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 |        J |        K |        L |        M |        N |        O |        P |        Q |     R |         S |        T |           U |
|------:|:-----------|:--------------------------------------------------|:---------------------------------|------:|----------:|----------:|----------:|---------:|---------:|---------:|---------:|---------:|---------:|---------:|---------:|---------:|------:|----------:|---------:|------------:|
| 23001 | H0001      | BSAS Recovery Support Outpatient Services         | Assessment                       | 18.71 |  1173     |  1449     |  1086.75  |  1690.5  |  1207.5  |  1621.5  |     0    |     0    |     0    |     0    |     0    |     0    |   477 |   8924.67 | 19.5994  |   9348.93   |
| 23001 | H0001      | BSAS Recovery Support Outpatient Services         | Assessment                       | 18.71 |     0     |     0     |     0     |     0    |     0    |     0    |   898.08 |   785.82 |   112.26 |     0    |     0    |   187.1  |   106 |   1983.26 | 19.5994  |   2077.54   |
| 23001 | H0006 - HN | BSAS Recovery Support Outpatient Services         | Case Mgmt-Non-Masters            | 14.7  | 23420.9   | 23210     | 18438.8   | 23644.9  | 25292.4  | 28271.1  |     0    |     0    |     0    |     0    |     0    |     0    | 10795 | 158686    | 16.221   | 175105      |
| 23001 | H0006 - HN | BSAS Recovery Support Outpatient Services         | Case Mgmt-Non-Masters            | 14.7  |     0     |     0     |     0     |     0    |     0    |     0    | 28371    | 23975.7  | 16993.2  | 38763.9  | 27165.6  | 25460.4  | 10934 | 160730    | 16.221   | 177360      |
| 23001 | H0006 - HO | BSAS Recovery Support Outpatient Services         | Case Mgmt-Masters                | 20.93 |  2180.66  |  1161.66  |   346.46  |     0    |    20.38 |   733.68 |     0    |     0    |     0    |     0    |     0    |     0    |   218 |   4562.74 | 20.1423  |   4391.01   |
| 23001 | H0038 - HF | BSAS Recovery Support Outpatient Services         | Recovery Coaching                | 14.57 | 86111.1   | 63214.2   | 44284.9   | 45123.1  | 39353.5  | 43558.5  |     0    |     0    |     0    |     0    |     0    |     0    | 23024 | 335460    | 14.9089  | 343263      |
| 23001 | H0038 - HF | BSAS Recovery Support Outpatient Services         | Recovery Coaching                | 14.57 |     0     |     0     |     0     |     0    |     0    |     0    | 47600.2  | 33656.7  | 41204    | 49421.4  | 52277.2  | 43986.8  | 18404 | 268146    | 14.9089  | 274383      |
| 23001 | H2015 - HF | BSAS Recovery Support Outpatient Services         | Telephone Recovery               | 11.84 |    61.14  |     0     |     0     |     0    |     0    |     0    |     0    |     0    |     0    |     0    |     0    |     0    |     6 |     71.04 | 13.2429  |     79.4573 |
| 23001 | H2015 - HF | BSAS Recovery Support Outpatient Services         | Telephone Recovery               | 11.84 |     0     |     0     |     0     |     0    |     0    |     0    |     0    |     0    |    11.84 |   153.92 |    59.2  |     0    |    19 |    224.96 | 13.2429  |    251.615  |
| 23001 | H2027      | BSAS Recovery Support Outpatient Services         | Psych-Ed Group                   |  3.89 |  6275.2   |  6523.1   |  5764.6   |  7736.7  |  6256.7  |  4921    |     0    |     0    |     0    |     0    |     0    |     0    | 10129 |  39401.8  |  4.25649 |  43113.9    |
| 23001 | H2027      | BSAS Recovery Support Outpatient Services         | Psych-Ed Group                   |  3.89 |     0     |     0     |     0     |     0    |     0    |     0    |  7601.06 |  5971.15 |  7103.14 |  7663.3  |  7601.06 |  5368.2  | 10619 |  41307.9  |  4.25649 |  45199.6    |
| 29000 | H0001      | BSAS Day Treatment                                | Assessment                       | 18.71 |     0     |     0     |   103.5   |     0    |     0    |     0    |     0    |     0    |     0    |     0    |     0    |     0    |     6 |    112.26 | 19.5994  |    117.597  |
| 29000 | H0001      | BSAS Day Treatment                                | Assessment                       | 18.71 |     0     |     0     |     0     |     0    |     0    |     0    |     0    |   112.26 |   112.26 |   261.94 |     0    |   411.62 |    48 |    898.08 | 19.5994  |    940.773  |
| 29000 | H0015 - HF | BSAS Day Treatment                                | Day Treatment                    | 84.11 | 11205.4   |  6901.05  |  9389.91  |  8640.38 |  5459.25 |  4804.14 |     0    |     0    |     0    |     0    |     0    |     0    |   642 |  53998.6  | 89.4639  |  57435.8    |
| 29000 | H0015 - HF | BSAS Day Treatment                                | Day Treatment                    | 84.11 |     0     |     0     |     0     |     0    |     0    |     0    |  9252.1  | 12027.7  | 10093.2  | 11006.4  | 10153.3  |  5887.7  |   695 |  58456.4  | 89.4639  |  62177.4    |
| 31000 | 90882 - HF | BSAS Clinical Outpatient Services                 | Case Consultation                | 37.43 |   234.57  |   483.14  |   134.54  |   230.57 |     0    |   197.06 |     0    |     0    |     0    |     0    |     0    |     0    |    38 |   1422.34 | 39.1989  |   1489.56   |
| 31000 | 90882 - HF | BSAS Clinical Outpatient Services                 | Case Consultation                | 37.43 |     0     |     0     |     0     |     0    |     0    |     0    |   187.15 |   146.4  |   254.81 |   262.01 |   105.64 |     0    |    26 |    973.18 | 39.1989  |   1019.17   |
| 31000 | H0001      | BSAS Clinical Outpatient Services                 | Assessment                       | 18.71 |  1503.64  |  1138.5   |   809     |  1352.18 |  1025    |   630.5  |     0    |     0    |     0    |     0    |     0    |     0    |   382 |   7147.22 | 19.5994  |   7486.98   |
| 31000 | H0001      | BSAS Clinical Outpatient Services                 | Assessment                       | 18.71 |     0     |     0     |     0     |     0    |     0    |     0    |  1309.7  |  1047.76 |   617.43 |   860.66 |   981.99 |   633.56 |   295 |   5519.45 | 19.5994  |   5781.83   |
| 31000 | H0004      | BSAS Clinical Outpatient Services                 | Individual                       | 18.71 | 19642.6   | 19595.7   | 18075.6   | 23798.5  | 18205.9  | 16870.2  |     0    |     0    |     0    |     0    |     0    |     0    |  6876 | 128650    | 19.5994  | 134766      |
| 31000 | H0004      | BSAS Clinical Outpatient Services                 | Individual                       | 18.71 |     0     |     0     |     0     |     0    |     0    |     0    | 20887.2  | 15712.4  | 16850.6  | 18065.2  | 13843.1  | 12232.5  |  5299 |  99144.3  | 19.5994  | 103857      |
| 31000 | H0005      | BSAS Clinical Outpatient Services                 | Group                            |  5.61 |  4104.97  |  3439.71  |  3187.85  |  4096.69 |  3451.94 |  2574    |     0    |     0    |     0    |     0    |     0    |     0    |  4747 |  26630.7  |  5.87983 |  27911.6    |
| 31000 | H0005      | BSAS Clinical Outpatient Services                 | Group                            |  5.61 |     0     |     0     |     0     |     0    |     0    |     0    |  5121.9  |  3351.71 |  3692.61 |  4554.21 |  3007.55 |  2424.01 |  4105 |  23029.1  |  5.87983 |  24136.7    |
| 31000 | H0006 - HN | BSAS Clinical Outpatient Services                 | Case Mgmt-Non-Masters            | 14.7  |   743.91  |   474.48  |   659     |  1186.2  |  1238.92 |   698.54 |     0    |     0    |     0    |     0    |     0    |     0    |   380 |   5586    | 16.221   |   6163.96   |
| 31000 | H0006 - HN | BSAS Clinical Outpatient Services                 | Case Mgmt-Non-Masters            | 14.7  |     0     |     0     |     0     |     0    |     0    |     0    |   926.1  |   689.26 |  1271.7  |  1146.6  |  1861    |  1346.5  |   500 |   7350    | 16.221   |   8110.48   |
| 31000 | H0006 - HO | BSAS Clinical Outpatient Services                 | Case Mgmt-Masters                | 20.93 |  2221.42  |  2302.94  |  2042.61  |  1915.72 |  3729.54 |  1039.38 |     0    |     0    |     0    |     0    |     0    |     0    |   651 |  13625.4  | 20.1423  |  13112.6    |
| 31000 | H0006 - HO | BSAS Clinical Outpatient Services                 | Case Mgmt-Masters                | 20.93 |     0     |     0     |     0     |     0    |     0    |     0    |  1381.38 |  1465.1  |  1444.17 |  1193.01 |   858.13 |    83.72 |   307 |   6425.51 | 20.1423  |   6183.68   |
| 31000 | H2027      | BSAS Clinical Outpatient Services                 | Psych-Ed Group                   |  3.89 |  1864.8   |  1783.4   |  1687.2   |  1694.6  |  1110    |  1450.4  |     0    |     0    |     0    |     0    |     0    |     0    |  2592 |  10082.9  |  4.25649 |  11032.8    |
| 31000 | H2027      | BSAS Clinical Outpatient Services                 | Psych-Ed Group                   |  3.89 |     0     |     0     |     0     |     0    |     0    |     0    |  1050.3  |  1664.92 |  1696.04 |  2723    |  2863.04 |  2785.24 |  3286 |  12782.5  |  4.25649 |  13986.8    |
| 31000 | T1006      | BSAS Clinical Outpatient Services                 | Family                           | 19.26 |    18.65  |    18.65  |     0     |     0    |     0    |    18.65 |     0    |     0    |     0    |     0    |     0    |     0    |     3 |     57.78 |  0       |      0      |
| 35000 | H0006 - HN | BSAS Case Management/Sec 35 CSP                   | Case Mgmt-Non-Masters            | 14.7  |  7855.28  |  4402.12  |  3479.52  |  3255.46 |  6273.68 |  7314.9  |     0    |     0    |     0    |     0    |     0    |     0    |  2472 |  36338.4  | 16.221   |  40098.2    |
| 35000 | H0006 - HN | BSAS Case Management/Sec 35 CSP                   | Case Mgmt-Non-Masters            | 14.7  |     0     |     0     |     0     |     0    |     0    |     0    |  8731.8  |  5571.3  |  5218.5  |  5541.9  |  7864.5  |  5365.5  |  2605 |  38293.5  | 16.221   |  42255.6    |
| 38000 | H0005      | BSAS Acupuncture Detoxification                   | Group                            |  5.61 |  1767.36  |  1178.24  |  1086.19  |   883.68 |  1012.55 |   533.89 |     0    |     0    |     0    |     0    |     0    |     0    |  1404 |   7876.44 |  5.87983 |   8255.28   |
| 38000 | H0005      | BSAS Acupuncture Detoxification                   | Group                            |  5.61 |     0     |     0     |     0     |     0    |     0    |     0    |  1615.68 |  1907.4  |  1099.56 |   830.28 |  1795.2  |  1211.76 |  1508 |   8459.88 |  5.87983 |   8866.78   |
| 49580 | H0001      | BSAS CJ Diversion                                 | Assessment                       | 18.71 |  1138.5   |   828     |   966     |   931.5  |  1069.5  |   810.75 |     0    |     0    |     0    |     0    |     0    |     0    |   333 |   6230.43 | 19.5994  |   6526.61   |
| 49580 | H0001      | BSAS CJ Diversion                                 | Assessment                       | 18.71 |     0     |     0     |     0     |     0    |     0    |     0    |  1983.26 |  1122.6  |  1721.32 |  1609.06 |  1496.8  |  1721.32 |   516 |   9654.36 | 19.5994  |  10113.3    |
| 49580 | H0006 - HN | BSAS CJ Diversion                                 | Case Mgmt-Non-Masters            | 14.7  | 18597     | 21786.5   | 18689.2   | 20863.9  | 22168.8  | 18847.4  |     0    |     0    |     0    |     0    |     0    |     0    |  9177 | 134902    | 16.221   | 148860      |
| 49580 | H0006 - HN | BSAS CJ Diversion                                 | Case Mgmt-Non-Masters            | 14.7  |     0     |     0     |     0     |     0    |     0    |     0    | 23475.9  | 21726.6  | 23799.3  | 23916.9  | 22270.5  | 25225.2  |  9552 | 140414    | 16.221   | 154943      |
| 49580 | H0006 - HO | BSAS CJ Diversion                                 | Case Mgmt-Masters                | 20.93 |  7071.86  |  6073.24  |  4789.3   |  5380.32 |  5278.42 |  5604.5  |     0    |     0    |     0    |     0    |     0    |     0    |  1678 |  35120.5  | 20.1423  |  33798.7    |
| 49580 | H0006 - HO | BSAS CJ Diversion                                 | Case Mgmt-Masters                | 20.93 |     0     |     0     |     0     |     0    |     0    |     0    |  6132.49 |  4688.32 |  6509.23 |  7325.5  |  8246.42 |  8832.46 |  1994 |  41734.4  | 20.1423  |  40163.7    |
| 49580 | H0038 - HF | BSAS CJ Diversion                                 | Recovery Coaching                | 14.57 |     0     |     0     |     0     |   349.25 |   223.52 |   447.04 |     0    |     0    |     0    |     0    |     0    |     0    |    73 |   1063.61 | 16.221   |   1184.13   |
| 49580 | H0038 - HF | BSAS CJ Diversion                                 | Recovery Coaching                | 14.57 |     0     |     0     |     0     |     0    |     0    |     0    |  8669.15 |  8465.17 |  7124.73 |  1325.87 |  2214.64 |  1675.55 |  2023 |  29475.1  | 16.221   |  32815      |
| 52000 | H0001      | BSAS Second Offender Aftercare Treatment Services | Assessment                       | 18.71 |     0     |     0     |    69     |    69    |   103.5  |     0    |     0    |     0    |     0    |     0    |     0    |     0    |    14 |    261.94 | 19.5994  |    274.392  |
| 52000 | H0001      | BSAS Second Offender Aftercare Treatment Services | Assessment                       | 18.71 |     0     |     0     |     0     |     0    |     0    |     0    |    74.84 |     0    |     0    |     0    |    93.55 |     0    |     9 |    168.39 | 19.5994  |    176.395  |
| 52000 | H0004 - H9 | BSAS Second Offender Aftercare Treatment Services | Individual                       | 18.71 |  1864.25  |   978.25  |  1396.14  |  1690.7  |   939.48 |   875.16 |     0    |     0    |     0    |     0    |     0    |     0    |   487 |   9111.77 | 19.5994  |   9544.93   |
| 52000 | H0004 - H9 | BSAS Second Offender Aftercare Treatment Services | Individual                       | 18.71 |     0     |     0     |     0     |     0    |     0    |     0    |  1365.85 |   292.36 |   946.34 |   486.3  |   508.88 |   306.78 |   224 |   4191.04 | 19.5994  |   4390.27   |
| 52000 | H0005 - H9 | BSAS Second Offender Aftercare Treatment Services | Group                            |  5.61 |  2857.4   |  3673.2   |  2990.56  |  3257.2  |  3008.27 |  2677.09 |     0    |     0    |     0    |     0    |     0    |     0    |  4251 |  23848.1  |  5.87983 |  24995.2    |
| 52000 | H0005 - H9 | BSAS Second Offender Aftercare Treatment Services | Group                            |  5.61 |     0     |     0     |     0     |     0    |     0    |     0    |  2284.13 |  1694.86 |  1608.5  |  1986.64 |  1750.74 |  1065.22 |  1962 |  11006.8  |  5.87983 |  11536.2    |
| 52000 | H0006 - HN | BSAS Second Offender Aftercare Treatment Services | Case Mgmt-Non-Masters            | 14.7  |     0     |     0     |    52.72  |    52.72 |    79.08 |    92.26 |     0    |     0    |     0    |     0    |     0    |     0    |    21 |    308.7  | 16.221   |    340.64   |
| 52000 | H0006 - HN | BSAS Second Offender Aftercare Treatment Services | Case Mgmt-Non-Masters            | 14.7  |     0     |     0     |     0     |     0    |     0    |     0    |   382.2  |    88.2  |    29.4  |   102.9  |   396.9  |   264.6  |    86 |   1264.2  | 16.221   |   1395      |
| 52000 | H0006 - HO | BSAS Second Offender Aftercare Treatment Services | Case Mgmt-Masters                | 20.93 |     0     |     0     |     0     |    20.38 |     0    |     0    |     0    |     0    |     0    |     0    |     0    |     0    |     1 |     20.93 | 20.1423  |     20.1423 |
| 52000 | H0006 - HO | BSAS Second Offender Aftercare Treatment Services | Case Mgmt-Masters                | 20.93 |     0     |     0     |     0     |     0    |     0    |     0    |     0    |     0    |    20.93 |     0    |     0    |     0    |     1 |     20.93 | 20.1423  |     20.1423 |
| 52000 | T1006      | BSAS Second Offender Aftercare Treatment Services | Family                           | 19.26 |     0     |     0     |     0     |    74.6  |     0    |     0    |     0    |     0    |     0    |     0    |     0    |     0    |     4 |     77.04 |  0       |      0      |
| 52000 | T1006      | BSAS Second Offender Aftercare Treatment Services | Family                           | 19.26 |     0     |     0     |     0     |     0    |     0    |     0    |     0    |     0    |     0    |     0    |   192.6  |   231.12 |    22 |    423.72 |  0       |      0      |
| 49351 | 90882 - HF | BSAS A-CRA & Intervention                         | Case Consultation (Inter-agency) | 37.43 |   313.966 |   313.966 |   303.838 |   310.59 |   379.61 |   241.57 |     0    |     0    |     0    |     0    |     0    |     0    |    54 |   2021.22 | 39.1989  |   2116.74   |
| 49351 | 90882 - HF | BSAS A-CRA & Intervention                         | Case Consultation (Inter-agency) | 37.43 |     0     |     0     |     0     |     0    |     0    |     0    |   224.58 |   411.73 |   299.44 |   112.29 |   262.01 |   112.29 |    38 |   1422.34 | 39.1989  |   1489.56   |
| 49351 | H0006 - HN | BSAS A-CRA & Intervention                         | Case Mgmt-Non-Masters            | 14.7  |  1367.85  |  1367.85  |  1323.73  |  2965.5  |   632.64 |   461.3  |     0    |     0    |     0    |     0    |     0    |     0    |   616 |   9055.2  | 16.221   |   9992.11   |
| 49351 | H0006 - HN | BSAS A-CRA & Intervention                         | Case Mgmt-Non-Masters            | 14.7  |     0     |     0     |     0     |     0    |     0    |     0    |   529.2  |   632.1  |   294    |     0    |     0    |     0    |    99 |   1455.3  | 16.221   |   1605.87   |
| 49351 | H0006 - HO | BSAS A-CRA & Intervention                         | Case Mgmt-Masters                | 20.93 |  5823.36  |  5823.36  |  5635.51  |  5461.84 |  4993.1  |  6827.3  |     0    |     0    |     0    |     0    |     0    |     0    |  1696 |  35497.3  | 20.1423  |  34161.3    |
| 49351 | H0006 - HO | BSAS A-CRA & Intervention                         | Case Mgmt-Masters                | 20.93 |     0     |     0     |     0     |     0    |     0    |     0    |  8623.16 |  4981.34 |  8330.14 |  7053.41 |  4311.58 |  2720.9  |  1721 |  36020.5  | 20.1423  |  34664.8    |
| 49351 | H2019 - HF | BSAS A-CRA & Intervention                         | In-Home Therapy                  | 21    |  1008.86  |  1008.86  |   976.317 |  1132.88 |  1051.96 |   809.2  |     0    |     0    |     0    |     0    |     0    |     0    |   296 |   6216    | 22.0911  |   6538.98   |
| 49351 | H2019 - HF | BSAS A-CRA & Intervention                         | In-Home Therapy                  | 21    |     0     |     0     |     0     |     0    |     0    |     0    |   756    |  1281    |   252    |   252    |    63    |     0    |   124 |   2604    | 22.0911  |   2739.3    |
| 49352 | H2027      | BSAS Family Intervention - Family Support         | Client-Centered Psych-Ed Group   |  3.89 |  5611.57  |  5611.57  |  5430.55  |  6907.9  |  4983.9  |  4761.9  |     0    |     0    |     0    |     0    |     0    |     0    |  9002 |  35017.8  |  4.25649 |  38316.9    |
| 49352 | H2027      | BSAS Family Intervention - Family Support         | Client-Centered Psych-Ed Group   |  3.89 |     0     |     0     |     0     |     0    |     0    |     0    |  6581.88 |  5741.64 |  1478.2  |  1470.42 |  1991.68 |  1307.04 |  4774 |  18570.9  |  4.25649 |  20320.5    |
| 49352 | T1006      | BSAS Family Intervention - Family Support         | Family Therapy                   | 19.26 |  1633.9   |  1633.9   |  1581.2   |  2088.8  |  1827.7  |   932.5  |     0    |     0    |     0    |     0    |     0    |     0    |   520 |  10015.2  |  0       |      0      |
| 49352 | T1006      | BSAS Family Intervention - Family Support         | Family Therapy                   | 19.26 |     0     |     0     |     0     |     0    |     0    |     0    |   963    |   231.12 |   154.08 |     0    |     0    |     0    |    70 |   1348.2  |  0       |      0      |



label: S=R*E
U=T*R
labeled_formulas: S=R*E
U=T*R
output: {"Arithmetic-Relationship": ["S=R*E", "U=T*R"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_262735___xlsx_50f99c57e6f22be8b6db861527aac4deb9a26c83.xlsx___line_303