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 |
|:--------------------------------|:----------------|------------:|----------:|-----------:|-----------:|----------:|----------:|
| Almonds                         | cwt.            |  12397.5    |  19000    | 0.652498   |  14471.8   |  21400    | 0.676251  |
| Apples2                         | cwt.            |    768.758  |   2000    | 0.384379   |    627     |   2500    | 0.2508    |
| Apricots                        | short tons      |      7.705  |     38.5  | 0.20013    |     12.803 |     55.95 | 0.228829  |
| Artichokes2                     | cwt.            |     32.5617 |    918    | 0.0354703  |     37.4   |    986    | 0.037931  |
| Asparagus2                      | cwt.            |      2.1    |    234    | 0.00897436 |      4.71  |    208    | 0.0226442 |
| Avocados2                       | short tons      |      8.498  |    201    | 0.0422786  |     12.192 |    143    | 0.0852587 |
| Beef and products2,3            | liveweight cwt. |   1304.87   |  18802    | 0.0694005  |   1443     |  18147    | 0.0795173 |
| Blueberries2                    | cwt.            |    232.935  |    639    | 0.36453    |    218     |    597    | 0.365159  |
| Broccoli2                       | cwt.            |   1871      |  20880    | 0.0896073  |   2082     |  21350    | 0.0975176 |
| Cabbage2                        | cwt.            |    365.287  |   5865    | 0.0622826  |    500     |   5760    | 0.0868056 |
| Carrots2                        | cwt.            |   1617      |  22928    | 0.0705251  |   1482     |  21873    | 0.0677548 |
| Cauliflower2                    | cwt.            |   1956      |   5814    | 0.336429   |   2309     |   5814    | 0.397145  |
| Celery2                         | cwt.            |   2324      |  16180    | 0.143634   |   2204     |  16000    | 0.13775   |
| Cherries                        | short tons      |     25.39   |     59.5  | 0.426723   |     19.376 |     52.5  | 0.369067  |
| Cotton                          | bales           |    597      |    526    | 1.13498    |    409     |    740    | 0.552703  |
| Cottonseed and byproducts       | short tons      |     19.042  |    199    | 0.0956884  |     21.554 |    277    | 0.0778123 |
| Dairy and products4             | cwt.            | 116053      | 408655    | 0.283988   | 118366     | 404359    | 0.292724  |
| Dates2                          | short tons      |      8.173  |     39    | 0.209564   |      8.467 |     31.1  | 0.272251  |
| Dried Plums2                    | short tons      |    146.076  |    319    | 0.457918   |    121.308 |    156.6  | 0.774636  |
| Dry Beans                       | cwt.            |    616.034  |   1029    | 0.598673   |    545     |   1141    | 0.477651  |
| Eggs                            | 100-dozens      |     49.59   |   2752.33 | 0.0180175  |     39.56  |   2894.58 | 0.0136669 |
| Figs2                           | short tons      |     14.425  |     31.7  | 0.455047   |     13.215 |     31.6  | 0.418196  |
| Garlic2                         | cwt.            |    683.3    |   3977    | 0.171813   |   1672.5   |   3690    | 0.453252  |
| Grapefruit2                     | short tons      |     76.874  |    152    | 0.50575    |     67.227 |    160    | 0.420169  |
| Grapes, all5                    | short tons      |   1404.97   |   6792    | 0.206856   |   1320     |   6726    | 0.196253  |
| Hay                             | short tons      |   1085.13   |   5451    | 0.19907    |   1227     |   5040    | 0.243452  |
| Kiwi2                           | short tons      |      7.578  |     20.9  | 0.362584   |      9.537 |     28.3  | 0.336996  |
| Lemons2                         | 76lb boxes      |   3474      |  21000    | 0.165429   |   3561     |  20500    | 0.173707  |
| Lettuce2                        | cwt.            |   4763.51   |  63828    | 0.0746304  |   4869     |  66117    | 0.0736422 |
| Melons                          | cwt.            |   1972      |  16651    | 0.118431   |   2004     |  17920    | 0.11183   |
| Olives and olive oil            | short tons      |     53.4566 |    179    | 0.29864    |     61.537 |    159.6  | 0.38557   |
| Onions                          | cwt.            |   4118      |  19665    | 0.209408   |   4010     |  19271    | 0.208085  |
| Oranges and products2           | short tons      |    831.276  |   2340    | 0.355246   |    854.482 |   2012    | 0.424693  |
| Peaches and nectarines2         | cwt.            |   1260      |  15372    | 0.0819672  |   1283     |  14542    | 0.0882272 |
| Pears2                          | short tons      |     25.533  |    191    | 0.133681   |     17.701 |    175    | 0.101149  |
| Peppers, bell and chili2        | cwt.            |    364      |   9932    | 0.0366492  |    335     |  11266    | 0.0297355 |
| Pistachios                      | cwt., in shell  |   2435      |   2700    | 0.901852   |   3460     |   8965    | 0.385945  |
| Plums                           | short tons      |     38.4907 |    105    | 0.366578   |     32.011 |    134.5  | 0.238     |
| Potatoes2                       | cwt.            |   1349      |  13808    | 0.097697   |   1865     |  13305    | 0.140173  |
| Raspberries and blackberries2,6 | cwt.            |    479      |   2060    | 0.232524   |    405     |   2150    | 0.188372  |
| Rice2                           | cwt.            |  18984.5    |  37877    | 0.501215   |  22514     |  47394    | 0.475039  |
| Spinach                         | cwt.            |    619      |   5192    | 0.119222   |    652     |   5176    | 0.125966  |
| Strawberries2                   | cwt.            |   2881      |  27697    | 0.104018   |   2963     |  28775    | 0.102971  |
| Sweet Potatoes                  | cwt.            |    862      |   6290    | 0.137043   |   1109     |   6200    | 0.178871  |
| Tangerines and mandarins        | short tons      |     39.8066 |    868    | 0.0458601  |     38     |    956    | 0.039749  |
| Tomatoes, fresh                 | cwt.            |    632      |   9424    | 0.0670628  |    664     |   9425    | 0.0704509 |
| Tomatoes, processed             | short tons      |   3926.28   |  14361    | 0.273399   |   3805.84  |  12647    | 0.300928  |
| Turkey                          | liveweight cwt. |    209.4    |   3381    | 0.0619343  |    205.9   |   3237.6  | 0.0635965 |
| Walnuts2                        | short tons      |    359.82   |    606    | 0.593762   |    454.2   |    686    | 0.662099  |
| Wheat2                          | bushels         |   2768      |  18595    | 0.148857   |   1244     |  17302    | 0.0718992 |



label: E=C/D
H=F/G
labeled_formulas: E=C/D
H=F/G
output: {"Arithmetic-Relationship": ["E=C/D", "H=F/G"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_586115___xlsx_3e080e973f34da1ee11cc798520255b0b84efa68.xlsx___line_305