 0.8  | 1.03 | 3.72 | 31.5726 | 4.21 | 27.8979 |
| 44441 | 117.37  | 1.01 | 0.88 | 0.8  | 1.03 | 3.72 | 31.5511 | 4.21 | 27.8789 |
| 44442 | 117.19  | 1.01 | 0.88 | 0.8  | 1.03 | 3.72 | 31.5027 | 4.21 | 27.8361 |
| 44446 | 115.79  | 1.01 | 0.88 | 0.8  | 1.03 | 3.72 | 31.1263 | 4.21 | 27.5036 |
| 44447 | 118.04  | 1.01 | 0.88 | 0.8  | 1.03 | 3.72 | 31.7312 | 4.21 | 28.038  |
| 44448 | 118.79  | 1.01 | 0.88 | 0.8  | 1.03 | 3.72 | 31.9328 | 4.21 | 28.2162 |
| 44449 | 119.34  | 1.01 | 0.88 | 0.8  | 1.03 | 3.72 | 32.0806 | 4.21 | 28.3468 |
| 44452 | 119.18  | 1.01 | 0.88 | 0.8  | 1.03 | 3.72 | 32.0376 | 4.21 | 28.3088 |
| 44453 | 118.86  | 1.01 | 0.88 | 0.8  | 1.03 | 3.72 | 31.9516 | 4.21 | 28.2328 |
| 44454 | 114.64  | 0.99 | 0.86 | 0.79 | 0.95 | 3.59 | 31.9331 | 4.06 | 28.2365 |
| 44455 | 114.67  | 0.99 | 0.86 | 0.79 | 0.95 | 3.59 | 31.9415 | 4.06 | 28.2438 |
| 44456 | 113.41  | 0.99 | 0.86 | 0.79 | 0.95 | 3.59 | 31.5905 | 4.06 | 27.9335 |
| 44459 | 111.82  | 0.99 | 0.86 | 0.79 | 0.95 | 3.59 | 31.1476 | 4.06 | 27.5419 |



label: H=B/G
J=B/I
labeled_formulas: H=B/G
J=B/I
output: {"Arithmetic-Relationship": ["H=B/G", "J=B/I"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_785446___xlsx_c117904f03145aa700e37942c3259ace5e64a69e.xlsx___line_465