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 |
|------:|--------:|-----:|---------:|--------:|
| 33604 | 2.5     | 3.7  | 0.303278 | 5.89672 |
| 33695 | 2.55    | 3.9  | 0.319884 | 6.13012 |
| 33786 | 2.6     | 3.75 | 0.341843 | 6.00816 |
| 33878 | 2.65    | 3.6  | 0.350407 | 5.89959 |
| 33970 | 2.7     | 3.5  | 0.365042 | 5.83496 |
| 34060 | 2.6875  | 3.7  | 0.384301 | 6.0032  |
| 34151 | 2.675   | 3.45 | 0.403713 | 5.72129 |
| 34243 | 2.6625  | 3.45 | 0.418757 | 5.69374 |
| 34335 | 2.65    | 3.45 | 0.428215 | 5.67178 |
| 34425 | 2.6625  | 3.5  | 0.430563 | 5.73194 |
| 34516 | 2.675   | 3.5  | 0.436944 | 5.73806 |
| 34608 | 2.6875  | 3.5  | 0.437288 | 5.75021 |
| 34700 | 2.7     | 3.3  | 0.449306 | 5.55069 |
| 34790 | 2.6     | 3.35 | 0.457405 | 5.49259 |
| 34881 | 2.5     | 3.2  | 0.466    | 5.234   |
| 34973 | 2.4     | 3    | 0.480467 | 4.91953 |
| 35065 | 2.3     | 3    | 0.498231 | 4.80177 |
| 35156 | 2.35    | 3    | 0.504574 | 4.84543 |
| 35247 | 2.4     | 3    | 0.512323 | 4.88768 |
| 35339 | 2.45    | 3    | 0.506833 | 4.94317 |
| 35431 | 2.5     | 3    | 0.51436  | 4.98564 |
| 35521 | 2.5     | 2.85 | 0.518667 | 4.83133 |
| 35612 | 2.5     | 3    | 0.518466 | 4.98153 |
| 35704 | 2.5     | 2.65 | 0.515044 | 4.63496 |
| 35796 | 2.5     | 2.6  | 0.508445 | 4.59155 |
| 35886 | 2.5     | 2.5  | 0.499003 | 4.501   |
| 35977 | 2.5     | 2.5  | 0.491586 | 4.50841 |
| 36069 | 2.5     | 2.5  | 0.48699  | 4.51301 |
| 36161 | 2.5     | 2.3  | 0.487637 | 4.31236 |
| 36251 | 2.6375  | 2.5  | 0.497761 | 4.63974 |
| 36342 | 2.775   | 2.5  | 0.501972 | 4.77303 |
| 36434 | 2.9125  | 2.5  | 0.50553  | 4.90697 |
| 36526 | 3.05    | 2.5  | 0.518315 | 5.03168 |
| 36617 | 3.1125  | 2.5  | 0.523371 | 5.08913 |
| 36708 | 3.175   | 2.5  | 0.519949 | 5.15505 |
| 36800 | 3.2375  | 2.5  | 0.521833 | 5.21567 |
| 36892 | 3.3     | 2.5  | 0.507924 | 5.29208 |
| 36982 | 3.225   | 2.5  | 0.497231 | 5.22777 |
| 37073 | 3.15    | 2.5  | 0.494077 | 5.15592 |
| 37165 | 3.075   | 2.55 | 0.503951 | 5.12105 |
| 37257 | 3       | 2.5  | 0.502958 | 4.99704 |
| 37347 | 3.05    | 2.5  | 0.510674 | 5.03933 |
| 37438 | 3.1     | 2.5  | 0.511989 | 5.08801 |
| 37530 | 3.15    | 2.45 | 0.506929 | 5.09307 |
| 37622 | 3.2     | 2.5  | 0.50676  | 5.19324 |
| 37712 | 3.25    | 2.5  | 0.498129 | 5.25187 |
| 37803 | 3.3     | 2.5  | 0.496675 | 5.30333 |
| 37895 | 3.35    | 2.5  | 0.498819 | 5.35118 |
| 37987 | 3.4     | 2.5  | 0.496397 | 5.4036  |
| 38078 | 3.375   | 2.5  | 0.489359 | 5.38564 |
| 38169 | 3.35    | 2.5  | 0.486651 | 5.36335 |
| 38261 | 3.325   | 2.5  | 0.476155 | 5.34884 |
| 38353 | 3.3     | 2.45 | 0.468105 | 5.28189 |
| 38443 | 3.275   | 2.5  | 0.461787 | 5.31321 |
| 38534 | 3.25    | 2.5  | 0.455911 | 5.29409 |
| 38626 | 3.225   | 2.5  | 0.442086 | 5.28291 |
| 38718 | 3.2     | 2.5  | 0.419795 | 5.28021 |
| 38808 | 3.15    | 2.5  | 0.412638 | 5.23736 |
| 38899 | 3.1     | 2.5  | 0.407222 | 5.19278 |
| 38991 | 3.05    | 2.5  | 0.395125 | 5.15488 |
| 39083 | 3       | 2.35 | 0.386556 | 4.96344 |
| 39173 | 2.9375  | 2.4  | 0.379933 | 4.95757 |
| 39264 | 2.875   | 2.4  | 0.369701 | 4.9053  |
| 39356 | 2.8125  | 2.4  | 0.36191  | 4.85059 |
| 39448 | 2.75    | 2.5  | 0.35914  | 4.89086 |
| 39539 | 2.7025  | 2.5  | 0.36165  | 4.84085 |
| 39630 | 2.655   | 2.5  | 0.352107 | 4.80289 |
| 39722 | 2.6075  | 2.5  | 0.340355 | 4.76714 |
| 39814 | 2.56    | 2.4  | 0.310566 | 4.64943 |
| 39904 | 2.595   | 2.5  | 0.307953 | 4.78705 |
| 39995 | 2.63    | 2.5  | 0.297925 | 4.83207 |
| 40087 | 2.665   | 2.26 | 0.294525 | 4.63048 |
| 40179 | 2.7     | 2.39 | 0.286109 | 4.80389 |
| 40269 | 2.735   | 2.4  | 0.282718 | 4.85228 |
| 40360 | 2.77    | 2.3  | 0.278411 | 4.79159 |
| 40452 | 2.805   | 2.2  | 0.277174 | 4.72783 |
| 40544 | 2.835   | 2.3  | 0.266699 | 4.8683  |
| 40634 | 2.79    | 2.4  | 0.27346  | 4.91654 |
| 40725 | 2.74    | 2.4  | 0.27521  | 4.86479 |
| 40817 | 2.69    | 2.5  | 0.255189 | 4.93481 |
| 40909 | 2.64    | 2.3  | 0.243159 | 4.69684 |
| 41000 | 2.605   | 2.48 | 0.235277 | 4.84972 |
| 41091 | 2.57    | 2.35 | 0.223611 | 4.69639 |
| 41183 | 2.535   | 2.3  | 0.222193 | 4.61281 |
| 41275 | 2.5     | 2.3  | 0.214597 | 4.5854  |
| 41365 | 2.525   | 2.3  | 0.207181 | 4.61782 |
| 41456 | 2.55    | 2.21 | 0.201087 | 4.55891 |
| 41548 | 2.575   | 2.3  | 0.199042 | 4.67596 |
| 41640 | 2.6     | 2.3  | 0.196105 | 4.70389 |
| 41730 | 2.575   | 2.25 | 0.191614 | 4.63339 |
| 41821 | 2.55    | 2.2  | 0.186764 | 4.56324 |
| 41913 | 2.525   | 2.2  | 0.196884 | 4.52812 |
| 42005 | 2.5     | 2.1  | 0.196233 | 4.40377 |
| 42095 | 2.445   | 2.14 | 0.199306 | 4.38569 |
| 42186 | 2.39    | 2.15 | 0.196732 | 4.34327 |
| 42278 | 2.335   | 2.15 | 0.201179 | 4.28382 |
| 42370 | 2.275   | 2.12 | 0.21095  | 4.18405 |
| 42461 | 2.3225  | 2.2  | 0.214513 | 4.30799 |
| 42552 | 2.365   | 2.15 | 0.218602 | 4.2964  |
| 42644 | 2.4075  | 2.22 | 0.226999 | 4.4005  |
| 42736 | 2.45    | 2.3  | 0.227378 | 4.52262 |
| 42826 | 2.375   | 2.3  | 0.224914 | 4.45009 |
| 42917 | 2.3     | 2.25 | 0.228679 | 4.32132 |
| 43009 | 2.225   | 2.2  | 0.236752 | 4.18825 |
| 43101 | 2.15    | 2.25 | 0.231402 | 4.1686  |
| 43191 | 2.10875 | 2.3  | 0.228604 | 4.18015 |
| 43282 | 2.0675  | 2.2  | 0.230072 | 4.03743 |
| 43374 | 2.02625 | 2.21 | 0.227424 | 4.00883 |
| 43466 | 1.985   | 2.2  | 0.244459 | 3.94054 |
| 43556 | 1.98875 | 2.2  | 0.233091 | 3.95566 |
| 43647 | 1.9925  | 2.2  | 0.230975 | 3.96153 |
| 43739 | 1.99625 | 2.2  | 0.223002 | 3.97325 |
| 43831 | 2       | 2.2  | 0.21693  | 3.98307 |
| 43922 | 2.0625  | 2.14 | 0.211889 | 3.99061 |
| 44013 | 2.125   | 2.03 | 0.214004 | 3.941   |
| 44105 | 2.1875  | 2.12 | 0.218225 | 4.08928 |
| 44197 | 2.25    | 2.2  | 0.222468 | 4.22753 |
| 44287 | 2.25    | 2.3  | 0.214627 | 4.33537 |
| 44378 | 2.25    | 2.44 | 0.204854 | 4.48515 |



label: E=B+C-D
labeled_formulas: E=B+C-D
output: {"Arithmetic-Relationship": ["E=B+C-D"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_523199___xlsx_cc14c6b5a891a8ec2d9583bf063b9147814a03c8.xlsx___line_600