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 |
|------:|:------------------|----------:|:------|-------:|--------:|----------:|-------:|----------:|-------:|
| 44127 | JINDAL STEEL      | 1182.03   | LONG  |  211.5 |  214    |  2955.08  |   2.5  |  2955.08  | 250000 |
| 44127 | ACC               |  154.036  | SHORT | 1623   | 1610    |  2002.46  |  13    |  2002.46  | 250000 |
| 44127 | MARUTI            |   35.5872 | LONG  | 7025   | 7085    |  2135.23  |  60    |  2135.23  | 250000 |
| 44126 | BPCL              |  713.267  | LONG  |  350.5 |  353.8  |  2353.78  |   3.3  |  2353.78  | 250000 |
| 44126 | SRTRANS           |  366.032  | LONG  |  683   |  690    |  2562.23  |   7    |  2562.23  | 250000 |
| 44125 | CEAT              |  234.962  | LONG  | 1064   | 1077.75 |  3230.73  |  13.75 |  3230.73  | 250000 |
| 44125 | ACC               |  156.055  | LONG  | 1602   | 1617    |  2340.82  |  15    |  2340.82  | 250000 |
| 44124 | ASTERDM           | 1805.05   | LONG  |  138.5 |  137.7  | -1444.04  |  -0.8  | -1444.04  | 250000 |
| 44124 | AUROPHA           |  310.559  | SHORT |  805   |  796    |  2795.03  |   9    |  2795.03  | 250000 |
| 44123 | PIDILITIND        |  166.113  | LONG  | 1505   | 1524    |  3156.15  |  19    |  3156.15  | 250000 |
| 44123 | ICICI BANK        |  609.459  | LONG  |  410.2 |  418    |  4753.78  |   7.8  |  4753.78  | 250000 |
| 44123 | APPLTD            |  257.732  | LONG  |  970   |  975    |  1288.66  |   5    |  1288.66  | 250000 |
| 44123 | HINDALCO          | 1369.86   | LONG  |  182.5 |  183.85 |  1849.32  |   1.35 |  1849.32  | 250000 |
| 44123 | BERGERPAINT       |  411.184  | LONG  |  608   |  612    |  1644.74  |   4    |  1644.74  | 250000 |
| 44120 | J K CEMENT        |  142.857  | LONG  | 1750   | 1759    |  1285.71  |   9    |  1285.71  | 250000 |
| 44120 | BAJAJ CORP        | 1355.01   | LONG  |  184.5 |  187.2  |  3658.54  |   2.7  |  3658.54  | 250000 |
| 44119 | JB CHEMICAL       |  237.643  | LONG  | 1052   | 1068    |  3802.28  |  16    |  3802.28  | 250000 |
| 44119 | ALEMBIC           | 2487.56   | SHORT |  100.5 |   99.2  |  3233.83  |   1.3  |  3233.83  | 250000 |
| 44119 | AUROPHA           |  310.559  | SHORT |  805   |  796    |  2795.03  |   9    |  2795.03  | 250000 |
| 44118 | LT                |  277.162  | LONG  |  902   |  915    |  3603.1   |  13    |  3603.1   | 250000 |
| 44118 | RAMCO CEMENT      |  332.447  | LONG  |  752   |  765    |  4321.81  |  13    |  4321.81  | 250000 |
| 44117 | WIPRO             |  683.06   | LONG  |  366   |  372.2  |  4234.97  |   6.2  |  4234.97  | 250000 |
| 44117 | ACC               |  161.082  | LONG  | 1552   | 1538.4  | -2190.72  | -13.6  | -2190.72  | 250000 |
| 44117 | KOTAKBANK         |  188.253  | LONG  | 1328   | 1348    |  3765.06  |  20    |  3765.06  | 250000 |
| 44117 | TCS               |  285.714  | LONG  |  875   |  868    | -2000     |  -7    | -2000     | 250000 |
| 44116 | LUPIN             |  242.483  | LONG  | 1031   | 1041    |  2424.83  |  10    |  2424.83  | 250000 |
| 44116 | MFSL              |  429.553  | LONG  |  582   |  589    |  3006.87  |   7    |  3006.87  | 250000 |
| 44113 | IOC               | 3289.47   | LONG  |   76   |   76.8  |  2631.58  |   0.8  |  2631.58  | 250000 |
| 44113 | UBL               |  253.293  | LONG  |  987   |  999    |  3039.51  |  12    |  3039.51  | 250000 |
| 44112 | TORRENT PHARMA    |   86.9565 | LONG  | 2875   | 2885    |   869.565 |  10    |   869.565 | 250000 |
| 44112 | COLPAL            |  182.216  | LONG  | 1372   | 1359.4  | -2295.92  | -12.6  | -2295.92  | 250000 |
| 44112 | HCL TECH          |  178.571  | LONG  | 1400   | 1417    |  3035.71  |  17    |  3035.71  | 250000 |
| 44111 | ICICI BANK        |  653.595  | LONG  |  382.5 |  384.2  |  1111.11  |   1.7  |  1111.11  | 250000 |
| 44111 | ACC               |  170.532  | LONG  | 1466   | 1480    |  2387.45  |  14    |  2387.45  | 250000 |
| 44111 | BAJAJAUTO         |   82.9463 | LONG  | 3014   | 3070    |  4644.99  |  56    |  4644.99  | 250000 |
| 44110 | BAJAJ FINANCE     |   73.185  | LONG  | 3416   | 3458    |  3073.77  |  42    |  3073.77  | 250000 |
| 44110 | TATA ELEXI        |  185.185  | LONG  | 1350   | 1375    |  4629.63  |  25    |  4629.63  | 250000 |
| 44109 | SUNPHARMA         |  486.855  | LONG  |  513.5 |  520    |  3164.56  |   6.5  |  3164.56  | 250000 |
| 44109 | PETRONET          | 1116.07   | LONG  |  224   |  227    |  3348.21  |   3    |  3348.21  | 250000 |
| 44105 | INDUSIND BANK     |  435.54   | LONG  |  574   |  590    |  6968.64  |  16    |  6968.64  | 250000 |
| 44105 | ASIAN PAINT       |  124.378  | LONG  | 2010   | 2030    |  2487.56  |  20    |  2487.56  | 250000 |
| 44105 | GODREJP           |  289.017  | SHORT |  865   |  873    | -2312.14  |  -8    | -2312.14  | 250000 |
| 44104 | TITAN             |  212.766  | LONG  | 1175   | 1190    |  3191.49  |  15    |  3191.49  | 250000 |
| 44104 | HDFC LTD          |  146.456  | LONG  | 1707   | 1727    |  2929.12  |  20    |  2929.12  | 250000 |
| 44103 | BIRLA CORP        |  370.096  | LONG  |  675.5 |  684    |  3145.82  |   8.5  |  3145.82  | 250000 |
| 44103 | PERSISTANCE       |  190.114  | LONG  | 1315   | 1330    |  2851.71  |  15    |  2851.71  | 250000 |
| 44102 | HEG               |  321.337  | SHORT |  778   |  769.4  |  2763.5   |   8.6  |  2763.5   | 250000 |
| 44102 | ADANI GAS         | 1329.79   | LONG  |  188   |  188.8  |  1063.83  |   0.8  |  1063.83  | 250000 |
| 44099 | CHOLA FINANCE     | 1050.42   | LONG  |  238   |  239.95 |  2048.32  |   1.95 |  2048.32  | 250000 |
| 44099 | TATAMOTORES       | 2008.03   | LONG  |  124.5 |  125.9  |  2811.24  |   1.4  |  2811.24  | 250000 |
| 44098 | FORTIS            | 1811.59   | LONG  |  138   |  140    |  3623.19  |   2    |  3623.19  | 250000 |
| 44098 | CHOLAFI           | 1116.07   | SHORT |  224   |  226.6  | -2901.79  |  -2.6  | -2901.79  | 250000 |
| 44098 | GRAPHITE          | 1488.1    | LONG  |  168   |  170    |  2976.19  |   2    |  2976.19  | 250000 |
| 44097 | BANDHAN BANK      |  943.396  | SHORT |  265   |  261    |  3773.58  |   4    |  3773.58  | 250000 |
| 44097 | GODREJ CONSUMER   |  364.964  | SHORT |  685   |  677    |  2919.71  |   8    |  2919.71  | 250000 |
| 44096 | HCL Tech          |  316.456  | LONG  |  790   |  800    |  3164.56  |  10    |  3164.56  | 250000 |
| 44096 | CANFINH           |  589.623  | LONG  |  424   |  419.4  | -2712.26  |  -4.6  | -2712.26  | 250000 |
| 44096 | ERIS LIFE SCIENCE |  477.099  | LONG  |  524   |  530    |  2862.6   |   6    |  2862.6   | 250000 |
| 44095 | BHARAT FORGE      |  603.865  | LONG  |  414   |  409.4  | -2777.78  |  -4.6  | -2777.78  | 250000 |
| 44095 | ADANI ENTERPRISES |  877.193  | SHORT |  285   |  281    |  3508.77  |   4    |  3508.77  | 250000 |
| 44095 | SUNPHARMA         |  484.496  | SHORT |  516   |  508    |  3875.97  |   8    |  3875.97  | 250000 |
| 44092 | ACC               |  174.216  | LONG  | 1435   | 1426    | -1567.94  |  -9    | -1567.94  | 250000 |
| 44092 | JUBILIANT FOOD    |  104.167  | SHORT | 2400   | 2378    |  2291.67  |  22    |  2291.67  | 250000 |
| 44092 | HDFC BANK         |  231.481  | SHORT | 1080   | 1070    |  2314.81  |  10    |  2314.81  | 250000 |
| 44091 | JSWSTEEL          |  871.08   | SHORT |  287   |  284    |  2613.24  |   3    |  2613.24  | 250000 |
| 44091 | BAJFINANCE        |   70.2247 | SHORT | 3560   | 3524    |  2528.09  |  36    |  2528.09  | 250000 |
| 44090 | GLENMARKPHARMA    |  508.13   | LONG  |  492   |  498    |  3048.78  |   6    |  3048.78  | 250000 |
| 44090 | CANFINH           |  576.037  | LONG  |  434   |  439    |  2880.18  |   5    |  2880.18  | 250000 |
| 44090 | DRREADY           |   78.3699 | LONG  | 3190   | 3230    |  3134.8   |  40    |  3134.8   | 250000 |
| 44089 | HDFC LTD          |  142.857  | LONG  | 1750   | 1765    |  2142.86  |  15    |  2142.86  | 250000 |
| 44089 | ASIAN PAINT       |  123.153  | SHORT | 2030   | 2010    |  2463.05  |  20    |  2463.05  | 250000 |
| 44088 | WIPRO             |  844.595  | LONG  |  296   |  299    |  2533.78  |   3    |  2533.78  | 250000 |
| 44088 | CANFINH           |  588.235  | LONG  |  425   |  419.9  | -3000     |  -5.1  | -3000     | 250000 |
| 44088 | INFOSYS           |  259.067  | LONG  |  965   |  975    |  2590.67  |  10    |  2590.67  | 250000 |
| 44085 | TECHMAINDRA       |  333.778  | LONG  |  749   |  757    |  2670.23  |   8    |  2670.23  | 250000 |
| 44085 | BAJFINANCE        |   72.2543 | LONG  | 3460   | 3500    |  2890.17  |  40    |  2890.17  | 250000 |
| 44084 | ASIANPAINTS       |  123.824  | LONG  | 2019   | 2040    |  2600.3   |  21    |  2600.3   | 250000 |
| 44084 | ACC               |  189.394  | LONG  | 1320   | 1334    |  2651.52  |  14    |  2651.52  | 250000 |
| 44084 | DIVISLAB          |   78.8644 | SHORT | 3170   | 3140    |  2365.93  |  30    |  2365.93  | 250000 |
| 44083 | TATAT STEEL       |  628.141  | LONG  |  398   |  402    |  2512.56  |   4    |  2512.56  | 250000 |
| 44083 | KOTAKBANK         |  186.567  | SHORT | 1340   | 1325    |  2798.51  |  15    |  2798.51  | 250000 |
| 44083 | BAJAJ FINANCE     |   72.8014 | SHORT | 3434   | 3464    | -2184.04  | -30    | -2184.04  | 250000 |
| 44082 | BAJFINANCE        |   70.1262 | SHORT | 3565   | 3520    |  3155.68  |  45    |  3155.68  | 250000 |
| 44082 | UPL               |  499.002  | SHORT |  501   |  496    |  2495.01  |   5    |  2495.01  | 250000 |
| 44081 | HDFCLIFE          |  434.028  | LONG  |  576   |  582    |  2604.17  |   6    |  2604.17  | 250000 |
| 44081 | WIPRO             |  915.751  | LONG  |  273   |  276    |  2747.25  |   3    |  2747.25  | 250000 |
| 44078 | INDUSIND BANK     |  403.226  | LONG  |  620   |  626    |  2419.35  |   6    |  2419.35  | 250000 |
| 44078 | HINDALACO         | 1329.79   | LONG  |  188   |  190    |  2659.57  |   2    |  2659.57  | 250000 |
| 44078 | INFRATE           | 1196.17   | SHORT |  209   |  211.6  | -3110.05  |  -2.6  | -3110.05  | 250000 |
| 44077 | DIVISLAB          |   76.2195 | LONG  | 3280   | 3320    |  3048.78  |  40    |  3048.78  | 250000 |
| 44077 | TECH              |  333.333  | LONG  |  750   |  758    |  2666.67  |   8    |  2666.67  | 250000 |
| 44076 | TITAN             |  226.04   | LONG  | 1106   | 1118    |  2712.48  |  12    |  2712.48  | 250000 |
| 44076 | Sunpharma         |  480.769  | SHORT |  520   |  515    |  2403.85  |   5    |  2403.85  | 250000 |
| 44075 | ASIAN PAINTS      |  129.199  | LONG  | 1935   | 1955    |  2583.98  |  20    |  2583.98  | 250000 |
| 44075 | WIPRO             |  896.057  | SHORT |  279   |  276    |  2688.17  |   3    |  2688.17  | 250000 |



label: C=J/E
I=H*C
labeled_formulas: C=J/E
I=H*C
output: {"Arithmetic-Relationship": ["C=J/E", "I=H*C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_441155___xlsx_bdc5eec1e3adf8fed239ba68f94d07336301ffed.xlsx___line_825