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 |
|------:|---------:|----------:|---------:|---------:|-----------:|
| 43831 |  1.37667 |  1.08145  | 18987.9  | 18987.9  |  0.295215  |
| 43739 |  1.79333 |  1.59113  | 19222    | 19222    |  0.202204  |
| 43647 |  1.79667 |  1.68594  | 19121.1  | 19121.1  |  0.110729  |
| 43556 |  2.33333 |  2.12794  | 19021.9  | 19021.9  |  0.205397  |
| 43466 |  2.65333 |  2.48508  | 18927.3  | 18927.3  |  0.168251  |
| 43374 |  3.03333 |  2.80279  | 18783.5  | 18783.5  |  0.230546  |
| 43282 |  2.92667 |  2.66587  | 18732.7  | 18732.7  |  0.260794  |
| 43191 |  2.92    |  2.47703  | 18598.1  | 18598.1  |  0.442969  |
| 43101 |  2.76    |  2.16049  | 18438.3  | 18438.3  |  0.599508  |
| 43009 |  2.37    |  1.69435  | 18322.5  | 18322.5  |  0.675645  |
| 42917 |  2.24333 |  1.3627   | 18163.6  | 18163.6  |  0.880635  |
| 42826 |  2.26333 |  1.29762  | 18021    | 18021    |  0.965714  |
| 42736 |  2.44333 |  1.24435  | 17925.3  | 17925.3  |  1.19898   |
| 42644 |  2.13    |  1.00951  | 17824.2  | 17824.2  |  1.12049   |
| 42552 |  1.56333 |  0.728125 | 17735.1  | 17735.1  |  0.835208  |
| 42461 |  1.75333 |  0.77125  | 17639.4  | 17639.4  |  0.982083  |
| 42370 |  1.92    |  0.83623  | 17556.8  | 17556.8  |  1.08377   |
| 42278 |  2.19    |  0.838226 | 17468.9  | 17468.9  |  1.35177   |
| 42186 |  2.22    |  0.6925   | 17463.2  | 17463.2  |  1.5275    |
| 42095 |  2.16667 |  0.612656 | 17405.7  | 17405.7  |  1.55401   |
| 42005 |  1.96667 |  0.60459  | 17277.6  | 17277.6  |  1.36208   |
| 41913 |  2.28    |  0.536613 | 17143    | 17143    |  1.74339   |
| 41821 |  2.49667 |  0.515    | 17047.1  | 17047.1  |  1.98167   |
| 41730 |  2.62333 |  0.419524 | 16841.5  | 16841.5  |  2.20381   |
| 41640 |  2.76333 |  0.374754 | 16616.5  | 16616.5  |  2.38858   |
| 41548 |  2.74667 |  0.327258 | 16663.6  | 16663.6  |  2.41941   |
| 41456 |  2.71    |  0.365938 | 16531.7  | 16531.7  |  2.34406   |
| 41365 |  1.99667 |  0.270156 | 16403.2  | 16403.2  |  1.72651   |
| 41275 |  1.95    |  0.262833 | 16383    | 16383    |  1.68717   |
| 41183 |  1.70667 |  0.267541 | 16239.1  | 16239.1  |  1.43913   |
| 41091 |  1.64333 |  0.257778 | 16220.7  | 16220.7  |  1.38556   |
| 41000 |  1.82333 |  0.289531 | 16198.8  | 16198.8  |  1.5338    |
| 40909 |  2.03667 |  0.289516 | 16129.4  | 16129.4  |  1.74715   |
| 40817 |  2.04667 |  0.263607 | 16004.1  | 16004.1  |  1.78306   |
| 40725 |  2.42667 |  0.279219 | 15820.7  | 15820.7  |  2.14745   |
| 40634 |  3.21    |  0.561587 | 15825.1  | 15825.1  |  2.64841   |
| 40544 |  3.46    |  0.69371  | 15712.8  | 15712.8  |  2.76629   |
| 40452 |  2.86333 |  0.487097 | 15750.6  | 15750.6  |  2.37624   |
| 40360 |  2.78667 |  0.53875  | 15672    | 15672    |  2.24792   |
| 40269 |  3.49    |  0.873125 | 15557.3  | 15557.3  |  2.61688   |
| 40179 |  3.71667 |  0.917705 | 15415.1  | 15415.1  |  2.79896   |
| 40087 |  3.46    |  0.877903 | 15356.1  | 15356.1  |  2.5821    |
| 39995 |  3.51667 |  1.03     | 15189.2  | 15189.2  |  2.48667   |
| 39904 |  3.31333 |  1.01762  | 15134.1  | 15134.1  |  2.29571   |
| 39814 |  2.73667 |  0.904262 | 15155.9  | 15155.9  |  1.8324    |
| 39722 |  3.25333 |  1.21548  | 15328    | 15328    |  2.03785   |
| 39630 |  3.86333 |  2.36     | 15667    | 15667    |  1.50333   |
| 39539 |  3.88667 |  2.41641  | 15752.3  | 15752.3  |  1.47026   |
| 39448 |  3.66333 |  2.02934  | 15671.4  | 15671.4  |  1.63399   |
| 39356 |  4.26    |  3.48968  | 15762    | 15762    |  0.770323  |
| 39264 |  4.73    |  4.39079  | 15666.7  | 15666.7  |  0.339206  |
| 39173 |  4.84667 |  4.80375  | 15582.1  | 15582.1  |  0.0429167 |
| 39083 |  4.68    |  4.76048  | 15493.3  | 15493.3  | -0.0804839 |
| 38991 |  4.63    |  4.73758  | 15456.9  | 15456.9  | -0.107581  |
| 38899 |  4.89667 |  4.92905  | 15326.4  | 15326.4  | -0.032381  |
| 38808 |  5.07    |  4.99794  | 15302.7  | 15302.7  |  0.0720635 |
| 38718 |  4.57    |  4.60468  | 15267    | 15267    | -0.0346774 |
| 38626 |  4.49    |  4.36459  | 15066.6  | 15066.6  |  0.12541   |
| 38534 |  4.21333 |  3.95797  | 14972.1  | 14972.1  |  0.255365  |
| 38443 |  4.16    |  3.64594  | 14839.8  | 14839.8  |  0.514062  |
| 38353 |  4.29667 |  3.45492  | 14771.6  | 14771.6  |  0.841749  |
| 38261 |  4.17333 |  2.82242  | 14609.9  | 14609.9  |  1.35091   |
| 38169 |  4.30333 |  2.55656  | 14465    | 14465    |  1.74677   |
| 38078 |  4.6     |  2.45468  | 14329.5  | 14329.5  |  2.14532   |
| 37987 |  4.02    |  1.68661  | 14221.1  | 14221.1  |  2.33339   |
| 37895 |  4.28667 |  1.85629  | 14145.6  | 14145.6  |  2.43038   |
| 37803 |  4.23333 |  1.67828  | 13985.1  | 13985.1  |  2.55505   |
| 37712 |  3.62    |  1.42159  | 13751.5  | 13751.5  |  2.19841   |
| 37622 |  3.92    |  1.64902  | 13634.3  | 13634.3  |  2.27098   |
| 37530 |  4.00667 |  1.88968  | 13559    | 13559    |  2.11699   |
| 37438 |  4.26    |  2.23875  | 13538.1  | 13538.1  |  2.02125   |
| 37347 |  5.1     |  3.23391  | 13478.2  | 13478.2  |  1.86609   |
| 37257 |  5.07667 |  3.2005   | 13397    | 13397    |  1.87617   |
| 37165 |  4.77    |  2.8671   | 13280.9  | 13280.9  |  1.9029    |
| 37073 |  4.98    |  3.67623  | 13244.8  | 13244.8  |  1.30377   |
| 36982 |  5.27    |  4.19175  | 13300    | 13300    |  1.07825   |
| 36892 |  5.05    |  4.58016  | 13222.7  | 13222.7  |  0.469839  |
| 36800 |  5.56667 |  5.71903  | 13260.5  | 13260.5  | -0.152366  |
| 36708 |  5.89333 |  6.21698  | 13178.4  | 13178.4  | -0.323651  |
| 36617 |  6.17667 |  6.5727   | 13160.8  | 13160.8  | -0.396032  |
| 36526 |  6.48    |  6.52635  | 12924.2  | 12924.2  | -0.0463492 |
| 36434 |  6.14    |  5.94823  | 12877.6  | 12877.6  |  0.191774  |
| 36342 |  5.88333 |  5.63234  | 12662.4  | 12662.4  |  0.25099   |
| 36251 |  5.54    |  5.28422  | 12498.7  | 12498.7  |  0.255781  |
| 36161 |  4.98333 |  4.86164  | 12403.3  | 12403.3  |  0.121694  |
| 36069 |  4.67    |  4.37629  | 12287    | 12287    |  0.29371   |
| 35977 |  5.20333 |  5.13609  | 12091.6  | 12091.6  |  0.0672396 |
| 35886 |  5.59667 |  5.5581   | 11942    | 11942    |  0.0385714 |
| 35796 |  5.58667 |  5.44967  | 11832.5  | 11832.5  |  0.136995  |
| 35704 |  5.90667 |  5.73452  | 11715.4  | 11715.4  |  0.172151  |
| 35612 |  6.24333 |  5.90375  | 11615.6  | 11615.6  |  0.339583  |
| 35521 |  6.69667 |  6.27594  | 11472.1  | 11472.1  |  0.420729  |
| 35431 |  6.56333 |  6.04467  | 11284.6  | 11284.6  |  0.518667  |
| 35339 |  6.34333 |  5.80371  | 11212.2  | 11212.2  |  0.539624  |
| 35247 |  6.78    |  6.17594  | 11097    | 11097    |  0.604063  |
| 35156 |  6.72    |  6.11078  | 10998.3  | 10998.3  |  0.609219  |
| 35065 |  5.91    |  5.27016  | 10817.9  | 10817.9  |  0.639839  |
| 34973 |  5.89333 |  5.50306  | 10737.5  | 10737.5  |  0.390269  |
| 34881 |  6.32333 |  5.86159  | 10665.1  | 10665.1  |  0.461746  |
| 34790 |  6.62    |  6.13175  | 10575.1  | 10575.1  |  0.488254  |
| 34700 |  7.48333 |  7.11452  | 10543.6  | 10543.6  |  0.368817  |
| 34608 |  7.83667 |  7.16262  | 10506.4  | 10506.4  |  0.674044  |
| 34516 |  7.33333 |  6.23313  | 10387.4  | 10387.4  |  1.10021   |
| 34425 |  7.08333 |  5.82677  | 10327    | 10327    |  1.25656   |
| 34335 |  6.06667 |  4.55968  | 10189    | 10189    |  1.50699   |
| 34243 |  5.60667 |  4.085    | 10091    | 10091    |  1.52167   |
| 34151 |  5.61667 |  3.97391  |  9955.64 |  9955.64 |  1.64276   |
| 34060 |  5.99    |  3.99571  |  9908.35 |  9908.35 |  1.99429   |
| 33970 |  6.28    |  4.13311  |  9850.97 |  9850.97 |  2.14689   |
| 33878 |  6.74333 |  4.44468  |  9834.51 |  9834.51 |  2.29866   |
| 33786 |  6.61667 |  4.15078  |  9732.98 |  9732.98 |  2.46589   |
| 33695 |  7.37667 |  5.20317  |  9637.73 |  9637.73 |  2.17349   |
| 33604 |  7.30333 |  5.29387  |  9534.35 |  9534.35 |  2.00946   |
| 33512 |  7.34667 |  5.50371  |  9421.57 |  9421.57 |  1.84296   |
| 33420 |  7.94    |  6.52109  |  9388.84 |  9388.84 |  1.41891   |
| 33329 |  8.13    |  6.89406  |  9341.64 |  9341.64 |  1.23594   |
| 33239 |  8.01667 |  7.036    |  9269.37 |  9269.37 |  0.980667  |
| 33147 |  8.39667 |  7.60581  |  9312.94 |  9312.94 |  0.79086   |
| 33055 |  8.70333 |  8.09873  |  9398.5  |  9398.5  |  0.604603  |
| 32964 |  8.67667 |  8.57111  |  9392.25 |  9392.25 |  0.105556  |
| 32874 |  8.42333 |  8.36484  |  9358.29 |  9358.29 |  0.0584946 |
| 32782 |  7.90667 |  7.85177  |  9257.13 |  9257.13 |  0.0548925 |
| 32690 |  8.10667 |  8.08587  |  9238.92 |  9238.92 |  0.0207937 |
| 32599 |  8.77333 |  8.94313  |  9170.98 |  9170.98 | -0.169792  |
| 32509 |  9.20667 |  9.41836  |  9101.51 |  9101.51 | -0.211694  |
| 32417 |  8.95667 |  8.70918  |  9009.91 |  9009.91 |  0.247486  |
| 32325 |  9.1     |  8.46516  |  8891.43 |  8891.43 |  0.634844  |
| 32234 |  8.91    |  7.8773   |  8839.64 |  8839.64 |  1.0327    |
| 32143 |  8.41667 |  7.35161  |  8725.01 |  8725.01 |  1.06505   |
| 32051 |  9.12333 |  7.99     |  8680.16 |  8680.16 |  1.13333   |
| 31959 |  8.87667 |  7.84     |  8533.64 |  8533.64 |  1.03667   |
| 31868 |  8.34333 |  7.45     |  8460.23 |  8460.23 |  0.893333  |
| 31778 |  7.19333 |  6.35115  |  8369.93 |  8369.93 |  0.842186  |
| 31686 |  7.26333 |  6.27581  |  8308.02 |  8308.02 |  0.987527  |
| 31594 |  7.30667 |  6.44969  |  8263.64 |  8263.64 |  0.856979  |
| 31503 |  7.60333 |  6.97781  |  8185.3  |  8185.3  |  0.625521  |
| 31413 |  8.55667 |  7.77767  |  8148.6  |  8148.6  |  0.779     |
| 31321 |  9.76    |  8.53452  |  8073.24 |  8073.24 |  1.22548   |
| 31229 | 10.3367  |  8.89603  |  8013.67 |  8013.67 |  1.44063   |
| 31138 | 10.8133  |  9.40159  |  7893.14 |  7893.14 |  1.41175   |
| 31048 | 11.5833  | 10.275    |  7824.25 |  7824.25 |  1.30833   |
| 30956 | 11.7433  | 10.8387   |  7749.15 |  7749.15 |  0.904645  |
| 30864 | 12.8667  | 12.5129   |  7686.06 |  7686.06 |  0.35381   |
| 30773 | 13.2     | 12.3667   |  7612.67 |  7612.67 |  0.833333  |
| 30682 | 11.9433  | 10.9247   |  7483.37 |  7483.37 |  1.01866   |
| 30590 | 11.6867  | 10.6935   |  7339.89 |  7339.89 |  0.993167  |
| 30498 | 11.6267  | 10.858    |  7189.9  |  7189.9  |  0.768698  |
| 30407 | 10.5433  |  9.75603  |  7048.98 |  7048.98 |  0.787302  |
| 30317 | 10.5633  |  9.54063  |  6892.14 |  6892.14 |  1.0227    |
| 30225 | 10.6667  |  9.87607  |  6802.5  |  6802.5  |  0.790601  |
| 30133 | 13.1167  | 12.6298   |  6799.78 |  6799.78 |  0.486823  |
| 30042 | 13.93    | 14.1592   |  6825.88 |  6825.88 | -0.229206  |
| 29952 | 14.2933  | 14.5025   |  6794.88 |  6794.88 | -0.209126  |
| 29860 | 14.0867  | 13.9452   |  6902.1  |  6902.1  |  0.141421  |
| 29768 | 14.8467  | 16.0216   |  6978.14 |  6978.14 | -1.1749    |
| 29677 | 13.75    | 14.6897   |  6895.56 |  6895.56 | -0.939683  |
| 29587 | 12.96    | 13.5666   |  6947.04 |  6947.04 | -0.606557  |
| 29495 | 12.4233  | 13.2028   |  6813.53 |  6813.53 | -0.779454  |
| 29403 | 10.9533  | 10.3562   |  6688.79 |  6688.79 |  0.597083  |
| 29312 | 10.4767  | 10.2267   |  6696.75 |  6696.75 |  0.25      |
| 29221 | 11.9867  | 13.2337   |  6837.64 |  6837.64 | -1.24704   |
| 29129 | 10.4467  | 11.5564   |  6816.2  |  6816.2  | -1.10973   |
| 29037 |  9.10333 |  9.5319   |  6799.2  |  6799.2  | -0.428571  |
| 28946 |  9.11333 |  9.59129  |  6749.06 |  6749.06 | -0.477957  |
| 28856 |  9.10667 |  9.79339  |  6741.85 |  6741.85 | -0.68672   |
| 28764 |  8.82    |  9.32344  |  6729.76 |  6729.76 | -0.503443  |
| 28672 |  8.49    |  8.46873  |  6640.5  |  6640.5  |  0.0212698 |
| 28581 |  8.32    |  8.00429  |  6574.39 |  6574.39 |  0.315714  |
| 28491 |  8.01    |  7.54131  |  6329.79 |  6329.79 |  0.468689  |
| 28399 |  7.59667 |  7.14233  |  6309.65 |  6309.65 |  0.454333  |
| 28307 |  7.35667 |  6.54413  |  6309.51 |  6309.51 |  0.81254   |
| 28216 |  7.37    |  6.11778  |  6197.69 |  6197.69 |  1.25222   |
| 28126 |  7.35333 |  6.02476  |  6079.49 |  6079.49 |  1.32857   |



label: F=B-C
labeled_formulas: F=B-C
output: {"Arithmetic-Relationship": ["F=B-C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_86629___xlsx_6d102fcb114ba971e429c64f2c8ecfe1fd19f470.xlsx___line_372