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 |
|:----------------------|:----------------------|:---------------------------|------:|--------:|------:|--------:|---------:|----------:|
| Alabama               | East South Central    | PADD 3 (Gulf Coast)        | 11.63 | 0.29075 | 2.802 | 0.47634 |  0.18559 |  0.389617 |
| Alaska                | Pacific Noncontiguous | PADD 5 (West Coast)        | 19.32 | 0.483   | 3.587 | 0.60979 |  0.12679 |  0.207924 |
| Arizona               | Mountain              | PADD 5 (West Coast)        | 10.11 | 0.25275 | 3.587 | 0.60979 |  0.35704 |  0.585513 |
| Arkansas              | West South Central    | PADD 3 (Gulf Coast)        |  8.83 | 0.22075 | 2.802 | 0.47634 |  0.25559 |  0.536571 |
| California            | Pacific Contiguous    | PADD 5 (West Coast)        | 15.01 | 0.37525 | 3.587 | 0.60979 |  0.23454 |  0.384624 |
| Colorado              | Mountain              | PADD 4 (Rocky Mountain)    | 10.15 | 0.25375 | 3.04  | 0.5168  |  0.26305 |  0.508998 |
| Connecticut           | New England           | PADD 1A (New England)      | 18.94 | 0.4735  | 3.127 | 0.53159 |  0.05809 |  0.109276 |
| Delaware              | South Atlantic        | PADD 1B (Central Atlantic) |  9.59 | 0.23975 | 3.264 | 0.55488 |  0.31513 |  0.567925 |
| District of Columbia* | South Atlantic        | PADD 1B (Central Atlantic) | 12.12 | 0.303   | 3.264 | 0.55488 |  0.25188 |  0.453936 |
| Florida               | South Atlantic        | PADD 1C (Lower Atlantic)   |  9.29 | 0.23225 | 2.962 | 0.50354 |  0.27129 |  0.538766 |
| Georgia               | South Atlantic        | PADD 1C (Lower Atlantic)   |  9.97 | 0.24925 | 2.962 | 0.50354 |  0.25429 |  0.505005 |
| Hawaii                | Pacific Noncontiguous | PADD 5 (West Coast)        | 32.37 | 0.80925 | 3.587 | 0.60979 | -0.19946 | -0.327096 |
| Idaho                 | Mountain              | PADD 4 (Rocky Mountain)    |  7.66 | 0.1915  | 3.04  | 0.5168  |  0.3253  |  0.62945  |
| Illinois              | East North Central    | PADD 2 (Midwest)           |  9.24 | 0.231   | 2.945 | 0.50065 |  0.26965 |  0.5386   |
| Indiana               | East North Central    | PADD 2 (Midwest)           | 11.06 | 0.2765  | 2.945 | 0.50065 |  0.22415 |  0.447718 |
| Iowa                  | West North Central    | PADD 2 (Midwest)           | 10.68 | 0.267   | 2.945 | 0.50065 |  0.23365 |  0.466693 |
| Kansas                | West North Central    | PADD 2 (Midwest)           | 10.45 | 0.26125 | 2.945 | 0.50065 |  0.2394  |  0.478178 |
| Kentucky              | East South Central    | PADD 2 (Midwest)           | 10.49 | 0.26225 | 2.945 | 0.50065 |  0.2384  |  0.476181 |
| Louisiana             | West South Central    | PADD 3 (Gulf Coast)        |  8.56 | 0.214   | 2.802 | 0.47634 |  0.26234 |  0.550741 |
| Maine                 | New England           | PADD 1A (New England)      | 12.64 | 0.316   | 3.127 | 0.53159 |  0.21559 |  0.405557 |
| Maryland              | South Atlantic        | PADD 1B (Central Atlantic) | 10    | 0.25    | 3.264 | 0.55488 |  0.30488 |  0.549452 |
| Massachusetts         | New England           | PADD 1A (New England)      | 15.7  | 0.3925  | 3.127 | 0.53159 |  0.13909 |  0.261649 |
| Michigan              | East North Central    | PADD 2 (Midwest)           | 11.71 | 0.29275 | 2.945 | 0.50065 |  0.2079  |  0.41526  |
| Minnesota             | West North Central    | PADD 2 (Midwest)           | 10.39 | 0.25975 | 2.945 | 0.50065 |  0.2409  |  0.481174 |
| Mississippi           | East South Central    | PADD 3 (Gulf Coast)        | 10.62 | 0.2655  | 2.802 | 0.47634 |  0.21084 |  0.442625 |
| Missouri              | West North Central    | PADD 2 (Midwest)           |  8.18 | 0.2045  | 2.945 | 0.50065 |  0.29615 |  0.591531 |
| Montana               | Mountain              | PADD 4 (Rocky Mountain)    | 10.49 | 0.26225 | 3.04  | 0.5168  |  0.25455 |  0.49255  |
| Nebraska              | West North Central    | PADD 2 (Midwest)           |  9    | 0.225   | 2.945 | 0.50065 |  0.27565 |  0.550584 |
| Nevada                | Mountain              | PADD 5 (West Coast)        |  7.56 | 0.189   | 3.587 | 0.60979 |  0.42079 |  0.690057 |
| New Hampshire         | New England           | PADD 1A (New England)      | 15.31 | 0.38275 | 3.127 | 0.53159 |  0.14884 |  0.27999  |
| New Jersey            | Middle Atlantic       | PADD 1B (Central Atlantic) | 12.11 | 0.30275 | 3.264 | 0.55488 |  0.25213 |  0.454387 |
| New Mexico            | Mountain              | PADD 3 (Gulf Coast)        |  9.71 | 0.24275 | 2.802 | 0.47634 |  0.23359 |  0.490385 |
| New York              | Middle Atlantic       | PADD 1B (Central Atlantic) | 13.25 | 0.33125 | 3.264 | 0.55488 |  0.22363 |  0.403024 |
| North Carolina        | South Atlantic        | PADD 1C (Lower Atlantic)   |  8.94 | 0.2235  | 2.962 | 0.50354 |  0.28004 |  0.556143 |
| North Dakota          | West North Central    | PADD 2 (Midwest)           |  8.87 | 0.22175 | 2.945 | 0.50065 |  0.2789  |  0.557076 |
| Ohio                  | East North Central    | PADD 2 (Midwest)           |  9.67 | 0.24175 | 2.945 | 0.50065 |  0.2589  |  0.517128 |
| Oklahoma              | West South Central    | PADD 2 (Midwest)           |  7.53 | 0.18825 | 2.945 | 0.50065 |  0.3124  |  0.623989 |
| Oregon                | Pacific Contiguous    | PADD 5 (West Coast)        |  9.14 | 0.2285  | 3.587 | 0.60979 |  0.38129 |  0.625281 |
| Pennsylvania          | Middle Atlantic       | PADD 1B (Central Atlantic) |  8.79 | 0.21975 | 3.264 | 0.55488 |  0.33513 |  0.603968 |
| Rhode Island          | New England           | PADD 1A (New England)      | 16.32 | 0.408   | 3.127 | 0.53159 |  0.12359 |  0.232491 |
| South Carolina        | South Atlantic        | PADD 1C (Lower Atlantic)   | 10.46 | 0.2615  | 2.962 | 0.50354 |  0.24204 |  0.480677 |
| South Dakota          | West North Central    | PADD 2 (Midwest)           |  9.46 | 0.2365  | 2.945 | 0.50065 |  0.26415 |  0.527614 |
| Tennessee             | East South Central    | PADD 2 (Midwest)           | 10.49 | 0.26225 | 2.945 | 0.50065 |  0.2384  |  0.476181 |
| Texas                 | West South Central    | PADD 3 (Gulf Coast)        |  7.77 | 0.19425 | 2.802 | 0.47634 |  0.28209 |  0.592203 |
| Utah                  | Mountain              | PADD 4 (Rocky Mountain)    |  8.22 | 0.2055  | 3.04  | 0.5168  |  0.3113  |  0.602361 |
| Vermont               | New England           | PADD 1A (New England)      | 16.67 | 0.41675 | 3.127 | 0.53159 |  0.11484 |  0.216031 |
| Virginia              | South Atlantic        | PADD 1C (Lower Atlantic)   |  7.95 | 0.19875 | 2.962 | 0.50354 |  0.30479 |  0.605295 |
| Washington            | Pacific Contiguous    | PADD 5 (West Coast)        | 12.12 | 0.303   | 3.587 | 0.60979 |  0.30679 |  0.503108 |
| West Virginia         | South Atlantic        | PADD 1C (Lower Atlantic)   |  9.56 | 0.239   | 2.962 | 0.50354 |  0.26454 |  0.52536  |
| Wisconsin             | East North Central    | PADD 2 (Midwest)           | 10.92 | 0.273   | 2.945 | 0.50065 |  0.22765 |  0.454709 |
| Wyoming               | Mountain              | PADD 4 (Rocky Mountain)    |  9.89 | 0.24725 | 3.04  | 0.5168  |  0.26955 |  0.521575 |



label: H=G-E
I=H/G
labeled_formulas: H=G-E
I=H/G
output: {"Arithmetic-Relationship": ["H=G-E", "I=H/G"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_512372___xlsx_31672c57ab872337928a36ac1bc12697da77b5c1.xlsx___line_155