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 |
|------:|----:|---------:|----:|---------:|----:|---------:|-----------------:|----------:|
| 37987 |  80 | 102313   |  24 | 0.3      |  21 |  4054.33 |      1.20976e+06 |   298.386 |
| 38018 | 109 | 132831   |  36 | 0.330275 |  33 | 13638.4  |      4.17041e+06 |   305.784 |
| 38047 |  84 | 126328   |  35 | 0.416667 |  37 | 13838.6  |      2.77381e+06 |   200.44  |
| 38078 |  21 |  27689.5 |   9 | 0.428571 |   9 |  2540.44 | 686310           |   270.154 |
| 38108 |  72 |  96587.9 |  28 | 0.388889 |  31 | 14771.1  |      3.74103e+06 |   253.267 |
| 38139 | 101 | 124977   |  25 | 0.247525 |  24 |  5544.19 |      1.94283e+06 |   350.427 |
| 38169 | 111 | 140324   |  31 | 0.279279 |  32 |  5817.56 |      2.04465e+06 |   351.462 |
| 38200 |  50 |  43044.9 |  26 | 0.52     |  27 |  6881.45 |      1.98965e+06 |   289.133 |
| 38231 | 150 | 225055   |  43 | 0.286667 |  48 | 10518.3  |      3.19326e+06 |   303.591 |
| 38261 | 136 | 199371   |  56 | 0.411765 |  75 | 16777.1  |      8.51811e+06 |   507.723 |
| 38292 |  74 |  81727.6 |  30 | 0.405405 |  33 |  8058.37 |      1.84215e+06 |   228.601 |
| 38322 |  72 |  47855.3 |  30 | 0.416667 |  32 |  3481.17 | 952899           |   273.729 |
| 38353 |  47 |  28880.1 |  23 | 0.489362 |  24 |  3472.91 |      1.11895e+06 |   322.194 |
| 38384 | 139 | 155225   |  50 | 0.359712 |  54 | 15760.7  |      5.70167e+06 |   361.765 |
| 38412 |  64 |  68473.9 |  17 | 0.265625 |  18 |  9143.27 |      2.99064e+06 |   327.086 |
| 38443 |  46 |  50416.8 |  26 | 0.565217 |  30 |  9349.02 |      3.48094e+06 |   372.332 |
| 38473 |  95 | 115385   |  43 | 0.452632 |  47 | 10719.2  |      5.31116e+06 |   495.48  |
| 38504 |  94 | 123785   |  42 | 0.446809 |  42 |  8891.85 |      2.70389e+06 |   304.086 |
| 38534 | 148 | 152778   |  52 | 0.351351 |  52 | 12760.3  |      4.65071e+06 |   364.468 |
| 38565 | 112 | 165294   |  39 | 0.348214 |  40 |  5431.63 |      1.83609e+06 |   338.037 |
| 38596 | 110 | 125382   |  42 | 0.381818 |  42 | 17996.1  |      5.60458e+06 |   311.432 |
| 38626 |  36 |  19207.6 |  31 | 0.861111 |  31 |  5577.8  |      1.32404e+06 |   237.376 |
| 38657 |  58 |  50384.3 |  24 | 0.413793 |  24 |  4484.06 |      1.613e+06   |   359.718 |
| 38687 |  75 |  88898.4 |  28 | 0.373333 |  33 |  8547.41 |      4.02443e+06 |   470.837 |
| 38718 |  47 |  47043.3 |  23 | 0.489362 |  26 |  4329.74 |      1.53732e+06 |   355.06  |
| 38749 |  30 |  27775.4 |  22 | 0.733333 |  21 |  4893.65 |      2.25904e+06 |   461.627 |
| 38777 |  90 | 102468   |  33 | 0.366667 |  35 | 11677.8  |      4.81388e+06 |   412.226 |
| 38808 |  68 |  71781.4 |  28 | 0.411765 |  30 |  6467.85 |      3.14152e+06 |   485.714 |
| 38838 |  97 | 120198   |  35 | 0.360825 |  31 | 16817.8  |      6.02537e+06 |   358.274 |
| 38869 |  38 |  31183.6 |  23 | 0.605263 |  21 |  3267.68 | 890924           |   272.647 |
| 38899 |  46 |  61199.6 |  17 | 0.369565 |  19 |  4912.02 |      1.59029e+06 |   323.755 |
| 38930 |  98 | 144142   |  37 | 0.377551 |  47 | 11769.2  |      4.27401e+06 |   363.15  |
| 38961 |  48 |  44760.9 |  26 | 0.541667 |  23 |  5029.74 |      2.00496e+06 |   398.621 |
| 38991 |  53 |  36007.9 |  28 | 0.528302 |  28 |  4383.7  |      1.84672e+06 |   421.271 |
| 39022 |  93 |  84329.3 |  43 | 0.462366 |  38 | 16457.6  |      5.05831e+06 |   307.354 |
| 39052 |  72 |  58722.4 |  37 | 0.513889 |  42 |  4490.06 |      2.21424e+06 |   493.142 |
| 39083 |  44 |  43615   |  23 | 0.522727 |  22 |  8504.44 |      4.56907e+06 |   537.257 |
| 39114 |  61 |  68927.9 |  36 | 0.590164 |  39 | 10701.9  |      1.10789e+07 |  1035.23  |
| 39142 |  37 |  55261.8 |  19 | 0.513514 |  23 |  5996.3  |      2.5672e+06  |   428.131 |
| 39173 |  58 |  60473.3 |  22 | 0.37931  |  24 | 10087.1  |      3.25053e+06 |   322.245 |
| 39203 |  77 |  67181.8 |  40 | 0.519481 |  44 |  6303.81 |      4.84431e+06 |   768.474 |
| 39234 |  99 | 159363   |  31 | 0.313131 |  31 |  8098.13 |      4.00859e+06 |   495.003 |
| 39264 |  90 |  87101.8 |  25 | 0.277778 |  27 |  8524.27 |      2.52996e+06 |   296.795 |
| 39295 |  83 | 112946   |  29 | 0.349398 |  28 | 10786.9  |      2.89258e+06 |   268.156 |
| 39326 |  45 |  34768.7 |  14 | 0.311111 |  14 |  3083.3  |      1.93624e+06 |   627.977 |
| 39356 |  47 |  41694.1 |  16 | 0.340426 |  18 |  5381.19 |      6.03547e+06 |  1121.59  |
| 39387 |  43 |  38583.2 |  22 | 0.511628 |  19 |  3024.47 |      1.17185e+06 |   387.458 |
| 39417 |  51 |  50406.5 |  26 | 0.509804 |  24 |  9097.2  |      2.41333e+06 |   265.283 |
| 39448 |  59 |  58403.3 |  24 | 0.40678  |  19 |  5503.94 |      1.30422e+06 |   236.962 |
| 39479 |  28 |  11245.6 |  13 | 0.464286 |  13 |  1407.7  | 433827           |   308.181 |
| 39508 | 115 | 155147   |  49 | 0.426087 |  42 | 17154.5  |      3.95901e+06 |   230.786 |
| 39539 |  59 |  57118.1 |  29 | 0.491525 |  24 |  3471.29 |      1.40997e+06 |   406.179 |
| 39569 |  46 |  40455.8 |  27 | 0.586957 |  20 |  4675.36 |      2.2879e+06  |   489.352 |
| 39600 |  81 |  52441.5 |  61 | 0.753086 |  38 |  9852.02 |      3.58299e+07 |  3636.81  |
| 39630 |  67 |  75779.6 |  38 | 0.567164 |  29 |  6568.76 |      4.8807e+07  |  7430.16  |
| 39661 |  72 |  31893   |  72 | 1        |  51 |  7432.76 |      9.38317e+07 | 12624.1   |



label: E=D/B
I=H/G
labeled_formulas: E=D/B
I=H/G
output: {"Arithmetic-Relationship": ["E=D/B", "I=H/G"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_154795___xlsx_26dd05907888417c7b7a2efd1fc4b35e57a1519f.xlsx___line_142