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 |
|----:|:-------------------|--------:|---------:|--------:|---------:|---------:|
|   1 | 01-AGRA            |  926.4  |    8.35  |  728.27 |  736.62  | 0.795142 |
|   2 | 02-ALIGARH         |  834.75 |   -0.75  |  664.24 |  663.49  | 0.794837 |
|   3 | 03-ALLAHABAD       | 1742.55 |  -92.83  | 1422.75 | 1329.92  | 0.763203 |
|   4 | 04-AMBEDKAR NAGAR  |  759    |  -21.62  |  608.44 |  586.82  | 0.773149 |
|   5 | 05-AURAIYA         |  538.05 |    0     |  421.83 |  421.83  | 0.783998 |
|   6 | 06-AZAMGARH        | 1405.95 |    0     | 1160.4  | 1160.4   | 0.825349 |
|   7 | 07-BADAUN          | 1080.6  |  -15.79  |  739.93 |  724.14  | 0.670128 |
|   8 | 08-BAGHPAT         |  256.35 |    0     |  202.47 |  202.47  | 0.789819 |
|   9 | 09-BAHRAICH        | 1477.5  |   61.52  | 1189.89 | 1251.41  | 0.846978 |
|  10 | 10-BALLIA          | 1104.75 |  -52.61  |  870.9  |  818.29  | 0.740702 |
|  11 | 11-BALRAMPUR       |  739.5  |   -9.46  |  579.23 |  569.77  | 0.77048  |
|  12 | 12-BANDA           |  792.9  |    0     |  640.19 |  640.19  | 0.807403 |
|  13 | 13-BARABANKI       | 1182    |  -85.41  |  943.03 |  857.62  | 0.725567 |
|  14 | 14-BAREILY         | 1009.35 |  -16.28  |  790.36 |  774.08  | 0.766909 |
|  15 | 15-BASTI           |  874.5  |   28.6   |  695.5  |  724.1   | 0.828016 |
|  16 | 16-BHADOHI         |  463.95 |    7.68  |  373.13 |  380.81  | 0.8208   |
|  17 | 17-BIJNOUR         |  893.7  |    0     |  722.83 |  722.83  | 0.808806 |
|  18 | 18-BULANDSHAHAR    |  837.45 |  165.96  |  664.9  |  830.86  | 0.992131 |
|  19 | 19-CHANDAULI       |  679.5  |  114.35  |  562.82 |  677.17  | 0.996571 |
|  20 | 20-CHITRAKOOT      |  547.05 |    0     |  433.84 |  433.84  | 0.793054 |
|  21 | 21-AMETHI          |  661.5  |  -45.54  |  526.39 |  480.85  | 0.726909 |
|  22 | 22-DEORIA          | 1054.95 |   -9.81  |  822.7  |  812.89  | 0.770548 |
|  23 | 23-ETAH            |  660.6  |  -37.99  |  518.58 |  480.59  | 0.727505 |
|  24 | 24-FAIZABAD        |  856.5  |  -47.75  |  684.4  |  636.65  | 0.743316 |
|  25 | 25-FARRUKHABAD     |  678    |    0     |  523.75 |  523.75  | 0.772493 |
|  26 | 26-FATEHPUR        |  989.1  |  -40.85  |  801.26 |  760.41  | 0.76879  |
|  27 | 27-FIROZABAD       |  657.75 |   -3.29  |  503.41 |  500.12  | 0.76035  |
|  28 | 28-G.B. NAGAR      |   25.05 |    0     |   19.23 |   19.23  | 0.767665 |
|  29 | 29-GHAZIPUR        | 1126.35 |  -66.42  |  904.44 |  838.02  | 0.744014 |
|  30 | 30-GHAZIYABAD      |  258.45 |    0     |  208.44 |  208.44  | 0.8065   |
|  31 | 31-GONDA           | 1240.65 |   86.93  |  982.59 | 1069.52  | 0.862064 |
|  32 | 32-GORAKHPUR       | 1225.95 |  -11.24  | 1007.19 |  995.95  | 0.81239  |
|  33 | 33-HAMEERPUR       |  427.35 |   -3.34  |  344    |  340.66  | 0.797145 |
|  34 | 34-HARDOI          | 1567.35 |   -4.97  | 1274.11 | 1269.14  | 0.809736 |
|  35 | 35-HATHRAS         |  425.25 |    0     |  343.19 |  343.19  | 0.807031 |
|  36 | 36-ITAWAH          |  573    |    0     |  444.23 |  444.23  | 0.775271 |
|  37 | 37-J.P. NAGAR      |  451.65 |  -10.62  |  364.58 |  353.96  | 0.783704 |
|  38 | 38-JALAUN          |  589.8  |    0     |  469.27 |  469.27  | 0.795643 |
|  39 | 39-JAUNPUR         | 1402.05 | -133.64  | 1107.13 |  973.49  | 0.694333 |
|  40 | 40-JHANSI          |  631.65 |    0     |  499.9  |  499.9   | 0.791419 |
|  41 | 41-KANNAUJ         |  601.35 |  -26.95  |  465.77 |  438.82  | 0.729725 |
|  42 | 42-KANPUR DEHAT    |  749.7  |    0     |  572.87 |  572.87  | 0.764132 |
|  43 | 43-KANPUR NAGAR    |  623.25 |    7.48  |  501.43 |  508.91  | 0.816542 |
|  44 | 44-KAAS GANJ       |  502.2  |   -0.72  |  394.55 |  393.83  | 0.784209 |
|  45 | 45-KAUSHAMBI       |  529.8  |    0     |  427.86 |  427.86  | 0.807588 |
|  46 | 46-KUSHINAGAR      | 1234.35 |    0.35  | 1006.2  | 1006.55  | 0.815449 |
|  47 | 47-LAKHIMPUR KHERI | 1580.55 |    0.18  | 1264.95 | 1265.13  | 0.800437 |
|  48 | 48-LALITPUR        |  615.9  |    0     |  482.23 |  482.23  | 0.782968 |
|  49 | 49-LUCKNOW         |  582    |    1.4   |  494.81 |  496.21  | 0.852595 |
|  50 | 50-MAHOBA          |  392.1  |    0     |  313.34 |  313.34  | 0.799133 |
|  51 | 51-MAHRAJGANJ      |  883.8  |    0.18  |  723.1  |  723.28  | 0.818375 |
|  52 | 52-MAINPURI        |  653.25 |   -1.47  |  503.63 |  502.16  | 0.76871  |
|  53 | 53-MATHURA         |   24.3  |    0     |   19.77 |   19.77  | 0.81358  |
|  54 | 54-MAU             |  645.75 |    0     |  529.25 |  529.25  | 0.81959  |
|  55 | 55-MEERUT          |  382.05 |   -3.94  |  309.5  |  305.56  | 0.799791 |
|  56 | 56-MIRZAPUR        |  953.25 |  138.96  |  776.77 |  915.73  | 0.96064  |
|  57 | 57-MORADABAD       |  589.8  |   14.411 |  483.35 |  497.761 | 0.843949 |
|  58 | 58-MUZAFFARNAGAR   |  463.35 |   41.29  |  369.88 |  411.17  | 0.887385 |
|  59 | 59-PILIBHIT        |  692.55 |    0     |  556.19 |  556.19  | 0.803104 |
|  60 | 60-PRATAPGARH      | 1054.8  |  104.69  |  828.22 |  932.91  | 0.884443 |
|  61 | 61-RAI BAREILY     |  982.35 |  164.86  |  797.02 |  961.88  | 0.979162 |
|  62 | 62-RAMPUR          |  655.5  |    0     |  531.13 |  531.13  | 0.810267 |
|  63 | 63-SAHARANPUR      |  663.75 |    0     |  540.31 |  540.31  | 0.814026 |
|  64 | 64-SANTKABIR NAGAR |  581.85 |   -0.04  |  471.68 |  471.64  | 0.810587 |
|  65 | 65-SHAHJAHANPUR    | 1276.95 |    0     | 1020.12 | 1020.12  | 0.798872 |
|  66 | 66-SHRAWASTI       |  504.45 |    0     |  405.09 |  405.09  | 0.803033 |
|  67 | 67-SIDDHARTHNAGAR  | 1040.1  |   39.02  |  859.13 |  898.15  | 0.863523 |
|  68 | 68-SITAPUR         | 1735.65 |  490.75  | 1375.59 | 1866.34  | 1.0753   |
|  69 | 69-SONBHADRA       |  904.65 |    1.02  |  696.02 |  697.04  | 0.770508 |
|  70 | 70-SULTANPUR       |  932.7  |    0     |  747.64 |  747.64  | 0.801587 |
|  71 | 71-UNNAO           | 1007.7  |   42.13  |  802.9  |  845.03  | 0.838573 |
|  72 | 72-VARANASI        |  723.6  |    0     |  607.99 |  607.99  | 0.840229 |
|  73 | 73-SAMBHAL         |  603    |    0     |  488.3  |  488.3   | 0.809784 |
|  74 | 74-HAPUR           |  260.7  |    0     |  210.53 |  210.53  | 0.807557 |
|  75 | 75-SHAMLI          |  268.05 |    1.14  |  213.15 |  214.29  | 0.79944  |



label: F=D+E
labeled_formulas: F=D+E
output: {"Arithmetic-Relationship": ["F=D+E"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_377352___xlsx_5e696bd67948a6dabbd8fc6de2fbfac425952fd0.xlsx___line_198