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:
|   I |     J |     K |    L |      M |       N |       O |
|----:|------:|------:|-----:|-------:|--------:|--------:|
|   1 |  8    | 139.6 | 8.14 | 1116.8 |  65.12  | 1181.92 |
|   2 |  8    | 139.6 | 8.14 | 1116.8 |  65.12  | 1181.92 |
|   3 |  8    | 139.6 | 8.14 | 1116.8 |  65.12  | 1181.92 |
|   4 |  8    | 139.6 | 8.14 | 1116.8 |  65.12  | 1181.92 |
|   5 |  8    | 139.6 | 8.14 | 1116.8 |  65.12  | 1181.92 |
|   6 |  8    | 139.6 | 8.14 | 1116.8 |  65.12  | 1181.92 |
|   7 |  8    | 139.6 | 8.14 | 1116.8 |  65.12  | 1181.92 |
|   8 |  8    | 139.6 | 8.14 | 1116.8 |  65.12  | 1181.92 |
|   9 |  8    | 139.6 | 8.14 | 1116.8 |  65.12  | 1181.92 |
|  10 |  8    | 139.6 | 8.14 | 1116.8 |  65.12  | 1181.92 |
|  11 |  8    | 139.6 | 8.14 | 1116.8 |  65.12  | 1181.92 |
|  12 |  8    | 139.6 | 8.14 | 1116.8 |  65.12  | 1181.92 |
|  13 |  8    | 139.6 | 8.14 | 1116.8 |  65.12  | 1181.92 |
|  14 |  8    | 139.6 | 8.14 | 1116.8 |  65.12  | 1181.92 |
|  15 |  8    | 139.6 | 8.14 | 1116.8 |  65.12  | 1181.92 |
|  16 |  8    | 139.6 | 8.14 | 1116.8 |  65.12  | 1181.92 |
|  17 |  8    | 139.6 | 8.14 | 1116.8 |  65.12  | 1181.92 |
|  18 |  8    | 139.6 | 8.14 | 1116.8 |  65.12  | 1181.92 |
|  19 |  8    | 139.6 | 8.14 | 1116.8 |  65.12  | 1181.92 |
|  20 |  8    | 139.6 | 8.14 | 1116.8 |  65.12  | 1181.92 |
|  21 |  8    | 139.6 | 8.14 | 1116.8 |  65.12  | 1181.92 |
|  22 |  8    | 139.6 | 8.14 | 1116.8 |  65.12  | 1181.92 |
|  23 |  8    | 139.6 | 8.14 | 1116.8 |  65.12  | 1181.92 |
|  24 |  8    | 139.6 | 8.14 | 1116.8 |  65.12  | 1181.92 |
|  25 |  8    | 139.6 | 8.14 | 1116.8 |  65.12  | 1181.92 |
|  26 |  8.25 | 139.6 | 8.14 | 1151.7 |  67.155 | 1218.86 |
|  27 |  8.5  | 139.6 | 8.14 | 1186.6 |  69.19  | 1255.79 |
|  28 |  8.75 | 139.6 | 8.14 | 1221.5 |  71.225 | 1292.72 |
|  29 |  9    | 139.6 | 8.14 | 1256.4 |  73.26  | 1329.66 |
|  30 |  9.25 | 139.6 | 8.14 | 1291.3 |  75.295 | 1366.6  |
|  31 |  9.5  | 139.6 | 8.14 | 1326.2 |  77.33  | 1403.53 |
|  32 |  9.75 | 139.6 | 8.14 | 1361.1 |  79.365 | 1440.46 |
|  33 | 10    | 139.6 | 8.14 | 1396   |  81.4   | 1477.4  |
|  34 | 10.25 | 139.6 | 8.14 | 1430.9 |  83.435 | 1514.33 |
|  35 | 10.5  | 139.6 | 8.14 | 1465.8 |  85.47  | 1551.27 |
|  36 | 10.75 | 139.6 | 8.14 | 1500.7 |  87.505 | 1588.21 |
|  37 | 11    | 139.6 | 8.14 | 1535.6 |  89.54  | 1625.14 |
|  38 | 11.25 | 139.6 | 8.14 | 1570.5 |  91.575 | 1662.08 |
|  39 | 11.5  | 139.6 | 8.14 | 1605.4 |  93.61  | 1699.01 |
|  40 | 11.75 | 139.6 | 8.14 | 1640.3 |  95.645 | 1735.94 |
|  41 | 12    | 139.6 | 8.14 | 1675.2 |  97.68  | 1772.88 |
|  42 | 12.25 | 139.6 | 8.14 | 1710.1 |  99.715 | 1809.82 |
|  43 | 12.5  | 139.6 | 8.14 | 1745   | 101.75  | 1846.75 |
|  44 | 12.75 | 139.6 | 8.14 | 1779.9 | 103.785 | 1883.68 |
|  45 | 13    | 139.6 | 8.14 | 1814.8 | 105.82  | 1920.62 |
|  46 | 13.25 | 139.6 | 8.14 | 1849.7 | 107.855 | 1957.56 |
|  47 | 13.5  | 139.6 | 8.14 | 1884.6 | 109.89  | 1994.49 |
|  48 | 13.75 | 139.6 | 8.14 | 1919.5 | 111.925 | 2031.42 |
|  49 | 14    | 139.6 | 8.14 | 1954.4 | 113.96  | 2068.36 |
|  50 | 14.25 | 139.6 | 8.14 | 1989.3 | 115.995 | 2105.3  |
|  51 | 14.5  | 139.6 | 8.14 | 2024.2 | 118.03  | 2142.23 |
|  52 | 14.75 | 139.6 | 8.14 | 2059.1 | 120.065 | 2179.16 |
|  53 | 15    | 139.6 | 8.14 | 2094   | 122.1   | 2216.1  |
|  54 | 15.25 | 139.6 | 8.14 | 2128.9 | 124.135 | 2253.04 |
|  55 | 15.5  | 139.6 | 8.14 | 2163.8 | 126.17  | 2289.97 |
|  56 | 15.75 | 139.6 | 8.14 | 2198.7 | 128.205 | 2326.91 |
|  57 | 16    | 139.6 | 8.14 | 2233.6 | 130.24  | 2363.84 |
|  58 | 16.25 | 139.6 | 8.14 | 2268.5 | 132.275 | 2400.78 |
|  59 | 16.5  | 139.6 | 8.14 | 2303.4 | 134.31  | 2437.71 |
|  60 | 16.75 | 139.6 | 8.14 | 2338.3 | 136.345 | 2474.64 |
|  61 | 17    | 139.6 | 8.14 | 2373.2 | 138.38  | 2511.58 |
|  62 | 17.25 | 139.6 | 8.14 | 2408.1 | 140.415 | 2548.51 |
|  63 | 17.5  | 139.6 | 8.14 | 2443   | 142.45  | 2585.45 |
|  64 | 17.75 | 139.6 | 8.14 | 2477.9 | 144.485 | 2622.39 |
|  65 | 18    | 139.6 | 8.14 | 2512.8 | 146.52  | 2659.32 |
|  66 | 18.25 | 139.6 | 8.14 | 2547.7 | 148.555 | 2696.26 |
|  67 | 18.5  | 139.6 | 8.14 | 2582.6 | 150.59  | 2733.19 |
|  68 | 18.75 | 139.6 | 8.14 | 2617.5 | 152.625 | 2770.12 |
|  69 | 19    | 139.6 | 8.14 | 2652.4 | 154.66  | 2807.06 |
|  70 | 19.25 | 139.6 | 8.14 | 2687.3 | 156.695 | 2843.99 |
|  71 | 19.5  | 139.6 | 8.14 | 2722.2 | 158.73  | 2880.93 |
|  72 | 19.75 | 139.6 | 8.14 | 2757.1 | 160.765 | 2917.86 |
|  73 | 20    | 139.6 | 8.14 | 2792   | 162.8   | 2954.8  |
|  74 | 20.25 | 139.6 | 8.14 | 2826.9 | 164.835 | 2991.74 |
|  75 | 20.5  | 139.6 | 8.14 | 2861.8 | 166.87  | 3028.67 |
|  76 | 20.75 | 139.6 | 8.14 | 2896.7 | 168.905 | 3065.61 |
|  77 | 21    | 139.6 | 8.14 | 2931.6 | 170.94  | 3102.54 |
|  78 | 21.25 | 139.6 | 8.14 | 2966.5 | 172.975 | 3139.47 |
|  79 | 21.5  | 139.6 | 8.14 | 3001.4 | 175.01  | 3176.41 |
|  80 | 21.75 | 139.6 | 8.14 | 3036.3 | 177.045 | 3213.34 |
|  81 | 22    | 139.6 | 8.14 | 3071.2 | 179.08  | 3250.28 |
|  82 | 22.25 | 139.6 | 8.14 | 3106.1 | 181.115 | 3287.22 |
|  83 | 22.5  | 139.6 | 8.14 | 3141   | 183.15  | 3324.15 |
|  84 | 22.75 | 139.6 | 8.14 | 3175.9 | 185.185 | 3361.09 |
|  85 | 23    | 139.6 | 8.14 | 3210.8 | 187.22  | 3398.02 |
|  86 | 23.25 | 139.6 | 8.14 | 3245.7 | 189.255 | 3434.95 |
|  87 | 23.5  | 139.6 | 8.14 | 3280.6 | 191.29  | 3471.89 |
|  88 | 23.75 | 139.6 | 8.14 | 3315.5 | 193.325 | 3508.82 |
|  89 | 24    | 139.6 | 8.14 | 3350.4 | 195.36  | 3545.76 |
|  90 | 24.25 | 139.6 | 8.14 | 3385.3 | 197.395 | 3582.7  |
|  91 | 24.5  | 139.6 | 8.14 | 3420.2 | 199.43  | 3619.63 |
|  92 | 24.75 | 139.6 | 8.14 | 3455.1 | 201.465 | 3656.57 |
|  93 | 25    | 139.6 | 8.14 | 3490   | 203.5   | 3693.5  |
|  94 | 25.25 | 139.6 | 8.14 | 3524.9 | 205.535 | 3730.43 |
|  95 | 25.5  | 139.6 | 8.14 | 3559.8 | 207.57  | 3767.37 |
|  96 | 25.75 | 139.6 | 8.14 | 3594.7 | 209.605 | 3804.3  |
|  97 | 26    | 139.6 | 8.14 | 3629.6 | 211.64  | 3841.24 |
|  98 | 26.25 | 139.6 | 8.14 | 3664.5 | 213.675 | 3878.18 |
|  99 | 26.5  | 139.6 | 8.14 | 3699.4 | 215.71  | 3915.11 |
| 100 | 26.75 | 139.6 | 8.14 | 3734.3 | 217.745 | 3952.05 |
| 101 | 27    | 139.6 | 8.14 | 3769.2 | 219.78  | 3988.98 |
| 102 | 27.25 | 139.6 | 8.14 | 3804.1 | 221.815 | 4025.91 |
| 103 | 27.5  | 139.6 | 8.14 | 3839   | 223.85  | 4062.85 |
| 104 | 27.75 | 139.6 | 8.14 | 3873.9 | 225.885 | 4099.78 |
| 105 | 28    | 139.6 | 8.14 | 3908.8 | 227.92  | 4136.72 |
| 106 | 28.25 | 139.6 | 8.14 | 3943.7 | 229.955 | 4173.65 |
| 107 | 28.5  | 139.6 | 8.14 | 3978.6 | 231.99  | 4210.59 |
| 108 | 28.75 | 139.6 | 8.14 | 4013.5 | 234.025 | 4247.52 |
| 109 | 29    | 139.6 | 8.14 | 4048.4 | 236.06  | 4284.46 |
| 110 | 29.25 | 139.6 | 8.14 | 4083.3 | 238.095 | 4321.4  |
| 111 | 29.5  | 139.6 | 8.14 | 4118.2 | 240.13  | 4358.33 |
| 112 | 29.75 | 139.6 | 8.14 | 4153.1 | 242.165 | 4395.27 |
| 113 | 30    | 139.6 | 8.14 | 4188   | 244.2   | 4432.2  |
| 114 | 30.25 | 139.6 | 8.14 | 4222.9 | 246.235 | 4469.13 |
| 115 | 30.5  | 139.6 | 8.14 | 4257.8 | 248.27  | 4506.07 |
| 116 | 30.75 | 139.6 | 8.14 | 4292.7 | 250.305 | 4543.01 |
| 117 | 31    | 139.6 | 8.14 | 4327.6 | 252.34  | 4579.94 |
| 118 | 31.25 | 139.6 | 8.14 | 4362.5 | 254.375 | 4616.88 |
| 119 | 31.5  | 139.6 | 8.14 | 4397.4 | 256.41  | 4653.81 |
| 120 | 31.75 | 139.6 | 8.14 | 4432.3 | 258.445 | 4690.74 |
| 121 | 32    | 139.6 | 8.14 | 4467.2 | 260.48  | 4727.68 |
| 122 | 32.25 | 139.6 | 8.14 | 4502.1 | 262.515 | 4764.61 |
| 123 | 32.5  | 139.6 | 8.14 | 4537   | 264.55  | 4801.55 |
| 124 | 32.75 | 139.6 | 8.14 | 4571.9 | 266.585 | 4838.48 |
| 125 | 33    | 139.6 | 8.14 | 4606.8 | 268.62  | 4875.42 |



label: M=J*K
N=L*J
O=M+N
labeled_formulas: M=J*K
N=L*J
O=M+N
output: {"Arithmetic-Relationship": ["M=J*K", "N=L*J", "O=M+N"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_522065___xlsx_425b0c6f1527ba3e81efa55216f1393071108df8.xlsx___line_301