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:
| C                      |   D |    E |      F |      G |     H |      I |       J |        K |        L |
|:-----------------------|----:|-----:|-------:|-------:|------:|-------:|--------:|---------:|---------:|
| 13.5inch fish plate    |  12 |  600 |   7200 | 0.033  | 14    | 19.8   | 30.8644 | 1409.39  | 1.21469  |
| 8.25inch plate         |  48 |  100 |   4800 | 0.022  | 22    |  2.2   | 48.5012 |  896.885 | 0.434284 |
| 8inch plate            |  48 |  100 |   4800 | 0.022  | 20.5  |  2.2   | 45.1943 |  962.511 | 0.398605 |
| 8inch plate            |  48 | 2200 | 105600 | 0.021  | 20    | 46.2   | 44.092  |  986.574 | 0.321975 |
| Salt and pepper bottle |  87 |   75 |   6525 | 0.018  | 16    |  1.35  | 35.2736 | 1233.22  | 0.212765 |
| Ashtray                |  96 |  600 |  57600 | 0.035  | 18    | 21     | 39.6828 | 1096.19  | 0.274767 |
| 8OZ mug                |  96 |  150 |  14400 | 0.057  | 19.5  |  8.55  | 42.9897 | 1011.87  | 0.256492 |
| 3.5inch bowl           | 120 |  150 |  18000 | 0.042  | 18    |  6.3   | 39.6828 | 1096.19  | 0.236807 |
| 150CC cup              | 120 |   60 |   7200 | 0.038  | 16    |  2.28  | 35.2736 | 1233.22  | 0.218867 |
| 8OZ mug                |  72 |   60 |   4320 | 0.039  | 18.5  |  2.34  | 40.7851 | 1066.57  | 0.312605 |
| 10OZ mug               | 120 |   60 |   7200 | 0.045  | 16.8  |  2.7   | 37.0373 | 1174.49  | 0.318564 |
| 250CC cup              |  96 |  200 |  19200 | 0.073  | 26.4  | 14.6   | 58.2014 |  747.404 | 0.319193 |
| 14OZ mug               |  48 |  600 |  28800 | 0.045  | 17    | 27     | 37.4782 | 1160.67  | 0.396714 |
| 16OZ mug               |  48 | 1000 |  48000 | 0.05   | 17.8  | 50     | 39.2419 | 1108.51  | 0.427111 |
| 5.5inch bowl           |  48 |  500 |  24000 | 0.05   | 23.5  | 25     | 51.8081 |  839.637 | 0.506378 |
| 6inch bowl             |  36 |   45 |   1620 | 0.045  | 16.9  |  2.025 | 37.2577 | 1167.54  | 0.523305 |
| 6inch bowl             |  36 |  150 |   5400 | 0.048  | 20    |  7.2   | 44.092  |  986.574 | 0.566865 |
| 6inch bowl             |  36 |  250 |   9000 | 0.045  | 18    | 11.25  | 39.6828 | 1096.19  | 0.546593 |
| 6inch bowl             |  36 |  500 |  18000 | 0.048  | 18    | 24     | 39.6828 | 1096.19  | 0.546593 |
| 6inch bowl             |  48 |  185 |   8880 | 0.022  | 17.7  |  4.07  | 39.0214 | 1114.77  | 0.474424 |
| 6inch bowl             |  36 |  100 |   3600 | 0.042  | 17.5  |  4.2   | 38.5805 | 1127.51  | 0.541525 |
| 6.25inch bowl          |  36 |  150 |   5400 | 0.042  | 18    |  6.3   | 39.6828 | 1096.19  | 0.546593 |
| 6.75inch bowl          |  32 |  150 |   4800 | 0.047  | 19    |  7.05  | 41.8874 | 1038.5   | 0.580802 |
| 7.5inch bowl           |  24 |  900 |  21600 | 0.037  | 19    | 33.3   | 41.8874 | 1038.5   | 0.640884 |
| 7.5inch bowl           |  36 |   60 |   2160 | 0.037  | 22.5  |  2.22  | 49.6035 |  876.954 | 0.592205 |
| 7.5inch bowl           |  36 |  220 |   7920 | 0.037  | 23    |  8.14  | 50.7058 |  857.89  | 0.597273 |
| 7inch bowl             |  36 |  450 |  16200 | 0.025  | 19.5  | 11.25  | 42.9897 | 1011.87  | 0.549659 |
| 8inch bowl             |  36 |  450 |  16200 | 0.025  | 19.5  | 11.25  | 42.9897 | 1011.87  | 0.573935 |
| 8.5inch bowl           |  18 |  180 |   3240 | 0.034  | 18    |  6.12  | 39.6828 | 1096.19  | 0.741181 |
| 9inch bowl             |  24 |  800 |  19200 | 0.042  | 20.2  | 33.6   | 44.5329 |  976.805 | 0.731957 |
| 9inch bowl             |  22 |  100 |   2200 | 0.042  | 19.5  |  4.2   | 42.9897 | 1011.87  | 0.748267 |
| 9inch bowl             |  24 |  120 |   2880 | 0.022  | 18.7  |  2.64  | 41.226  | 1055.16  | 0.794118 |
| 9inch bowl             |  36 |  200 |   7200 | 0.022  | 20    |  4.4   | 44.092  |  986.574 | 0.530451 |
| 21x12.5cm              |   6 |   40 |    240 | 0.0449 |  9.5  |  1.796 | 20.9437 | 2077     | 1.48812  |
| 6inch plate            |  72 |   80 |   5760 | 0.02   | 18    |  1.6   | 39.6828 | 1096.19  | 0.236882 |
| 8inch plate            |  48 | 2000 |  96000 | 0.0213 | 19.45 | 42.6   | 42.8795 | 1014.47  | 0.317794 |
| 9.75inch plate         |  30 |  400 |  12000 | 0.023  | 20    |  9.2   | 44.092  |  986.574 | 0.558857 |
| 9.75inch plate         |  30 |  200 |   6000 | 0.023  | 20    |  4.6   | 44.092  |  986.574 | 0.655962 |
| 10.5inch plate         |  30 | 4000 | 120000 | 0.024  | 25    | 96     | 55.115  |  789.259 | 0.668226 |
| 10.5inch plate         |  30 |  400 |  12000 | 0.024  | 25    |  9.6   | 55.115  |  789.259 | 0.741055 |
| 10.5inch plate         |  30 | 1500 |  45000 | 0.024  | 25    | 36     | 55.115  |  789.259 | 0.741055 |
| 10.5inch plate         |  30 |  150 |   4500 | 0.024  | 25    |  3.6   | 55.115  |  789.259 | 0.765331 |
| 10.5inch plate         |  30 |  120 |   3600 | 0.024  | 25    |  2.88  | 55.115  |  789.259 | 0.765331 |
| 12inch plate           |  24 |   80 |   1920 | 0.03   | 24    |  2.4   | 52.9104 |  822.145 | 0.959667 |
| 9inch plate            |  36 |   40 |   1440 | 0.0252 | 21    |  1.008 | 46.2966 |  939.594 | 0.528449 |
| 7inch bowl             |  36 |   30 |   1080 | 0.0259 | 22    |  0.777 | 48.5012 |  896.885 | 0.63569  |
| 10.5inch plate         |  30 |   20 |    600 | 0.026  | 24.6  |  0.52  | 54.2332 |  802.092 | 0.760466 |
| 8inch bowl             |  36 |   20 |    720 | 0.05   | 22    |  1     | 48.5012 |  896.885 | 0.587137 |
| 10.25inch plate        |  30 |  600 |  18000 | 0.027  | 23    | 16.2   | 50.7058 |  857.89  | 0.716728 |
| 7.5inch plate          |  48 |  250 |  12000 | 0.022  | 19.45 |  5.5   | 42.8795 | 1014.47  | 0.34207  |
| 6inch bowl             |  36 |  100 |   3600 | 0.045  | 16.9  |  4.5   | 37.2577 | 1167.54  | 0.535443 |
| 12OZ mug               |  48 |  450 |  21600 | 0.04   | 15    | 18     | 33.069  | 1315.43  | 0.368931 |
| 10.5inch plate         |  20 |  200 |   4000 | 0.028  | 20    |  5.6   | 44.092  |  986.574 | 0.826148 |
| 8inch plate            |  36 |   70 |   2520 | 0.0213 | 17.5  |  1.491 | 38.5805 | 1127.51  | 0.371591 |
| 6inch bowl             |  24 |  100 |   2400 | 0.048  | 20    |  4.8   | 44.092  |  986.574 | 0.668226 |
| 10.5inch plate         |  24 |  300 |   7200 | 0.028  | 20    |  8.4   | 44.092  |  986.574 | 0.765331 |
| 8inch plate            |  36 |  270 |   9720 | 0.0213 | 17.5  |  5.751 | 38.5805 | 1127.51  | 0.371591 |
| 7.5inch bowl           |  24 |  300 |   7200 | 0.036  | 19    | 10.8   | 41.8874 | 1038.5   | 0.653022 |
| 10.5inch plate         |  30 |  400 |  12000 | 0.0285 | 24.8  | 11.4   | 54.6741 |  795.624 | 0.738622 |
| 7.5inch plate          |  48 |  200 |   9600 | 0.021  | 18.5  |  4.2   | 40.7851 | 1066.57  | 0.334848 |
| 8inch bowl             |  36 |  300 |  10800 | 0.0389 | 21.7  | 11.67  | 47.8398 |  909.284 | 0.584097 |
| 10.5inch plate         |  30 |  600 |  18000 | 0.0285 | 24.8  | 17.1   | 54.6741 |  795.624 | 0.344133 |
| 7.5inch plate          |  48 |   50 |   2400 | 0.021  | 18.5  |  1.05  | 40.7851 | 1066.57  | 0.334848 |
| 8.75inch bowl          |  24 |  250 |   6000 | 0.0389 | 20    |  9.725 | 44.092  |  986.574 | 0.680364 |
| 10.5inch plate         |  30 |  600 |  18000 | 0.031  | 25    | 18.6   | 55.115  |  789.259 | 0.765331 |
| 7.5inch bowl           |  24 |  900 |  21600 | 0.037  | 19    | 33.3   | 41.8874 | 1038.5   | 0.640884 |
| 10.5inch plate         |  30 |  200 |   6000 | 0.0285 | 24.8  |  5.7   | 54.6741 |  795.624 | 0.738622 |
| 8inch plate            |  48 |  100 |   4800 | 0.0213 | 19.45 |  2.13  | 42.8795 | 1014.47  | 0.34207  |
| 8inch bowl             |  36 |  100 |   3600 | 0.0389 | 21.7  |  3.89  | 47.8398 |  909.284 | 0.584097 |
| 5.5inch bowl           |  48 |   60 |   2880 | 0.05   | 25.3  |  3     | 55.7764 |  779.9   | 0.532199 |
| 10.5inch plate         |  30 |  800 |  24000 | 0.029  | 25    | 23.2   | 55.115  |  789.259 | 0.765331 |
| 7.5inch bowl           |  36 |  900 |  32400 | 0.023  | 20    | 20.7   | 44.092  |  986.574 | 0.566865 |
| 10inch plate           |  30 |  150 |   4500 | 0.025  | 23    |  3.75  | 50.7058 |  857.89  | 0.741004 |
| 8inch bowl             |  36 |  500 |  18000 | 0.0243 | 21    | 12.15  | 46.2966 |  939.594 | 0.577001 |
| 180CC cup              |  96 |  150 |  14400 | 0.044  | 21    |  6.6   | 46.2966 |  939.594 | 0.262193 |



label: F=E*D
I=E*G
labeled_formulas: F=E*D
I=E*G
output: {"Arithmetic-Relationship": ["F=E*D", "I=E*G"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_279111___xlsx_a3fd7940b82f8bf3ff87d105a6fd7a42f387c880.xlsx___line_528