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 |
|:------------|:-----------------------------------------------------------------------------------------------------------------------------------------------|:----|------:|-----------:|---------:|-----------:|
| TS-1        | Mobilization/Demobilization                                                                                                                    | LS  |     1 | 42000      |  42000   | 42000      |
| TS-5        | implementation of Construction Safety Plan and Maintenance of Traffic                                                                          | LS  |     1 | 16000      |  16000   | 16000      |
| P-101-5.1   | Asphalt Pavement Removal                                                                                                                       | SY  |  1040 |     5.5    |   5720   |     5.5    |
| P-101-5.2   | Aircraft Tie-Down Removal (Grassed Area)                                                                                                       | EA  |     9 |   375      |   3375   |   375      |
| P-101-5.3   | Aircraft Tie-Down Removal (Paved Area)                                                                                                         | EA  |     3 |   560      |   1680   |   560      |
| P-101-5.4   | Pavement Marking Removal                                                                                                                       | SF  |   345 |    27      |   9315   |    27      |
| P-101-5.5   | Cold Milling (1.5" Asphaltic Pavement)                                                                                                         | SY  |    90 |     7.5    |    675   |     7.5    |
| P-101-5.6   | Cold Milling (2" Asphaltic Pavement)                                                                                                           | SY  |  4970 |     6.5    |  32305   |     6.5    |
| P-101-5.7   | Asphalt Pavement Crack Sealing, Type I (Cracks Greater Than 1/8" But Less Than 1/4" Wide)                                                      | LF  |  1720 |     6.15   |  10578   |     6.15   |
| P-101-5.8   | Asphalt Pavement Crack Sealing, Type I (Cracks 1/4" to 1/2" Wide)                                                                              | LF  |   850 |     6.5    |   5525   |     6.5    |
| P-152-4.1   | Unclassified Excavation                                                                                                                        | CY  | 19200 |     9      | 172800   |     9      |
| P-152-4.2   | Borrow Excavation (Off-Site Source)                                                                                                            | CY  |  4800 |    19.6    |  94080   |    19.6    |
| P-156-5.1   | Temporary Silt Fence (Without Backing)                                                                                                         | LF  |  5200 |     2.4    |  12480   |     2.4    |
| P-156-5.2   | Temporary Silt Fence (With Backing)                                                                                                            | LF  |  1200 |     5.25   |   6300   |     5.25   |
| P-156-5.3   | Enhanced Rock Check Dam                                                                                                                        | EA  |     4 |   925      |   3700   |   925      |
| P-156-5.4   | Culvert Protection Type 1 or 2                                                                                                                 | EA  |     6 |  1700      |  10200   |  1700      |
| P-156-5.5   | Catch Basin Protection (Type E)                                                                                                                | EA  |     1 |  1560      |   1560   |  1560      |
| P-156-5.6   | Erosion Control Blanket                                                                                                                        | SY  | 37500 |     1.5    |  56250   |     1.5    |
| P-156-5.7   | High-Visiblity Construction Fence                                                                                                              | LF  |  1300 |     2.65   |   3445   |     2.65   |
| P-156-5.8   | Construction Entrance                                                                                                                          | EA  |     1 |  5400      |   5400   |  5400      |
| P-156-5.9   | Temporary Seeding and Mulching                                                                                                                 | AC  |     5 |  2420      |  12100   |  2420      |
| TS-10-5.1   | Riprap Class 2, 15" Min. Layer Thickness, Including Fabric                                                                                     | SY  |    90 |    66      |   5940   |    66      |
| P-209-5.1   | Crushed Aggregate Base Course, 4 Inch Min. Thickness                                                                                           | SY  |    90 |    12.4    |   1116   |    12.4    |
| P-209-5.2   | Crushed Aggregate Base Course, 6 Inch Min. Thickness                                                                                           | SY  |  7450 |    12.3501 |  92008   |    12.3501 |
| P-401-8.1.1 | Bituminous Surface Course, 2 Inch Min. Thickness                                                                                               | TON |  2310 |   118      | 272580   |   118      |
| P-401-8.1.2 | Bituminous Leveling Course                                                                                                                     | TON |     5 |   152      |    760   |   152      |
| P-602-5.1   | Bituminous Prime Coat                                                                                                                          | GAL |  1770 |     4      |   7080   |     4      |
| P-603-5.1   | Bituminous Tack Coat                                                                                                                           | GAL |  1320 |     5.25   |   6930   |     5.25   |
| P-610-5.1   | Structural Portland Cement Concrete, Class "A"                                                                                                 | CY  |     5 |   650      |   3250   |   650      |
| P-620-5.1   | Temporary Pavement Marking, White, Non-Reflectorized                                                                                           | SF  |   510 |    12.3    |   6273   |    12.3    |
| P-620-5.2   | Temporary Pavement Marking, Yellow, Non-Reflectorized                                                                                          | SF  |  1000 |     6.15   |   6150   |     6.15   |
| P-620-5.3   | Permanent Pavement Marking, White, Reflectorized                                                                                               | SF  |   900 |     8      |   7200   |     8      |
| P-620-5.4   | Permanent Pavement Marking, Yellow, Reflectorized                                                                                              | SF  |  1150 |     7.4    |   8510   |     7.4    |
| P-620-5.5   | Permanent Pavement Marking, Black, Non-Reflectorized                                                                                           | SF  |   380 |    17.2    |   6536   |    17.2    |
| P-620-5.6   | 4 Inch Solid White Traffic Stripe, Non-Reflectorized                                                                                           | LF  |   300 |    18.4    |   5520   |    18.4    |
| P-620-5.7   | HC Accessible Parking Stall Signage and Marking                                                                                                | EA  |     1 |  3070      |   3070   |  3070      |
| P-620-5.8   | Reflective Media (Type I Beads)                                                                                                                | LB  |    20 |   154      |   3080   |   154      |
| F-162-5.1   | Chain-Link Fence, 6-Foot Fabric Height, 3 Strand Barbed Wire                                                                                   | LF  |   170 |    42      |   7140   |    42      |
| D-701-5.1   | 24 Inch Dia. Reinforced Concrete Pipe, CL. IV                                                                                                  | LF  |   154 |    95      |  14630   |    95      |
| D-701-5.2   | 36 Inch Dia. Reinforced Concrete Pipe CL. IV                                                                                                   | LF  |   382 |   150      |  57300   |   150      |
| D-705-5.1   | Pavement Underdrain, 6" Perforated P.V.C. Pipe (Including Pours Backfill and Filter Fabric)                                                    | LF  |  1587 |    24.5    |  38881.5 |    24.5    |
| D-705-5.2   | Underdrain Connection to RCP                                                                                                                   | EA  |     8 |  1685      |  13480   |  1685      |
| D-751-5.1   | Junction Box with Grate Inlet                                                                                                                  | EA  |     1 |  8600      |   8600   |  8600      |
| D-752-5.1   | Headwall (Slope Paved)                                                                                                                         | EA  |     4 |  7525      |  30100   |  7525      |
| D-754-5.1   | Concrete for Valley Gutter                                                                                                                     | CY  |     2 |   468      |    936   |   468      |
| D-754-5.2   | Concrete for Trench Drain                                                                                                                      | CY  |     6 |   530      |   3180   |   530      |
| D-754-5.3   | Trench Drain Grate                                                                                                                             | LF  |    70 |   245      |  17150   |   245      |
| D-754-5.4   | Concrete Curb Stop                                                                                                                             | EA  |     5 |   810      |   4050   |   810      |
| D-754-5.5   | Aircraft Tie-Down                                                                                                                              | EA  |    36 |   395      |  14220   |   395      |
| T-901-5.1   | Seeding with Hydromulch                                                                                                                        | AC  |    12 |  5620      |  67440   |  5620      |
| T-904-5.1   | Sod                                                                                                                                            | SY  |  2150 |     7.5    |  16125   |     7.5    |
| T-905-5.1   | Topsoiling (Stockpiled Onsite)                                                                                                                 | CY  |  2420 |    10.5    |  25410   |    10.5    |
| L-107-5.1   | L-807, Style 1-B, Size 2 Wind Cone and Foundation, In-Place                                                                                    | EA  |     1 | 13850      |  13850   | 13850      |
| L-107-5.2   | Relocate Segmented Circle Marker System, In-Place                                                                                              | EA  |     1 |  1250      |   1250   |  1250      |
| L-108-5.1   | Trenching for Direct Burial Cable, 24 Inch Min. Depth                                                                                          | LF  |  1600 |     5.4    |   8640   |     5.4    |
| L-108-5.2   | Trenching for Counterpoise Wire, 8 Inch Min. Depth                                                                                             | LF  |  1300 |     2.7    |   3510   |     2.7    |
| L-108-5.3   | #8 AWG, 5kV, L-824, Type C Cable, Installed in Duct Bank or Conduit                                                                            | LF  |   700 |     3.45   |   2415   |     3.45   |
| L-108-5.4   | #8 AWG, 5kV, L-824, Type C Cable, Installed in Trench                                                                                          | LF  |  2500 |     2.1    |   5250   |     2.1    |
| L-108-5.5   | #6 AWG, Solid, Bare Counterpoise Wire, Installed in Trench, Including Ground Rods and Ground Connectors                                        | LF  |  1600 |     2      |   3200   |     2      |
| L-108-5.6   | #6 AWG, Insulated, Stranded Equipment Ground, Installed in Duct Bank or Conduit                                                                | LF  |   500 |     1.85   |    925   |     1.85   |
| L-108-5.7   | #6 AWG, Insulated, Stranded Equipment Ground, Installed in Trench                                                                              | LF  |  1600 |     1.85   |   2960   |     1.85   |
| L-108-5.8   | #6 AWG, 600 v, L-824, Type C Cable, Installed in Trench                                                                                        | LF  |    60 |     2.5    |    150   |     2.5    |
| L-108-5.9   | #8 AWG, 600 v, L-824, Type C Cable, Installed in Trench                                                                                        | LF  |    60 |     2      |    120   |     2      |
| L-110-5.1   | Ductbank, 4' x 4'                                                                                                                              | LF  |   190 |    78      |  14820   |    78      |
| L-110-5.2   | Ductbank, 4' x 2'                                                                                                                              | LF  |    60 |    66      |   3960   |    66      |
| TS-102-4.1  | Removal of Existing Airport Lighting Fixtures, Transformers, Conductors, Conduit, Condrete Foundations, and All Miscellaneous Electrical Items | EA  |     1 |  6850      |   6850   |  6850      |
| TS-125-5.1  | L-861T (L) Medium Intensity Taxiway Edge Light, LED, Color Blue Stake Mounted Includes 26 Inch Dia. Rubber Airfield Mat                        | EA  |    24 |   864.583  |  20750   |   864.583  |
| TS-125-5.2  | Airfield Guidance Sign (One Module)                                                                                                            | EA  |     2 |  6215      |  12430   |  6215      |
| TS-125-5.3  | Airfield Guidance Sign (Two Module)                                                                                                            | EA  |     1 |  6540      |   6540   |  6540      |
| P-101-5.9   | Pavement Marking Cleaning (Runway Only; No Removal of Markings)                                                                                | SF  | 42456 |     2      |  84912   |     2      |



label: G=H/F
labeled_formulas: G=H/F
output: {"Arithmetic-Relationship": ["G=H/F"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_634602___xlsx_d966de5b7e6221dbb580a53efb0dba11ebc73d91.xlsx___line_773