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:
| B                                                |       C |           D |           E |           F |           G |            H |           I |            J |
|:-------------------------------------------------|--------:|------------:|------------:|------------:|------------:|-------------:|------------:|-------------:|
| Algoma Power Inc.                                |  0.681  |  0.663947   |  0.712178   |  0.680756   |  0.706032   |  0.685627    |  0.699655   |  0.0140284   |
| Atikokan Hydro Inc.                              |  0.077  |  0.328734   |  0.116276   | -0.0489274  |  0.0973029  |  0.132028    |  0.0548839  | -0.0771437   |
| Bluewater Power Distribution Corporation         |  0.017  |  0.0640037  |  0.0591996  |  0.00327786 |  0.00791168 |  0.0421604   |  0.023463   | -0.0186973   |
| Brant County Power Inc.                          |  0.2242 |  0.115415   |  0.0545423  | -0.0357901  | -0.13566    |  0.0447223   | -0.0389694  | -0.0836916   |
| Brantford Power Inc.                             | -0.025  |  0.0468902  |  0.00707004 | -0.0364888  | -0.0605312  |  0.00582381  | -0.0299833  | -0.0358071   |
| Burlington Hydro Inc.                            | -0.0713 | -0.0903465  | -0.0751534  | -0.0935982  | -0.102736   | -0.086366    | -0.0904958  | -0.00412975  |
| Cambridge And North Dumfries Hydro Inc.          | -0.0777 | -0.0326033  |  0.004727   | -0.0190942  | -0.0361718  | -0.0156568   | -0.0168463  | -0.00118949  |
| Canadian Niagara Power Inc.                      |  0.1562 |  0.100107   |  0.138344   |  0.128935   |  0.129549   |  0.122462    |  0.132276   |  0.00981405  |
| Centre Wellington Hydro Ltd.                     | -0.0485 |  0.00368206 |  0.00419325 | -0.030999   | -0.0117884  | -0.00770789  | -0.0128647  | -0.00515682  |
| Chapleau Public Utilities Corporation            |  0.1476 |  0.240044   |  0.204722   |  0.276959   |  0.238781   |  0.240575    |  0.240154   | -0.000420751 |
| Collus PowerStream Corp.                         | -0.0947 | -0.0121286  | -0.122587   | -0.142377   | -0.141871   | -0.0923641   | -0.135612   | -0.0432474   |
| Cooperative Hydro Embrun Inc.                    | -0.1693 | -0.2643     | -0.188545   | -0.296626   | -0.332484   | -0.249824    | -0.272552   | -0.0227279   |
| E.L.K. Energy Inc.                               | -0.2616 | -0.254377   | -0.332186   | -0.449376   | -0.347095   | -0.345313    | -0.376219   | -0.0309062   |
| Enersource Hydro Mississauga Inc.                | -0.1608 | -0.095      | -0.107346   | -0.139144   | -0.0822358  | -0.11383     | -0.109575   |  0.00425475  |
| Entegrus Powerlines Inc.                         | -0.1344 | -0.10865    | -0.125474   | -0.167249   | -0.173385   | -0.133791    | -0.155369   | -0.0215783   |
| Enwin Utilities Ltd.                             |  0.1684 |  0.2385     |  0.1026     |  0.108646   |  0.0990817  |  0.149915    |  0.103443   | -0.0464728   |
| Erie Thames Powerlines Corporation               |  0.1435 |  0.0390158  |  0.0790626  |  0.0701235  |  0.070077   |  0.062734    |  0.0730877  |  0.0103537   |
| Espanola Regional Hydro Distribution Corporation | -0.2184 | -0.154852   | -0.192648   | -0.254219   | -0.203612   | -0.200573    | -0.216826   | -0.0162533   |
| Essex Powerlines Corporation                     | -0.171  | -0.125953   | -0.172354   | -0.12675    | -0.134621   | -0.141686    | -0.144575   | -0.00288929  |
| Festival Hydro Inc.                              |  0.1798 |  0.20201    |  0.196426   |  0.166297   |  0.13983    |  0.188244    |  0.167518   | -0.0207264   |
| Fort Frances Power Corporation                   |  0.1049 |  0.117089   |  0.0636708  |  0.0559782  |  0.051053   |  0.0789128   |  0.0569007  | -0.0220121   |
| Greater Sudbury Hydro Inc.                       |  0.1408 |  0.167297   |  0.0482312  |  0.149263   |  0.0801232  |  0.121597    |  0.0925392  | -0.0290579   |
| Grimsby Power Incorporated                       | -0.1864 | -0.0961     | -0.168509   | -0.172663   | -0.169816   | -0.145757    | -0.170329   | -0.024572    |
| Guelph Hydro Electric Systems Inc.               |  0.1465 | -0.0200656  |  0.00772468 | -0.0483665  | -0.0375081  | -0.0202358   | -0.02605    | -0.00581414  |
| Haldimand County Hydro Inc.                      | -0.241  | -0.186952   | -0.236989   | -0.235957   | -0.213908   | -0.219966    | -0.228951   | -0.0089853   |
| Halton Hills Hydro Inc.                          | -0.249  | -0.274975   | -0.356871   | -0.312732   | -0.281603   | -0.31486     | -0.317069   | -0.00220935  |
| Hearst Power Distribution Company Limited        | -0.3014 | -0.284369   | -0.330717   | -0.223738   | -0.0780851  | -0.279608    | -0.210847   |  0.0687613   |
| Horizon Utilities Corporation                    | -0.1369 | -0.0691     | -0.0553367  | -0.0533162  | -0.0207285  | -0.059251    | -0.0431272  |  0.0161238   |
| Hydro 2000 Inc.                                  | -0.1219 | -0.00826435 | -0.00960597 | -0.152895   | -0.0617661  | -0.0569218   | -0.0747557  | -0.0178339   |
| Hydro Hawkesbury Inc.                            | -0.5936 | -0.557924   | -0.510867   | -0.64315    | -0.681043   | -0.570647    | -0.611687   | -0.0410396   |
| Hydro One Brampton Networks Inc.                 | -0.0743 | -0.0915271  | -0.0571902  | -0.0326862  | -0.0291098  | -0.0604679   | -0.0396621  |  0.0208058   |
| Hydro One Networks Inc.                          |  0.5732 |  0.58673    |  0.343008   |  0.346127   |  0.219548   |  0.425288    |  0.302894   | -0.122394    |
| Hydro Ottawa Limited                             | -0.0256 |  0.0779     |  0.0846633  |  0.126757   |  0.152492   |  0.0964403   |  0.121304   |  0.024864    |
| InnPower                                         | -0.0615 | -0.0241291  | -0.0278724  | -0.0279168  |  0.0853323  | -0.0266394   |  0.00984769 |  0.0364871   |
| Kenora Hydro Electric Corporation Ltd.           | -0.0464 | -0.0518637  | -0.112368   | -0.110015   | -0.0387031  | -0.0914154   | -0.0870286  |  0.00438686  |
| Kingston Hydro Corporation                       |  0.0223 |  0.0238651  |  0.0365973  | -0.035992   | -0.0312351  |  0.0081568   | -0.0102099  | -0.0183667   |
| Kitchener-Wilmot Hydro Inc.                      | -0.2282 | -0.207225   | -0.193206   | -0.190271   | -0.223473   | -0.196901    | -0.202316   | -0.00541585  |
| Lakefront Utilities Inc.                         | -0.1251 | -0.187026   | -0.0739467  | -0.160461   | -0.220595   | -0.140478    | -0.151668   | -0.0111897   |
| Lakeland Power Distribution Ltd.                 | -0.0999 | -0.0639577  | -0.00918919 | -0.0188307  | -0.0758261  | -0.0306592   | -0.0346153  | -0.00395614  |
| London Hydro Inc.                                | -0.101  | -0.111138   | -0.110246   | -0.128195   | -0.0993796  | -0.116526    | -0.112607   |  0.00391932  |
| Midland Power Utility Corporation                |  0.1704 |  0.196171   |  0.185878   |  0.151539   |  0.13848    |  0.177863    |  0.158632   | -0.0192306   |
| Milton Hydro Distribution Inc.                   | -0.0298 | -0.376282   | -0.0449346  | -0.0395748  |  0.0269328  | -0.153597    | -0.0191922  |  0.134405    |
| Newmarket-Tay Power Distribution Ltd.            | -0.21   | -0.194634   | -0.1946     | -0.185703   | -0.193015   | -0.191646    | -0.191106   |  0.000539632 |
| Niagara Peninsula Energy Inc.                    |  0.0516 |  0.1016     |  0.0114969  |  0.0774465  |  0.0454429  |  0.0635145   |  0.0447954  | -0.018719    |
| Niagara-On-The-Lake Hydro Inc.                   |  0.0646 |  0.0269407  | -0.00666495 | -0.0284958  | -0.0658839  | -0.00274001  | -0.0336815  | -0.0309415   |
| North Bay Hydro Distribution Limited             |  0.0553 |  0.0584     |  0.0537731  |  0.0824901  |  0.0698454  |  0.0648877   |  0.0687028  |  0.00381512  |
| Northern Ontario Wires Inc.                      | -0.3566 | -0.257559   | -0.215061   | -0.325965   | -0.422488   | -0.266195    | -0.321172   | -0.0549761   |
| Oakville Hydro Electricity Distribution Inc.     |  0.124  |  0.105534   |  0.138023   |  0.086818   |  0.0689022  |  0.110125    |  0.0979143  | -0.0122106   |
| Orangeville Hydro Limited                        |  0.016  |  0.0078     |  0.0012751  | -0.0397811  | -0.0764805  | -0.0102353   | -0.0383288  | -0.0280935   |
| Orillia Power Distribution Corporation           | -0.0193 | -0.0370139  | -0.0473186  | -0.0527611  | -0.0798074  | -0.0456979   | -0.0599624  | -0.0142645   |
| Oshawa PUC Networks Inc.                         | -0.1798 | -0.145121   | -0.173808   | -0.180949   | -0.149454   | -0.166626    | -0.16807    | -0.00144425  |
| Ottawa River Power Corporation                   |  0.0268 | -0.0003719  |  0.0434913  | -0.0690637  | -0.0933847  | -0.0086481   | -0.0396524  | -0.0310043   |
| Peterborough Distribution Incorporated           |  0.1557 |  0.13218    |  0.145015   |  0.144809   |  0.110399   |  0.140668    |  0.133408   | -0.00726026  |
| Powerstream Inc.                                 | -0.0636 |  0.012      |  0.0303122  |  0.0555191  |  0.0916328  |  0.0326104   |  0.0591547  |  0.0265443   |
| PUC Distribution Inc.                            | -0.0522 |  0.133501   |  0.226634   |  0.145643   |  0.161646   |  0.168593    |  0.177974   |  0.00938166  |
| Renfrew Hydro Inc.                               |  0.1834 |  0.1831     |  0.157347   |  0.103943   |  0.105773   |  0.14813     |  0.122354   | -0.0257758   |
| Rideau St. Lawrence Distribution Inc.            | -0.1383 | -0.0673     | -0.072473   | -0.0807775  | -0.0479184  | -0.0735169   | -0.0670563  |  0.00646052  |
| Sioux Lookout Hydro Inc.                         | -0.0136 |  0.0717124  |  0.0294256  |  0.0620732  | -0.0426473  |  0.0544037   |  0.0162838  | -0.0381199   |
| St. Thomas Energy Inc.                           | -0.0449 |  0.0680223  | -0.00313673 | -0.0630306  | -0.102795   |  0.000618301 | -0.0563207  | -0.056939    |
| Thunder Bay Hydro Electricity Distribution Inc.  |  0.0802 | -0.0282924  |  0.0817952  |  0.0735569  |  0.0863087  |  0.0423532   |  0.0805536  |  0.0382003   |
| Tillsonburg Hydro Inc.                           |  0.1072 |  0.122263   |  0.194669   |  0.0443584  | -0.00476528 |  0.12043     |  0.0780875  | -0.0423428   |
| Toronto Hydro-Electric System Limited            |  0.4772 |  0.450807   |  0.483683   |  0.498919   |  0.514746   |  0.477803    |  0.499116   |  0.0213132   |
| Veridian Connections Inc.                        | -0.0453 |  0.0240068  | -0.0452373  | -0.0296781  | -0.0268435  | -0.0169695   | -0.0339196  | -0.0169501   |
| Wasaga Distribution Inc.                         | -0.4629 | -0.377732   | -0.415632   | -0.415757   | -0.455503   | -0.40304     | -0.428964   | -0.0259237   |
| Waterloo North Hydro Inc.                        |  0.064  |  0.0433478  |  0.105529   |  0.110345   |  0.0819797  |  0.0864074   |  0.0992847  |  0.0128773   |
| Welland Hydro-Electric System Corp.              | -0.1621 | -0.103568   | -0.151912   | -0.172739   | -0.186576   | -0.142739    | -0.170409   | -0.0276694   |
| Wellington North Power Inc.                      |  0.1798 |  0.127822   |  0.176798   |  0.142248   |  0.1183     |  0.148956    |  0.145782   | -0.00317407  |
| West Coast Huron Energy Inc.                     |  0.16   |  0.348126   |  0.413879   |  0.327905   |  0.334759   |  0.363303    |  0.358848   | -0.00445571  |
| Westario Power Inc.                              | -0.0019 | -0.0138647  |  0.0223337  | -0.0415189  | -0.0599475  | -0.0110166   | -0.0263775  | -0.0153609   |
| Whitby Hydro Electric Corporation                | -0.0302 | -0.0698     | -0.0574654  | -0.0677909  | -0.0261032  | -0.0650188   | -0.0504532  |  0.0145656   |
| Woodstock Hydro Services Inc.                    |  0.3286 |  0.289619   |  0.259254   |  0.229601   |  0.194715   |  0.259492    |  0.227857   | -0.0316348   |



label: J=I-H
labeled_formulas: J=I-H
output: {"Arithmetic-Relationship": ["J=I-H"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_9338___xlsx_eb725b0112bc0d870f27882d5b849abe8fd2bd63.xlsx___line_913