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 |
|------:|-----------------:|--------:|----------:|--------:|-----------------:|
| 40969 |      3e+06       | 30018.4 | 9375      | 20643.4 |      2.97936e+06 |
| 41000 |      2.97936e+06 | 30018.4 | 9310.49   | 20707.9 |      2.95865e+06 |
| 41030 |      2.95865e+06 | 30018.4 | 9245.78   | 20772.6 |      2.93788e+06 |
| 41061 |      2.93788e+06 | 30018.4 | 9180.86   | 20837.5 |      2.91704e+06 |
| 41091 |      2.91704e+06 | 30018.4 | 9115.75   | 20902.6 |      2.89614e+06 |
| 41122 |      2.89614e+06 | 30018.4 | 9050.43   | 20967.9 |      2.87517e+06 |
| 41153 |      2.87517e+06 | 30018.4 | 8984.9    | 21033.5 |      2.85413e+06 |
| 41183 |      2.85413e+06 | 30018.4 | 8919.17   | 21099.2 |      2.83304e+06 |
| 41214 |      2.83304e+06 | 30018.4 | 8853.24   | 21165.1 |      2.81187e+06 |
| 41244 |      2.81187e+06 | 30018.4 | 8787.09   | 21231.3 |      2.79064e+06 |
| 41275 |      2.79064e+06 | 30018.4 | 8720.75   | 21297.6 |      2.76934e+06 |
| 41306 |      2.76934e+06 | 30018.4 | 8654.19   | 21364.2 |      2.74798e+06 |
| 41334 |      2.74798e+06 | 30018.4 | 8587.43   | 21430.9 |      2.72655e+06 |
| 41365 |      2.72655e+06 | 30018.4 | 8520.46   | 21497.9 |      2.70505e+06 |
| 41395 |      2.70505e+06 | 30018.4 | 8453.28   | 21565.1 |      2.68348e+06 |
| 41426 |      2.68348e+06 | 30018.4 | 8385.89   | 21632.5 |      2.66185e+06 |
| 41456 |      2.66185e+06 | 30018.4 | 8318.28   | 21700.1 |      2.64015e+06 |
| 41487 |      2.64015e+06 | 30018.4 | 8250.47   | 21767.9 |      2.61838e+06 |
| 41518 |      2.61838e+06 | 30018.4 | 8182.45   | 21835.9 |      2.59655e+06 |
| 41548 |      2.59655e+06 | 30018.4 | 8114.21   | 21904.2 |      2.57464e+06 |
| 41579 |      2.57464e+06 | 30018.4 | 8045.76   | 21972.6 |      2.55267e+06 |
| 41609 |      2.55267e+06 | 30018.4 | 7977.09   | 22041.3 |      2.53063e+06 |
| 41640 |      2.53063e+06 | 30018.4 | 7908.21   | 22110.2 |      2.50852e+06 |
| 41671 |      2.50852e+06 | 30018.4 | 7839.12   | 22179.3 |      2.48634e+06 |
| 41699 |      2.48634e+06 | 30018.4 | 7769.81   | 22248.6 |      2.46409e+06 |
| 41730 |      2.46409e+06 | 30018.4 | 7700.28   | 22318.1 |      2.44177e+06 |
| 41760 |      2.44177e+06 | 30018.4 | 7630.54   | 22387.8 |      2.41938e+06 |
| 41791 |      2.41938e+06 | 30018.4 | 7560.58   | 22457.8 |      2.39693e+06 |
| 41821 |      2.39693e+06 | 30018.4 | 7490.4    | 22528   |      2.3744e+06  |
| 41852 |      2.3744e+06  | 30018.4 | 7420      | 22598.4 |      2.3518e+06  |
| 41883 |      2.3518e+06  | 30018.4 | 7349.38   | 22669   |      2.32913e+06 |
| 41913 |      2.32913e+06 | 30018.4 | 7278.54   | 22739.8 |      2.30639e+06 |
| 41944 |      2.30639e+06 | 30018.4 | 7207.47   | 22810.9 |      2.28358e+06 |
| 41974 |      2.28358e+06 | 30018.4 | 7136.19   | 22882.2 |      2.2607e+06  |
| 42005 |      2.2607e+06  | 30018.4 | 7064.68   | 22953.7 |      2.23775e+06 |
| 42036 |      2.23775e+06 | 30018.4 | 6992.95   | 23025.4 |      2.21472e+06 |
| 42064 |      2.21472e+06 | 30018.4 | 6921      | 23097.4 |      2.19162e+06 |
| 42095 |      2.19162e+06 | 30018.4 | 6848.82   | 23169.6 |      2.16845e+06 |
| 42125 |      2.16845e+06 | 30018.4 | 6776.41   | 23242   |      2.14521e+06 |
| 42156 |      2.14521e+06 | 30018.4 | 6703.78   | 23314.6 |      2.1219e+06  |
| 42186 |      2.1219e+06  | 30018.4 | 6630.93   | 23387.4 |      2.09851e+06 |
| 42217 |      2.09851e+06 | 30018.4 | 6557.84   | 23460.5 |      2.07505e+06 |
| 42248 |      2.07505e+06 | 30018.4 | 6484.53   | 23533.8 |      2.05151e+06 |
| 42278 |      2.05151e+06 | 30018.4 | 6410.98   | 23607.4 |      2.02791e+06 |
| 42309 |      2.02791e+06 | 30018.4 | 6337.21   | 23681.2 |      2.00423e+06 |
| 42339 |      2.00423e+06 | 30018.4 | 6263.21   | 23755.2 |      1.98047e+06 |
| 42370 |      1.98047e+06 | 30018.4 | 6188.97   | 23829.4 |      1.95664e+06 |
| 42401 |      1.95664e+06 | 30018.4 | 6114.5    | 23903.9 |      1.93274e+06 |
| 42430 |      1.93274e+06 | 30018.4 | 6039.8    | 23978.6 |      1.90876e+06 |
| 42461 |      1.90876e+06 | 30018.4 | 5964.87   | 24053.5 |      1.88471e+06 |
| 42491 |      1.88471e+06 | 30018.4 | 5889.7    | 24128.7 |      1.86058e+06 |
| 42522 |      1.86058e+06 | 30018.4 | 5814.3    | 24204.1 |      1.83637e+06 |
| 42552 |      1.83637e+06 | 30018.4 | 5738.66   | 24279.7 |      1.81209e+06 |
| 42583 |      1.81209e+06 | 30018.4 | 5662.79   | 24355.6 |      1.78774e+06 |
| 42614 |      1.78774e+06 | 30018.4 | 5586.68   | 24431.7 |      1.76331e+06 |
| 42644 |      1.76331e+06 | 30018.4 | 5510.33   | 24508   |      1.7388e+06  |
| 42675 |      1.7388e+06  | 30018.4 | 5433.74   | 24584.6 |      1.71421e+06 |
| 42705 |      1.71421e+06 | 30018.4 | 5356.92   | 24661.5 |      1.68955e+06 |
| 42736 |      1.68955e+06 | 30018.4 | 5279.85   | 24738.5 |      1.66481e+06 |
| 42767 |      1.66481e+06 | 30018.4 | 5202.54   | 24815.8 |      1.64e+06    |
| 42795 |      1.64e+06    | 30018.4 | 5124.99   | 24893.4 |      1.6151e+06  |
| 42826 |      1.6151e+06  | 30018.4 | 5047.2    | 24971.2 |      1.59013e+06 |
| 42856 |      1.59013e+06 | 30018.4 | 4969.16   | 25049.2 |      1.56508e+06 |
| 42887 |      1.56508e+06 | 30018.4 | 4890.89   | 25127.5 |      1.53996e+06 |
| 42917 |      1.53996e+06 | 30018.4 | 4812.36   | 25206   |      1.51475e+06 |
| 42948 |      1.51475e+06 | 30018.4 | 4733.59   | 25284.8 |      1.48947e+06 |
| 42979 |      1.48947e+06 | 30018.4 | 4654.58   | 25363.8 |      1.4641e+06  |
| 43009 |      1.4641e+06  | 30018.4 | 4575.32   | 25443.1 |      1.43866e+06 |
| 43040 |      1.43866e+06 | 30018.4 | 4495.81   | 25522.6 |      1.41314e+06 |
| 43070 |      1.41314e+06 | 30018.4 | 4416.05   | 25602.3 |      1.38753e+06 |
| 43101 |      1.38753e+06 | 30018.4 | 4336.04   | 25682.3 |      1.36185e+06 |
| 43132 |      1.36185e+06 | 30018.4 | 4255.78   | 25762.6 |      1.33609e+06 |
| 43160 |      1.33609e+06 | 30018.4 | 4175.28   | 25843.1 |      1.31025e+06 |
| 43191 |      1.31025e+06 | 30018.4 | 4094.52   | 25923.9 |      1.28432e+06 |
| 43221 |      1.28432e+06 | 30018.4 | 4013.5    | 26004.9 |      1.25832e+06 |
| 43252 |      1.25832e+06 | 30018.4 | 3932.24   | 26086.1 |      1.23223e+06 |
| 43282 |      1.23223e+06 | 30018.4 | 3850.72   | 26167.7 |      1.20606e+06 |
| 43313 |      1.20606e+06 | 30018.4 | 3768.95   | 26249.4 |      1.17981e+06 |
| 43344 |      1.17981e+06 | 30018.4 | 3686.92   | 26331.5 |      1.15348e+06 |
| 43374 |      1.15348e+06 | 30018.4 | 3604.63   | 26413.7 |      1.12707e+06 |
| 43405 |      1.12707e+06 | 30018.4 | 3522.09   | 26496.3 |      1.10057e+06 |
| 43435 |      1.10057e+06 | 30018.4 | 3439.29   | 26579.1 |      1.07399e+06 |
| 43466 |      1.07399e+06 | 30018.4 | 3356.23   | 26662.1 |      1.04733e+06 |
| 43497 |      1.04733e+06 | 30018.4 | 3272.91   | 26745.5 |      1.02059e+06 |
| 43525 |      1.02059e+06 | 30018.4 | 3189.33   | 26829   | 993756           |
| 43556 | 993756           | 30018.4 | 3105.49   | 26912.9 | 966843           |
| 43586 | 966843           | 30018.4 | 3021.39   | 26997   | 939846           |
| 43617 | 939846           | 30018.4 | 2937.02   | 27081.4 | 912765           |
| 43647 | 912765           | 30018.4 | 2852.39   | 27166   | 885599           |
| 43678 | 885599           | 30018.4 | 2767.5    | 27250.9 | 858348           |
| 43709 | 858348           | 30018.4 | 2682.34   | 27336   | 831012           |
| 43739 | 831012           | 30018.4 | 2596.91   | 27421.5 | 803591           |
| 43770 | 803591           | 30018.4 | 2511.22   | 27507.2 | 776083           |
| 43800 | 776083           | 30018.4 | 2425.26   | 27593.1 | 748490           |
| 43831 | 748490           | 30018.4 | 2339.03   | 27679.3 | 720811           |
| 43862 | 720811           | 30018.4 | 2252.53   | 27765.8 | 693045           |
| 43891 | 693045           | 30018.4 | 2165.77   | 27852.6 | 665193           |
| 43922 | 665193           | 30018.4 | 2078.73   | 27939.6 | 637253           |
| 43952 | 637253           | 30018.4 | 1991.42   | 28027   | 609226           |
| 43983 | 609226           | 30018.4 | 1903.83   | 28114.5 | 581111           |
| 44013 | 581111           | 30018.4 | 1815.97   | 28202.4 | 552909           |
| 44044 | 552909           | 30018.4 | 1727.84   | 28290.5 | 524618           |
| 44075 | 524618           | 30018.4 | 1639.43   | 28378.9 | 496239           |
| 44105 | 496239           | 30018.4 | 1550.75   | 28467.6 | 467772           |
| 44136 | 467772           | 30018.4 | 1461.79   | 28556.6 | 439215           |
| 44166 | 439215           | 30018.4 | 1372.55   | 28645.8 | 410569           |
| 44197 | 410569           | 30018.4 | 1283.03   | 28735.3 | 381834           |
| 44228 | 381834           | 30018.4 | 1193.23   | 28825.1 | 353009           |
| 44256 | 353009           | 30018.4 | 1103.15   | 28915.2 | 324094           |
| 44287 | 324094           | 30018.4 | 1012.79   | 29005.6 | 295088           |
| 44317 | 295088           | 30018.4 |  922.151  | 29096.2 | 265992           |
| 44348 | 265992           | 30018.4 |  831.225  | 29187.1 | 236805           |
| 44378 | 236805           | 30018.4 |  740.015  | 29278.4 | 207526           |
| 44409 | 207526           | 30018.4 |  648.52   | 29369.9 | 178157           |
| 44440 | 178157           | 30018.4 |  556.739  | 29461.6 | 148695           |
| 44470 | 148695           | 30018.4 |  464.672  | 29553.7 | 119141           |
| 44501 | 119141           | 30018.4 |  372.316  | 29646.1 |  89495.2         |
| 44531 |  89495.2         | 30018.4 |  279.672  | 29738.7 |  59756.5         |
| 44562 |  59756.5         | 30018.4 |  186.739  | 29831.6 |  29924.9         |
| 44593 |  29924.9         | 30018.4 |   93.5152 | 29924.9 |      1.51704e-09 |



label: E=C-D
F=B-E
labeled_formulas: E=C-D
F=B-E
output: {"Arithmetic-Relationship": ["E=C-D", "F=B-E"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_344230___xlsx_9c4198107968e6a9ab5378fb887d83f70f6f3856.xlsx___line_658