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 |
|:------------|:--------------------------------------------------------------------------------------|:----|---------:|----------:|----------:|-------------:|----------:|-------------:|
| S-100-3.1   | Owner Furnished Safety Barricade                                                      | EA  |    30    |    100    |   3000    |    218.39    |   6551.7  |    159.195   |
| S-100-3.2   | Orange Security Fence                                                                 | LF  |  1800    |      2.2  |   3960    |      3.5     |   6300    |      2.85    |
| S-100-3.3   | Runway Closure “X”, Complete                                                          | EA  |     4    |    220    |    880    |    532.5     |   2130    |    376.25    |
| P-140-3.1   | Mobilization                                                                          | LS  |     1    | 218000    | 218000    | 150000       | 150000    | 184000       |
| P-150-4.1   | Pipe Demolition (8” dia. and larger)                                                  | LF  |   196    |     15    |   2940    |     57.78    |  11324.9  |     36.39    |
| P-150-4.2   | Headwall Demolition                                                                   | EA  |     5    |    110    |    550    |    686.72    |   3433.6  |    398.36    |
| P-150-4.3   | Electrical Demolition (Phases 1 and 1A)                                               | LS  |     1    |  20000    |  20000    |   3000       |   3000    |  11500       |
| P-150-4.4   | Electrical Demolition (Phases 2 and 2A)                                               | LS  |     1    |  25000    |  25000    |   7500       |   7500    |  16250       |
| P-152-5.1   | Unclassified Excavation                                                               | CY  | 14200    |      8.25 | 117150    |     11       | 156200    |      9.625   |
| P-152-5.2   | Undercut Excavation                                                                   | CY  |   400    |     27.5  |  11000    |     16.43    |   6572    |     21.965   |
| P-152-5.3   | Rock Excavation                                                                       | CY  |   400    |    100    |  40000    |    109.96    |  43984    |    104.98    |
| P-152-5.4   | Select Borrow                                                                         | CY  |  2000    |     18.7  |  37400    |     25       |  50000    |     21.85    |
| P-152-5.5   | Pavement Excavation (Asphalt)                                                         | SY  | 13500    |      6.45 |  87075    |     10       | 135000    |      8.225   |
| P-152-5.6   | Granular Backfill for Undercut                                                        | CY  |   400    |     55    |  22000    |     54.61    |  21844    |     54.805   |
| P-156-5.1   | Temporary Seeding, Mulching, and Fertilizing                                          | AC  |     2    |   1980    |   3960    |   1980       |   3960    |   1980       |
| P-156-5.2   | Silt Fence (no wire backing) Installation and Removal                                 | LF  |  4920    |      1.65 |   8118    |      4.57    |  22484.4  |      3.11    |
| P-156-5.3   | Inlet Protection Installation and Removal                                             | EA  |     2    |    385    |    770    |    385       |    770    |    385       |
| P-156-5.4   | Rock Check Dam Installation and Removal                                               | EA  |     4    |    440    |   1760    |    440       |   1760    |    440       |
| P-156-5.5   | Rock Filter Ring Installation and Removal                                             | EA  |     2    |    550    |   1100    |    550       |   1100    |    550       |
| P-209-5.1   | Crushed Aggregate Base Course (12 inches thick)                                       | SY  | 11190    |     27.23 | 304704    |     27.23    | 304704    |     27.23    |
| P-301-6.1   | Soil-Cement Base Course (12” deep)                                                    | SY  | 11190    |      2.48 |  27751.2  |      3       |  33570    |      2.74    |
| P-301-6.2   | Portland Cement                                                                       | TON |   277    |    193    |  53461    |    193.05    |  53474.9  |    193.025   |
| P-401-8.1   | Bituminous Surface Course (2 inches thick)                                            | SY  | 20620    |     20.57 | 424153    |     20.57    | 424153    |     20.57    |
| P-602-5.1   | Bituminous Prime Coat                                                                 | GAL |  2800    |      4.46 |  12488    |      4.46    |  12488    |      4.46    |
| P-603-5.1   | Bituminous Tack Coat                                                                  | GAL |  1030    |      4.46 |   4593.8  |      4.46    |   4593.8  |      4.46    |
| P-620-5.1   | Pavement Marking (reflective)                                                         | SF  |  1210    |      2.2  |   2662    |      2.37    |   2867.7  |      2.285   |
| P-620-5.2   | Pavement Marking (non-reflective)                                                     | SF  |  4920    |      0.83 |   4083.6  |      1.91    |   9397.2  |      1.37    |
| P-620-5.3   | Pavement Markings  (Dayton TN)                                                        | LS  |     1    |    220    |    220    |   1045       |   1045    |    632.5     |
| P-620-5.4   | Marking Removal                                                                       | SF  |   260    |      5.5  |   1430    |     31.74    |   8252.4  |     18.62    |
| D-701-5.1   | 30” Reinforced Concrete Pipe (Class V)                                                | LF  |   116    |    135    |  15660    |    150       |  17400    |    142.5     |
| D-701-5.2   | 36” Reinforced Concrete Pipe (Class V)                                                | LF  |   188    |    157    |  29516    |    150       |  28200    |    153.5     |
| D-705-5.1   | Gravel Underdrain with 4 inch Perforated Pipe                                         | LF  |   260    |     12    |   3120    |     16.51    |   4292.6  |     14.255   |
| D-705-5.2   | Outfall Underdrain with 4 inch Non-Perforated Pipe                                    | LF  |    55    |     12    |    660    |     17.25    |    948.75 |     14.625   |
| D-705-5.3   | Endwall for Outfall Underdrain                                                        | EA  |     1    |    400    |    400    |   5349.81    |   5349.81 |   2874.91    |
| D-751-5.1   | 6’ Dia. Manhole                                                                       | EA  |     1    |   8500    |   8500    |   8679.04    |   8679.04 |   8589.52    |
| D-752-5.1   | Type D Headwall for 30” pipe                                                          | EA  |     2    |   1650    |   3300    |   1656.4     |   3312.8  |   1653.2     |
| D-752-5.2   | Type D Headwall for 36” pipe                                                          | EA  |     3    |   1650    |   4950    |   1656.4     |   4969.2  |   1653.2     |
| D-754-5.1   | Concrete Swale (4’ width)                                                             | LF  |   400    |     26    |  10400    |     32.82    |  13128    |     29.41    |
| T-901-5.1   | Seeding                                                                               | AC  |    10.15 |   2745    |  27861.8  |   2744.5     |  27856.7  |   2744.75    |
| T-904-5.1   | Sodding                                                                               | SY  |  2755    |      6.05 |  16667.8  |      6.89    |  18982    |      6.47    |
| T-908-5.1   | Topsoil (from on-site stockpiles – 4 inches thick)                                    | CY  |  5755    |      9    |  51795    |      8.55    |  49205.3  |      8.775   |
| SP-1625-5.1 | Coal Tar Seal Coat                                                                    | GAL |  4025    |      8.25 |  33206.2  |      4.35    |  17508.8  |      6.3     |
| TAD-615-5.1 | Minor Joint and Crack Sealing                                                         | LF  | 10700    |      1    |  10700    |      1.27    |  13589    |      1.135   |
| TAD-615-5.2 | Major Joint and Crack Sealing                                                         | LF  |  1885    |      5.5  |  10367.5  |      7.12    |  13421.2  |      6.31    |
| TD-709-5.1  | Class A-1 Riprap                                                                      | SY  |    65    |     41    |   2665    |     26.05    |   1693.25 |     33.525   |
| L-108-5.1   | No. 8 L-824C 5kV Cable Installed in Duct or Conduit                                   | LF  |  5665    |      1.82 |  10310.3  |      1.65    |   9347.25 |      1.735   |
| L-108-5.2   | No. 8 L-824C 5kV Cable Direct Earth Buried                                            | LF  |   800    |      1.82 |   1456    |      1.65    |   1320    |      1.735   |
| L-108-5.3   | No. 4 L-824C 600 Volt Cable Installed in Duct or Conduit                              | LF  |  2075    |      1.87 |   3880.25 |      2.86    |   5934.5  |      2.365   |
| L-108-5.4   | No. 6 Solid BSDC Counterpoise Wire, Including Ground Rods and Connectors              | LF  |  5170    |      1.93 |   9978.1  |      1.65    |   8530.5  |      1.79    |
| L-108-5.5   | No. 6 BSDC Ground, Including Ground Rods and Connectors                               | LF  |   445    |      1.93 |    858.85 |      1.65    |    734.25 |      1.79    |
| L-108-5.6   | 1/C #8 5kV Temporary Jumper Cable Including Trench, Conduit, and Protective Measures  | LF  |   500    |      7.7  |   3850    |     12.76    |   6380    |     10.23    |
| L-110-5.1   | 1W-2” Sch. 40 PVC DEB, Including Trench & Backfill                                    | LF  |  3915    |      3.85 |  15072.8  |     12.32    |  48232.8  |      8.085   |
| L-110-5.2   | 3W-2” Sch. 40 PVC DEB, Including Trench & Backfill                                    | LF  |   290    |     22    |   6380    |     50.71    |  14705.9  |     36.355   |
| L-110-5.3   | 4W-4” Sch. 40, Concrete Encased Duct Bank Under Pavement, Including Trench & Backfill | LF  |   115    |     99    |  11385    |    109.67    |  12612    |    104.335   |
| L-111-5.1   | Ground Rod Earth Resistance Testing                                                   | EA  |    45    |    165    |   7425    |    209       |   9405    |    187       |
| L-115-5.1   | L-867 Junction Can                                                                    | EA  |     4    |    924    |   3696    |   1496       |   5984    |   1210       |
| L-125-5.1   | Furnish & Install L-867 Base in Soil, Complete                                        | EA  |    45    |    726    |  32670    |   1151.7     |  51826.5  |    938.85    |
| L-125-5.2   | Furnish & Install L-861T Taxiway Edge Fixture & Transformer                           | EA  |    45    |    523    |  23535    |    442.2     |  19899    |    482.6     |
| L-125-5.3   | Furnish & Install L-853 Stake Mounted Retroreflective Blue Edge Marker                | EA  |    16    |     80    |   1280    |     95.15    |   1522.4  |     87.575   |
| L-125-5.4   | Furnish & Install L-858 Sign, 1 Face, 1 Module, w/Transformer, Including Foundation   | EA  |     1    |   2728    |   2728    |   4097.5     |   4097.5  |   3412.75    |
| L-125-5.5   | Furnish & Install L-858 Sign, 1 Face, 2 Module, w/Transformer, Including Foundation   | EA  |     2    |   3515    |   7030    |   4315.3     |   8630.6  |   3915.15    |
| L-125-5.6   | Furnish & Install L-858 Sign, 1 Face, 3 Module, w/Transformer, Including Foundation   | EA  |     3    |   4362    |  13086    |   4930.2     |  14790.6  |   4646.1     |
| D-705-5.1   | Gravel Underdrain with 4 inch Perforated Pipe                                         | LF  |  3325    |     12    |  39900    |     13.63    |  45319.8  |     12.815   |
| D-705-5.2   | Outfall Underdrain with 4 inch Non-Perforated Pipe                                    | LF  |   155    |     12    |   1860    |      1.45677 |    225.8  |      6.72839 |
| D-705-5.3   | Endwall for Outfall Underdrain                                                        | EA  |     2    |    500    |   1000    |   5349.81    |  10699.6  |   2924.91    |



label: G=H/F
I=J/F
labeled_formulas: G=H/F
I=J/F
output: {"Arithmetic-Relationship": ["G=H/F", "I=J/F"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_634599___xlsx_d966de5b7e6221dbb580a53efb0dba11ebc73d91.xlsx___line_770