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 |
|------:|------:|-------:|-------:|-------:|------------:|
| 41306 | 41275 | 65.995 | 64.756 |  1.239 |  0.0187741  |
| 41334 | 41306 | 66.204 | 64.758 |  1.446 |  0.0218416  |
| 41365 | 41334 | 65.235 | 64.549 |  0.686 |  0.0105158  |
| 41395 | 41365 | 64.148 | 64.228 | -0.08  | -0.00124712 |
| 41426 | 41395 | 63.151 | 63.772 | -0.621 | -0.00983357 |
| 41456 | 41426 | 61.781 | 63.045 | -1.264 | -0.0204594  |
| 41487 | 41456 | 62.666 | 62.54  |  0.126 |  0.00201066 |
| 41518 | 41487 | 63.293 | 62.213 |  1.08  |  0.0170635  |
| 41548 | 41518 | 61.986 | 61.483 |  0.503 |  0.00811474 |
| 41579 | 41548 | 60.119 | 60.52  | -0.401 | -0.0066701  |
| 41609 | 41579 | 58.805 | 59.716 | -0.911 | -0.0154919  |
| 41640 | 41609 | 58.099 | 59.034 | -0.935 | -0.0160932  |
| 41671 | 41640 | 59.829 | 58.689 |  1.14  |  0.0190543  |
| 41699 | 41671 | 59.277 | 57.961 |  1.316 |  0.0222009  |
| 41730 | 41699 | 57.696 | 57.071 |  0.625 |  0.0108326  |
| 41760 | 41730 | 56.047 | 56.187 | -0.14  | -0.0024979  |
| 41791 | 41760 | 54.722 | 55.34  | -0.618 | -0.0112934  |
| 41821 | 41791 | 52.892 | 54.043 | -1.151 | -0.0217613  |
| 41852 | 41821 | 52.628 | 52.415 |  0.213 |  0.00404728 |
| 41883 | 41852 | 53.258 | 52.266 |  0.992 |  0.0186263  |
| 41913 | 41883 | 52.377 | 51.899 |  0.478 |  0.00912614 |
| 41944 | 41913 | 51.398 | 51.674 | -0.276 | -0.00536986 |
| 41974 | 41944 | 50.019 | 50.764 | -0.745 | -0.0148943  |
| 42005 | 41974 | 49.064 | 49.833 | -0.769 | -0.0156734  |
| 42036 | 42005 | 49.577 | 48.674 |  0.903 |  0.0182141  |
| 42064 | 42036 | 47.737 | 46.622 |  1.115 |  0.0233571  |
| 42095 | 42064 | 45.885 | 45.303 |  0.582 |  0.0126839  |
| 42125 | 42095 | 44.172 | 44.27  | -0.098 | -0.0022186  |
| 42156 | 42125 | 42.809 | 43.434 | -0.625 | -0.0145997  |
| 42186 | 42156 | 42.49  | 43.44  | -0.95  | -0.0223582  |
| 42217 | 42186 | 43.019 | 42.703 |  0.316 |  0.00734559 |
| 42248 | 42217 | 42.763 | 41.795 |  0.968 |  0.0226364  |
| 42278 | 42248 | 41.148 | 40.73  |  0.418 |  0.0101585  |
| 42309 | 42278 | 39.756 | 40.05  | -0.294 | -0.00739511 |
| 42339 | 42309 | 38.689 | 39.457 | -0.768 | -0.0198506  |
| 42370 | 42339 | 38.246 | 39.031 | -0.785 | -0.020525   |
| 42401 | 42370 | 39.32  | 38.718 |  0.602 |  0.0153103  |
| 42430 | 42401 | 39.489 | 38.519 |  0.97  |  0.0245638  |
| 42461 | 42430 | 39.01  | 38.377 |  0.633 |  0.0162266  |
| 42491 | 42461 | 37.494 | 37.601 | -0.107 | -0.00285379 |
| 42522 | 42491 | 36.294 | 36.904 | -0.61  | -0.0168072  |
| 42552 | 42522 | 35.682 | 36.565 | -0.883 | -0.0247464  |
| 42583 | 42552 | 36.329 | 36.138 |  0.191 |  0.00525751 |
| 42614 | 42583 | 36.073 | 35.256 |  0.817 |  0.0226485  |
| 42644 | 42614 | 35.173 | 34.778 |  0.395 |  0.0112302  |
| 42675 | 42644 | 33.668 | 33.944 | -0.276 | -0.0081977  |
| 42705 | 42675 | 32.763 | 33.461 | -0.698 | -0.0213045  |
| 42736 | 42705 | 31.995 | 32.688 | -0.693 | -0.0216596  |
| 42767 | 42736 | 32.447 | 32.091 |  0.356 |  0.0109717  |
| 42795 | 42767 | 32.623 | 31.76  |  0.863 |  0.0264537  |
| 42826 | 42795 | 32.251 | 31.583 |  0.668 |  0.0207125  |
| 42856 | 42826 | 31.412 | 31.324 |  0.088 |  0.00280148 |
| 42887 | 42856 | 30.468 | 30.948 | -0.48  | -0.0157542  |
| 42917 | 42887 | 29.806 | 30.592 | -0.786 | -0.0263705  |
| 42948 | 42917 | 30.336 | 30.254 |  0.082 |  0.00270306 |
| 42979 | 42948 | 30.788 | 30.035 |  0.753 |  0.0244576  |
| 43009 | 42979 | 29.712 | 29.341 |  0.371 |  0.0124865  |
| 43040 | 43009 | 29.014 | 29.293 | -0.279 | -0.00961605 |
| 43070 | 43040 | 28.27  | 28.965 | -0.695 | -0.0245844  |
| 43101 | 43070 | 28.556 | 29.197 | -0.641 | -0.0224471  |
| 43132 | 43101 | 29.023 | 28.76  |  0.263 |  0.00906178 |
| 43160 | 43132 | 29.559 | 28.728 |  0.831 |  0.0281133  |
| 43191 | 43160 | 29.369 | 28.68  |  0.689 |  0.0234601  |
| 43221 | 43191 | 29.149 | 28.821 |  0.328 |  0.0112525  |
| 43252 | 43221 | 28.556 | 28.927 | -0.371 | -0.012992   |
| 43282 | 43252 | 27.983 | 28.76  | -0.777 | -0.0277669  |
| 43313 | 43282 | 28.336 | 28.414 | -0.078 | -0.00275268 |
| 43344 | 43313 | 28.989 | 28.362 |  0.627 |  0.0216289  |
| 43374 | 43344 | 29.42  | 29.069 |  0.351 |  0.0119307  |
| 43405 | 43374 | 29.056 | 29.316 | -0.26  | -0.00894824 |
| 43435 | 43405 | 28.853 | 29.504 | -0.651 | -0.0225626  |
| 43466 | 43435 | 28.776 | 29.375 | -0.599 | -0.020816   |
| 43497 | 43466 | 29.512 | 29.253 |  0.259 |  0.00877609 |
| 43525 | 43497 | 29.696 | 29.037 |  0.659 |  0.0221915  |
| 43556 | 43525 | 29.831 | 29.39  |  0.441 |  0.0147833  |
| 43586 | 43556 | 29.8   | 29.6   |  0.2   |  0.00671141 |
| 43617 | 43586 | 29.3   | 29.9   | -0.6   | -0.0204778  |
| 43647 | 43617 | 29.4   | 30     | -0.6   | -0.0204082  |
| 43678 | 43647 | 29.722 | 29.784 | -0.062 | -0.002086   |
| 43709 | 43678 | 29.7   | 29.3   |  0.4   |  0.013468   |
| 43739 | 43709 | 29.7   | 29.7   |  0     |  0          |
| 43770 | 43739 | 30.559 | 30.655 | -0.096 | -0.00314146 |
| 43800 | 43770 | 29.781 | 30.096 | -0.315 | -0.0105772  |
| 43831 | 43800 | 29.997 | 30.249 | -0.252 | -0.00840084 |
| 43862 | 43831 | 29.73  | 29.614 |  0.116 |  0.00390178 |
| 43891 | 43862 | 29.934 | 29.642 |  0.292 |  0.00975479 |
| 43922 | 43891 | 30.226 | 29.774 |  0.452 |  0.014954   |
| 43952 | 43922 | 56.528 | 56.604 | -0.076 | -0.00134447 |
| 43983 | 43952 | 63.982 | 64.255 | -0.273 | -0.00426683 |
| 44013 | 43983 | 62.045 | 62.277 | -0.232 | -0.00373922 |
| 44044 | 44013 | 62.073 | 61.977 |  0.096 |  0.00154657 |
| 44075 | 44044 | 62.531 | 61.954 |  0.577 |  0.00922742 |
| 44105 | 44075 | 60.902 | 60.63  |  0.272 |  0.00446619 |
| 44136 | 44105 | 59.219 | 59.477 | -0.258 | -0.00435671 |
| 44166 | 44136 | 58.843 | 59.147 | -0.304 | -0.00516629 |
| 44197 | 44166 | 57.208 | 57.683 | -0.475 | -0.00830303 |
| 44228 | 44197 | 55.897 | 56.685 | -0.788 | -0.0140974  |



label: E=C-D
F=E/C
labeled_formulas: E=C-D
F=E/C
output: {"Arithmetic-Relationship": ["E=C-D", "F=E/C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_573964___xlsx_c283e1fb758909f18f4dfba9145e9b811bb75b94.xlsx___line_608