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 |                L |
|----:|----:|------------:|------------:|-----------------:|------------:|----:|------------:|------------:|----:|-----------------:|
|   1 |  31 | 0           | 2.72156e+06 |      0           | 2.72156e+06 |   0 | 2.72156e+06 | 4.39672e+08 |   0 | 226797           |
|   2 |  32 | 2.72156e+06 | 2.88485e+06 | 163294           | 5.7697e+06  |   0 | 2.88485e+06 | 4.36624e+08 |   0 | 240404           |
|   3 |  33 | 5.7697e+06  | 3.05794e+06 | 346182           | 9.17383e+06 |   0 | 3.05794e+06 | 4.3322e+08  |   0 | 254829           |
|   4 |  34 | 9.17383e+06 | 3.24142e+06 | 550430           | 1.29657e+07 |   0 | 3.24142e+06 | 4.29428e+08 |   0 | 270118           |
|   5 |  35 | 1.29657e+07 | 3.4359e+06  | 777941           | 1.71795e+07 |   0 | 3.4359e+06  | 4.25214e+08 |   0 | 286325           |
|   6 |  36 | 1.71795e+07 | 3.64206e+06 |      1.03077e+06 | 2.18524e+07 |   0 | 3.64206e+06 | 4.20541e+08 |   0 | 303505           |
|   7 |  37 | 2.18524e+07 | 3.86058e+06 |      1.31114e+06 | 2.70241e+07 |   0 | 3.86058e+06 | 4.1537e+08  |   0 | 321715           |
|   8 |  38 | 2.70241e+07 | 4.09222e+06 |      1.62144e+06 | 3.27377e+07 |   0 | 4.09222e+06 | 4.09656e+08 |   0 | 341018           |
|   9 |  39 | 3.27377e+07 | 4.33775e+06 |      1.96426e+06 | 3.90398e+07 |   0 | 4.33775e+06 | 4.03354e+08 |   0 | 361479           |
|  10 |  40 | 3.90398e+07 | 4.59802e+06 |      2.34239e+06 | 4.59802e+07 |   0 | 4.59802e+06 | 3.96414e+08 |   0 | 383168           |
|  11 |  41 | 4.59802e+07 | 4.8739e+06  |      2.75881e+06 | 5.36129e+07 |   0 | 4.8739e+06  | 3.88781e+08 |   0 | 406158           |
|  12 |  42 | 5.36129e+07 | 5.16633e+06 |      3.21677e+06 | 6.1996e+07  |   0 | 5.16633e+06 | 3.80398e+08 |   0 | 430528           |
|  13 |  43 | 6.1996e+07  | 5.47631e+06 |      3.71976e+06 | 7.1192e+07  |   0 | 5.47631e+06 | 3.71202e+08 |   0 | 456359           |
|  14 |  44 | 7.1192e+07  | 5.80489e+06 |      4.27152e+06 | 8.12684e+07 |   0 | 5.80489e+06 | 3.61125e+08 |   0 | 483741           |
|  15 |  45 | 8.12684e+07 | 6.15318e+06 |      4.87611e+06 | 9.22977e+07 |   0 | 6.15318e+06 | 3.50096e+08 |   0 | 512765           |
|  16 |  46 | 9.22977e+07 | 6.52237e+06 |      5.53786e+06 | 1.04358e+08 |   0 | 6.52237e+06 | 3.38036e+08 |   0 | 543531           |
|  17 |  47 | 1.04358e+08 | 6.91372e+06 |      6.26148e+06 | 1.17533e+08 |   0 | 6.91372e+06 | 3.24861e+08 |   0 | 576143           |
|  18 |  48 | 1.17533e+08 | 7.32854e+06 |      7.05199e+06 | 1.31914e+08 |   0 | 7.32854e+06 | 3.1048e+08  |   0 | 610712           |
|  19 |  49 | 1.31914e+08 | 7.76825e+06 |      7.91482e+06 | 1.47597e+08 |   0 | 7.76825e+06 | 2.94797e+08 |   0 | 647354           |
|  20 |  50 | 1.47597e+08 | 8.23435e+06 |      8.85581e+06 | 1.64687e+08 |   0 | 8.23435e+06 | 2.77707e+08 |   0 | 686195           |
|  21 |  51 | 1.64687e+08 | 8.72841e+06 |      9.88121e+06 | 1.83297e+08 |   0 | 8.72841e+06 | 2.59097e+08 |   0 | 727367           |
|  22 |  52 | 1.83297e+08 | 9.25211e+06 |      1.09978e+07 | 2.03546e+08 |   0 | 9.25211e+06 | 2.38847e+08 |   0 | 771009           |
|  23 |  53 | 2.03546e+08 | 9.80724e+06 |      1.22128e+07 | 2.25566e+08 |   0 | 9.80724e+06 | 2.16827e+08 |   0 | 817270           |
|  24 |  54 | 2.25566e+08 | 1.03957e+07 |      1.3534e+07  | 2.49496e+08 |   0 | 1.03957e+07 | 1.92898e+08 |   0 | 866306           |
|  25 |  55 | 2.49496e+08 | 1.10194e+07 |      1.49698e+07 | 2.75485e+08 |   0 | 1.10194e+07 | 1.66908e+08 |   0 | 918284           |
|  26 |  56 | 2.75485e+08 | 1.16806e+07 |      1.65291e+07 | 3.03695e+08 |   0 | 1.16806e+07 | 1.38699e+08 |   0 | 973381           |
|  27 |  57 | 3.03695e+08 | 1.23814e+07 |      1.82217e+07 | 3.34298e+08 |   0 | 1.23814e+07 | 1.08096e+08 |   0 |      1.03178e+06 |
|  28 |  58 | 3.34298e+08 | 1.31243e+07 |      2.00579e+07 | 3.6748e+08  |   0 | 1.31243e+07 | 7.49135e+07 |   0 |      1.09369e+06 |
|  29 |  59 | 3.6748e+08  | 1.39118e+07 |      2.20488e+07 | 4.03441e+08 |   0 | 1.39118e+07 | 3.89529e+07 |   0 |      1.15931e+06 |
|  30 |  60 | 4.03441e+08 | 1.47465e+07 |      2.42065e+07 | 4.42394e+08 |   0 | 1.47465e+07 | 0           |   0 |      1.22887e+06 |
|  31 |   0 | 0           | 0           |      0           | 0           |   0 | 0           | 4.42394e+08 |   0 |      0           |
|  32 |   0 | 0           | 0           |      0           | 0           |   0 | 0           | 4.42394e+08 |   0 |      0           |
|  33 |   0 | 0           | 0           |      0           | 0           |   0 | 0           | 4.42394e+08 |   0 |      0           |
|  34 |   0 | 0           | 0           |      0           | 0           |   0 | 0           | 4.42394e+08 |   0 |      0           |
|  35 |   0 | 0           | 0           |      0           | 0           |   0 | 0           | 4.42394e+08 |   0 |      0           |
|  36 |   0 | 0           | 0           |      0           | 0           |   0 | 0           | 4.42394e+08 |   0 |      0           |
|  37 |   0 | 0           | 0           |      0           | 0           |   0 | 0           | 4.42394e+08 |   0 |      0           |
|  38 |   0 | 0           | 0           |      0           | 0           |   0 | 0           | 4.42394e+08 |   0 |      0           |
|  39 |   0 | 0           | 0           |      0           | 0           |   0 | 0           | 4.42394e+08 |   0 |      0           |
|  40 |   0 | 0           | 0           |      0           | 0           |   0 | 0           | 4.42394e+08 |   0 |      0           |
|  41 |   0 | 0           | 0           |      0           | 0           |   0 | 0           | 4.42394e+08 |   0 |      0           |
|  42 |   0 | 0           | 0           |      0           | 0           |   0 | 0           | 4.42394e+08 |   0 |      0           |
|  43 |   0 | 0           | 0           |      0           | 0           |   0 | 0           | 4.42394e+08 |   0 |      0           |
|  44 |   0 | 0           | 0           |      0           | 0           |   0 | 0           | 4.42394e+08 |   0 |      0           |
|  45 |   0 | 0           | 0           |      0           | 0           |   0 | 0           | 4.42394e+08 |   0 |      0           |
|  46 |   0 | 0           | 0           |      0           | 0           |   0 | 0           | 4.42394e+08 |   0 |      0           |
|  47 |   0 | 0           | 0           |      0           | 0           |   0 | 0           | 4.42394e+08 |   0 |      0           |
|  48 |   0 | 0           | 0           |      0           | 0           |   0 | 0           | 4.42394e+08 |   0 |      0           |
|  49 |   0 | 0           | 0           |      0           | 0           |   0 | 0           | 4.42394e+08 |   0 |      0           |
|  50 |   0 | 0           | 0           |      0           | 0           |   0 | 0           | 4.42394e+08 |   0 |      0           |
|  51 |   0 | 0           | 0           |      0           | 0           |   0 | 0           | 4.42394e+08 |   0 |      0           |
|  52 |   0 | 0           | 0           |      0           | 0           |   0 | 0           | 4.42394e+08 |   0 |      0           |
|  53 |   0 | 0           | 0           |      0           | 0           |   0 | 0           | 4.42394e+08 |   0 |      0           |
|  54 |   0 | 0           | 0           |      0           | 0           |   0 | 0           | 4.42394e+08 |   0 |      0           |
|  55 |   0 | 0           | 0           |      0           | 0           |   0 | 0           | 4.42394e+08 |   0 |      0           |
|  56 |   0 | 0           | 0           |      0           | 0           |   0 | 0           | 4.42394e+08 |   0 |      0           |
|  57 |   0 | 0           | 0           |      0           | 0           |   0 | 0           | 4.42394e+08 |   0 |      0           |
|  58 |   0 | 0           | 0           |      0           | 0           |   0 | 0           | 4.42394e+08 |   0 |      0           |
|  59 |   0 | 0           | 0           |      0           | 0           |   0 | 0           | 4.42394e+08 |   0 |      0           |
|  60 |   0 | 0           | 0           |      0           | 0           |   0 | 0           | 4.42394e+08 |   0 |      0           |



label: G=D+E+F
labeled_formulas: G=D+E+F
output: {"Arithmetic-Relationship": ["G=D+E+F"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_178110___xlsx_bab8a52fee2afb2aabcbc15d2217ec0143402e99.xlsx___line_627