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 |
|----:|----:|------:|--------:|-----------:|----:|----:|----:|----:|------:|----:|
|   1 |   1 | 4.301 | 5.04297 | 0.741972   |   0 |   0 |   0 |   1 | 1.446 |   1 |
|   2 |   3 | 5.77  | 5.57236 | 0.197636   |   0 |   0 |   0 |   1 | 1.683 |   1 |
|   3 |  12 | 5.939 | 5.73556 | 0.203443   |   0 |   1 |   0 |   1 | 1.452 |   1 |
|   4 |  13 | 6.824 | 6.28269 | 0.541313   |   0 |   0 |   0 |   1 | 2.001 |   1 |
|   5 |  14 | 5.569 | 5.53389 | 0.0351098  |   0 |   0 |   0 |   0 | 2.034 |   1 |
|   6 |  15 | 6.387 | 6.48622 | 0.0992175  |   0 |   2 |   0 |   1 | 1.484 |   1 |
|   7 |  16 | 6.276 | 6.11069 | 0.16531    |   0 |   0 |   0 |   1 | 1.924 |   1 |
|   8 |  18 | 5.959 | 6.18007 | 0.221067   |   0 |   1 |   0 |   1 | 1.651 |   1 |
|  12 |  24 | 5.444 | 5.92989 | 0.48589    |   0 |   1 |   0 |   1 | 1.539 |   1 |
|  14 |  28 | 6.167 | 6.14643 | 0.0205701  |   0 |   0 |   0 |   1 | 1.94  |   1 |
|  15 |  29 | 5.638 | 5.5612  | 0.0768047  |   0 |   0 |   0 |   1 | 1.678 |   1 |
|  16 |  31 | 6.409 | 6.19794 | 0.211063   |   0 |   1 |   0 |   1 | 1.659 |   1 |
|  17 |  32 | 6.502 | 6.18007 | 0.321933   |   0 |   1 |   0 |   1 | 1.651 |   1 |
|  18 |  37 | 6.131 | 6.14656 | 0.015561   |   0 |   1 |   0 |   1 | 1.636 |   1 |
|  19 |  38 | 7.377 | 6.05051 | 1.32649    |   0 |   1 |   0 |   1 | 1.593 |   1 |
|  20 |  39 | 7     | 6.13986 | 0.86014    |   0 |   1 |   0 |   1 | 1.633 |   1 |
|  21 |  41 | 6.854 | 6.30069 | 0.553312   |   0 |   1 |   0 |   1 | 1.705 |   1 |
|  22 |  42 | 6.81  | 6.39004 | 0.419964   |   0 |   1 |   0 |   1 | 1.745 |   1 |
|  24 |  48 | 4.959 | 5.55686 | 0.597859   |   0 |   1 |   0 |   1 | 1.372 |   1 |
|  25 |  49 | 6.523 | 6.51959 | 0.00340775 |   0 |   1 |   0 |   1 | 1.803 |   1 |
|  26 |  50 | 5.721 | 5.92096 | 0.199955   |   0 |   1 |   0 |   1 | 1.535 |   1 |
|  27 |  51 | 6.357 | 6.09295 | 0.264048   |   0 |   1 |   0 |   1 | 1.612 |   1 |
|  29 |  54 | 5.699 | 5.46081 | 0.238191   |   0 |   1 |   0 |   1 | 1.329 |   1 |
|  30 |  56 | 6.337 | 6.24498 | 0.0920242  |   0 |   2 |   0 |   1 | 1.376 |   1 |
|  31 |  57 | 6.553 | 6.09519 | 0.457815   |   0 |   1 |   0 |   1 | 1.613 |   1 |
|  32 |  60 | 6.319 | 6.3543  | 0.035297   |   0 |   1 |   0 |   1 | 1.729 |   1 |
|  34 |  62 | 5.714 | 5.06169 | 0.652313   |   0 |   0 |   0 |   1 | 1.777 |   0 |
|  36 |  64 | 4.983 | 4.36427 | 0.618734   |   0 |   0 |   0 |   0 | 1.833 |   0 |
|  41 |  72 | 5.959 | 5.85841 | 0.100589   |   0 |   1 |   0 |   1 | 1.507 |   1 |
|  43 |  75 | 5.735 | 5.90085 | 0.165852   |   0 |   1 |   0 |   1 | 1.526 |   1 |
|  44 |  76 | 6.081 | 6.15103 | 0.0700285  |   0 |   1 |   0 |   1 | 1.638 |   1 |
|  45 | 137 | 6.638 | 6.40121 | 0.236795   |   0 |   1 |   0 |   1 | 1.75  |   1 |
|  46 | 138 | 6.367 | 6.52406 | 0.15706    |   0 |   1 |   0 |   1 | 1.805 |   1 |
|  47 | 140 | 6.398 | 6.47268 | 0.0746841  |   0 |   1 |   0 |   1 | 1.782 |   1 |
|  48 | 174 | 7.051 | 6.63351 | 0.417488   |   0 |   1 |   0 |   1 | 1.854 |   1 |
|  51 | 177 | 6.602 | 6.41461 | 0.187393   |   0 |   1 |   0 |   1 | 1.756 |   1 |
|  54 | 180 | 6.26  | 6.59777 | 0.337772   |   0 |   1 |   0 |   1 | 1.838 |   1 |
|  58 | 221 | 4.77  | 3.97796 | 0.792036   |   0 |   1 |   0 |   0 | 1.356 |   0 |
|  61 | 225 | 4.114 | 4.09337 | 0.0206292  |   1 |   0 |   0 |   0 | 1.579 |   0 |
|  62 | 226 | 4.046 | 3.93776 | 0.108243   |   0 |   1 |   0 |   0 | 1.338 |   0 |
|  63 | 228 | 3.699 | 3.8216  | 0.122603   |   0 |   1 |   0 |   0 | 1.286 |   0 |
|  64 | 229 | 4.056 | 4.27505 | 0.219049   |   0 |   1 |   0 |   0 | 1.489 |   0 |
|  74 | 245 | 4.721 | 4.28547 | 0.435529   |   1 |   0 |   0 |   0 | 1.665 |   0 |
|  75 | 246 | 4.553 | 4.10901 | 0.443993   |   1 |   0 |   0 |   0 | 1.586 |   0 |
|  76 | 247 | 3.889 | 3.81192 | 0.077078   |   1 |   0 |   0 |   0 | 1.453 |   0 |
|  77 | 248 | 4.004 | 3.47463 | 0.52937    |   1 |   0 |   0 |   0 | 1.302 |   0 |
|  78 | 249 | 4.215 | 4.22963 | 0.0146277  |   1 |   0 |   0 |   0 | 1.64  |   0 |
|  79 | 250 | 4.357 | 4.46864 | 0.111636   |   1 |   0 |   0 |   0 | 1.747 |   0 |
|  80 | 251 | 3.889 | 4.03753 | 0.148528   |   1 |   0 |   0 |   0 | 1.554 |   0 |
|  81 | 252 | 4.553 | 4.2676  | 0.285399   |   1 |   0 |   0 |   0 | 1.657 |   0 |
|  83 | 254 | 6.013 | 5.90755 | 0.105447   |   0 |   1 |   0 |   1 | 1.529 |   1 |
|  84 | 255 | 5.854 | 5.92766 | 0.0736565  |   0 |   1 |   0 |   1 | 1.538 |   1 |
|  85 | 258 | 4.928 | 5.93436 | 1.00636    |   0 |   1 |   0 |   1 | 1.541 |   1 |
|  86 | 260 | 5.745 | 6.43011 | 0.685112   |   0 |   0 |   0 |   1 | 2.067 |   1 |
|  87 | 262 | 5.26  | 5.83902 | 0.579022   |   0 |   0 |   0 |   1 | 2.125 |   0 |
|  88 | 263 | 6.18  | 5.48078 | 0.699219   |   0 |   0 |   0 |   1 | 1.642 |   1 |
|  89 | 264 | 5.444 | 5.15019 | 0.293809   |   0 |   0 |   0 |   1 | 1.494 |   1 |
|  90 | 267 | 6.194 | 5.70415 | 0.489847   |   0 |   0 |   0 |   1 | 1.742 |   1 |
|  91 | 268 | 5.62  | 6.05274 | 0.432745   |   0 |   1 |   0 |   1 | 1.594 |   1 |
|  92 | 369 | 4.377 | 4.66051 | 0.283506   |   0 |   0 |   0 |   0 | 1.643 |   1 |
|  93 | 370 | 3.854 | 3.5713  | 0.282704   |   0 |   0 |   0 |   0 | 1.478 |   0 |
|  94 | 371 | 4.222 | 4.63505 | 0.413047   |   0 |   0 |   0 |   1 | 1.586 |   0 |
|  95 | 372 | 4.553 | 4.49209 | 0.0609112  |   0 |   0 |   0 |   1 | 1.522 |   0 |
|  96 | 373 | 5.745 | 5.5947  | 0.150299   |   0 |   0 |   0 |   1 | 1.693 |   1 |
|  97 | 374 | 4.377 | 4.49521 | 0.11821    |   0 |   0 |   0 |   0 | 1.569 |   1 |
|  98 | 376 | 4.959 | 4.56133 | 0.397666   |   0 |   0 |   0 |   1 | 1.553 |   0 |
| 100 | 378 | 4.523 | 5.49145 | 0.968449   |   0 |   0 |   0 |   0 | 2.015 |   1 |
| 101 | 379 | 4.208 | 4.12079 | 0.0872092  |   0 |   0 |   0 |   0 | 1.724 |   0 |
| 102 | 380 | 5.046 | 4.99914 | 0.0468568  |   0 |   0 |   0 |   1 | 1.749 |   0 |
| 103 | 381 | 4.26  | 4.45138 | 0.191381   |   0 |   0 |   0 |   0 | 1.872 |   0 |
| 104 | 382 | 6.469 | 6.12409 | 0.344907   |   0 |   0 |   0 |   1 | 1.93  |   1 |
| 106 | 385 | 6.143 | 6.71616 | 0.57316    |   0 |   1 |   0 |   1 | 1.891 |   1 |
| 107 | 386 | 6.854 | 6.43471 | 0.419289   |   0 |   1 |   0 |   1 | 1.765 |   1 |
| 108 | 387 | 6.62  | 6.32749 | 0.292508   |   0 |   1 |   0 |   1 | 1.717 |   1 |
| 109 | 389 | 5.959 | 6.28282 | 0.323818   |   0 |   1 |   0 |   1 | 1.697 |   1 |
| 110 | 391 | 5.398 | 6.24484 | 0.846845   |   0 |   1 |   0 |   1 | 1.68  |   1 |
| 111 | 392 | 6.495 | 6.43024 | 0.0647566  |   0 |   1 |   0 |   1 | 1.763 |   1 |
| 112 | 393 | 5.721 | 6.20464 | 0.483638   |   0 |   1 |   0 |   1 | 1.662 |   1 |
| 113 | 394 | 6.456 | 6.43248 | 0.0235228  |   0 |   1 |   0 |   1 | 1.764 |   1 |
| 114 | 395 | 6.585 | 6.25601 | 0.328987   |   0 |   1 |   0 |   1 | 1.685 |   1 |
| 115 | 396 | 6.409 | 6.28505 | 0.123948   |   0 |   1 |   0 |   1 | 1.698 |   1 |
| 116 | 399 | 5.959 | 5.94106 | 0.0179412  |   0 |   1 |   0 |   1 | 1.544 |   1 |
| 117 | 402 | 5.387 | 5.5612  | 0.174195   |   0 |   0 |   0 |   1 | 1.678 |   1 |
| 118 | 404 | 5.921 | 5.77787 | 0.143134   |   0 |   0 |   0 |   1 | 1.775 |   1 |
| 119 | 406 | 4.357 | 4.48265 | 0.125653   |   0 |   0 |   0 |   0 | 1.886 |   0 |
| 120 | 407 | 4     | 4.42234 | 0.422343   |   0 |   0 |   0 |   0 | 1.859 |   0 |
| 121 | 408 | 4.585 | 4.95089 | 0.365889   |   0 |   0 |   0 |   0 | 1.773 |   1 |
| 122 | 410 | 5.137 | 5.37976 | 0.242763   |   0 |   0 |   0 |   0 | 1.965 |   1 |



labeled_formulas: H=F*I
H=(A*F)*I
H=(B*F)*I
H=(C*F)*I
H=(D*F)*I
H=(E*F)*I
H=(F*I)*J
H=(I-K)*G
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_13373___xlsx_501dd7d9137e3d8ea7717dd6decd67e2b28803e5.xlsx___line_207