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 |
|:-------|:-----------|:-------|----------:|---------:|---------:|
| PID101 | Widget 101 | 1 X 1  |   30      | 3.59     |  107.7   |
| PID102 | Widget 102 | 1 X 2  |   40      | 2.29     |   91.6   |
| PID103 | Widget 103 | 2 X 1  |   20      | 3.29     |   65.8   |
| PID104 | Widget 104 | 2 X 2  |   10      | 1.95     |   19.5   |
| PID105 | Widget 105 | 2 X 1  |    5      | 1.8      |    9     |
| PID106 | Widget 106 | 2 X 2  |   60      | 1.408    |   84.48  |
| PID107 | Widget 107 | 3 X 1  |  100      | 1.016    |  101.6   |
| PID108 | Widget 108 | 3 X 2  |   71.4286 | 5.95     |  425     |
| PID109 | Widget 109 | 3 X 1  |   79.8214 | 2.895    |  231.083 |
| PID110 | Widget 110 | 3 X 2  |   88.2143 | 2.94683  |  259.953 |
| PID111 | Widget 111 | 4 X 1  |   96.6071 | 2.99867  |  289.693 |
| PID112 | Widget 112 | 4 X 2  |  105      | 3.0505   |  320.303 |
| PID113 | Widget 113 | 4 X 1  |  113.393  | 3.10233  |  351.782 |
| PID114 | Widget 114 | 4 X 2  |  121.786  | 4.15417  |  505.918 |
| PID115 | Widget 115 | 5 X 1  |  130.179  | 3.206    |  417.352 |
| PID116 | Widget 116 | 5 X 2  |  138.571  | 3.25783  |  451.443 |
| PID117 | Widget 117 | 5 X 1  |  146.964  | 3.30967  |  486.403 |
| PID118 | Widget 118 | 5 X 2  |  155.357  | 3.3615   |  522.233 |
| PID119 | Widget 119 | 6 X 1  |  163.75   | 5.41333  |  886.433 |
| PID120 | Widget 120 | 6 X 2  |  172.143  | 3.46517  |  596.504 |
| PID121 | Widget 121 | 6 X 1  |  180.536  | 3.517    |  634.944 |
| PID122 | Widget 122 | 6 X 2  |  188.929  | 3.56883  |  674.255 |
| PID123 | Widget 123 | 7 X 1  |  197.321  | 2.62067  |  517.114 |
| PID124 | Widget 124 | 7 X 2  |  205.714  | 2.0725   |  426.343 |
| PID125 | Widget 125 | 7 X 1  |  214.107  | 1.52433  |  326.371 |
| PID126 | Widget 126 | 7 X 2  |  222.5    | 0.976167 |  217.197 |
| PID127 | Widget 127 | 8 X 1  |  230.893  | 3.59     |  828.905 |
| PID128 | Widget 128 | 8 X 2  |  239.286  | 2.29     |  547.964 |
| PID129 | Widget 129 | 8 X 1  |  247.679  | 3.29     |  814.862 |
| PID130 | Widget 130 | 8 X 2  |  256.071  | 1.95     |  499.339 |
| PID131 | Widget 131 | 9 X 1  |  264.464  | 1.8      |  476.036 |
| PID132 | Widget 132 | 9 X 2  |  272.857  | 1.408    |  384.183 |
| PID133 | Widget 133 | 9 X 1  |  281.25   | 1.016    |  285.75  |
| PID134 | Widget 134 | 9 X 2  |  289.643  | 5.95     | 1723.37  |
| PID135 | Widget 135 | 10 X 1 |  298.036  | 2.895    |  862.813 |
| PID136 | Widget 136 | 10 X 2 |  306.429  | 3.10233  |  950.644 |
| PID137 | Widget 137 | 10 X 1 |  314.821  | 4.15417  | 1307.82  |
| PID138 | Widget 138 | 10 X 2 |  323.214  | 3.206    | 1036.22  |
| PID139 | Widget 139 | 11 X 1 |  331.607  | 3.25783  | 1080.32  |
| PID140 | Widget 140 | 11 X 2 |  340      | 3.30967  | 1125.29  |
| PID141 | Widget 141 | 11 X 1 |  348.393  | 3.2615   | 1136.28  |
| PID142 | Widget 142 | 11 X 2 |  356.786  | 3.21333  | 1146.47  |
| PID143 | Widget 143 | 12 X 1 |  365.179  | 3.16517  | 1155.85  |
| PID144 | Widget 144 | 12 X 2 |  373.571  | 3.117    | 1164.42  |
| PID145 | Widget 145 | 12 X 1 |  381.964  | 3.06883  | 1172.18  |
| PID146 | Widget 146 | 12 X 2 |  390.357  | 3.02067  | 1179.14  |
| PID147 | Widget 147 | 13 X 1 |  398.75   | 2.9725   | 1185.28  |
| PID148 | Widget 148 | 13 X 2 |  407.143  | 2.92433  | 1190.62  |
| PID149 | Widget 149 | 13 X 1 |  415.536  | 2.87617  | 1195.15  |
| PID150 | Widget 150 | 13 X 2 |  423.929  | 4.15417  | 1761.07  |
| PID151 | Widget 151 | 14 X 1 |  432.321  | 3.206    | 1386.02  |
| PID152 | Widget 152 | 14 X 2 |  440.714  | 3.25783  | 1435.77  |
| PID153 | Widget 153 | 14 X 1 |  449.107  | 3.30967  | 1486.39  |
| PID154 | Widget 154 | 14 X 2 |  457.5    | 3.3615   | 1537.89  |
| PID155 | Widget 155 | 15 X 1 |  465.893  | 5.41333  | 2522.03  |
| PID156 | Widget 156 | 15 X 2 |  474.286  | 4.46517  | 2117.76  |
| PID157 | Widget 157 | 15 X 1 |  482.679  | 4.65986  | 2249.21  |
| PID158 | Widget 158 | 15 X 2 |  491.071  | 4.85455  | 2383.93  |
| PID159 | Widget 159 | 16 X 1 |  499.464  | 5.04924  | 2521.91  |
| PID160 | Widget 160 | 16 X 2 |  507.857  | 5.24393  | 2663.17  |
| PID161 | Widget 161 | 16 X 1 |  516.25   | 5.43862  | 2807.69  |
| PID162 | Widget 162 | 16 X 2 |  524.643  | 5.63331  | 2955.48  |
| PID163 | Widget 163 | 17 X 1 |  533.036  | 5.828    | 3106.53  |
| PID164 | Widget 164 | 17 X 2 |  541.429  | 6.02269  | 3260.86  |
| PID165 | Widget 165 | 17 X 1 |  549.821  | 6.21738  | 3418.45  |
| PID166 | Widget 166 | 17 X 2 |  558.214  | 6.41207  | 3579.31  |
| PID167 | Widget 167 | 18 X 1 |  566.607  | 6.60676  | 3743.44  |
| PID168 | Widget 168 | 18 X 2 |  575      | 6.80145  | 3910.84  |
| PID169 | Widget 169 | 18 X 1 |  583.393  | 5.95     | 3471.19  |
| PID170 | Widget 170 | 18 X 2 |  591.786  | 2.895    | 1713.22  |
| PID171 | Widget 171 | 19 X 1 |  600.179  | 3.10233  | 1861.95  |
| PID172 | Widget 172 | 19 X 2 |  608.571  | 4.15417  | 2528.11  |
| PID173 | Widget 173 | 19 X 1 |  616.964  | 3.206    | 1977.99  |
| PID174 | Widget 174 | 19 X 2 |  625.357  | 3.25783  | 2037.31  |
| PID175 | Widget 175 | 20 X 1 |  633.75   | 3.30967  | 2097.5   |
| PID176 | Widget 176 | 20 X 2 |  642.143  | 3.2615   | 2094.35  |
| PID177 | Widget 177 | 20 X 1 |  650.536  | 3.21333  | 2090.39  |
| PID178 | Widget 178 | 20 X 2 |  658.929  | 3.16517  | 2085.62  |
| PID179 | Widget 179 | 21 X 1 |  667.321  | 3.117    | 2080.04  |
| PID180 | Widget 180 | 21 X 2 |  675.714  | 3.06883  | 2073.65  |
| PID181 | Widget 181 | 21 X 1 |  684.107  | 3.02067  | 2066.46  |
| PID182 | Widget 182 | 21 X 2 |  692.5    | 2.9725   | 2058.46  |
| PID183 | Widget 183 | 22 X 1 |  700.893  | 2.92433  | 2049.64  |
| PID184 | Widget 184 | 22 X 2 |  709.286  | 2.87617  | 2040.02  |
| PID185 | Widget 185 | 22 X 1 |  717.679  | 4.15417  | 2981.36  |
| PID186 | Widget 186 | 22 X 2 |  726.071  | 3.206    | 2327.78  |
| PID187 | Widget 187 | 23 X 1 |  734.464  | 3.25783  | 2392.76  |
| PID188 | Widget 188 | 23 X 2 |  742.857  | 3.30967  | 2458.61  |
| PID189 | Widget 189 | 23 X 1 |  751.25   | 3.3615   | 2525.33  |
| PID190 | Widget 190 | 23 X 2 |  759.643  | 5.41333  | 4112.2   |
| PID191 | Widget 191 | 24 X 1 |  768.036  | 4.46517  | 3429.41  |
| PID192 | Widget 192 | 24 X 2 |  776.429  | 4.65986  | 3618.05  |
| PID193 | Widget 193 | 24 X 1 |  784.821  | 3.59     | 2817.51  |
| PID194 | Widget 194 | 24 X 2 |  793.214  | 2.29     | 1816.46  |
| PID195 | Widget 195 | 25 X 1 |  801.607  | 3.29     | 2637.29  |
| PID196 | Widget 196 | 25 X 2 |  810      | 1.95     | 1579.5   |
| PID197 | Widget 197 | 25 X 1 |  818.393  | 1.8      | 1473.11  |
| PID198 | Widget 198 | 25 X 2 |  826.786  | 1.408    | 1164.11  |
| PID199 | Widget 199 | 26 X 1 |  835.179  | 1.016    |  848.541 |
| PID200 | Widget 200 | 26 X 2 |  843.571  | 5.95     | 5019.25  |
| PID201 | Widget 201 | 26 X 1 |  851.964  | 2.895    | 2466.44  |
| PID202 | Widget 202 | 26 X 2 |  860.357  | 2.94683  | 2535.33  |
| PID203 | Widget 203 | 27 X 1 |  868.75   | 2.99867  | 2605.09  |
| PID204 | Widget 204 | 27 X 2 |  877.143  | 3.0505   | 2675.72  |
| PID205 | Widget 205 | 27 X 1 |  885.536  | 3.10233  | 2747.23  |
| PID206 | Widget 206 | 27 X 2 |  893.929  | 4.15417  | 3713.53  |
| PID207 | Widget 207 | 28 X 1 |  902.321  | 3.206    | 2892.84  |
| PID208 | Widget 208 | 28 X 2 |  910.714  | 3.25783  | 2966.96  |
| PID209 | Widget 209 | 28 X 1 |  919.107  | 3.30967  | 3041.94  |
| PID210 | Widget 210 | 28 X 2 |  927.5    | 3.3615   | 3117.79  |
| PID211 | Widget 211 | 29 X 1 |  935.893  | 5.43862  | 5089.96  |
| PID212 | Widget 212 | 29 X 2 |  944.286  | 5.63331  | 5319.45  |
| PID213 | Widget 213 | 29 X 1 |  952.679  | 5.828    | 5552.21  |
| PID214 | Widget 214 | 29 X 2 |  961.071  | 6.02269  | 5788.24  |
| PID215 | Widget 215 | 30 X 1 |  969.464  | 6.21738  | 6027.53  |
| PID216 | Widget 216 | 30 X 2 |  977.857  | 6.41207  | 6270.09  |
| PID217 | Widget 217 | 30 X 1 |  986.25   | 6.60676  | 6515.92  |
| PID218 | Widget 218 | 30 X 2 |  994.643  | 6.80145  | 6765.02  |
| PID219 | Widget 219 | 31 X 1 | 1003.04   | 5.95     | 5968.06  |
| PID220 | Widget 220 | 31 X 2 | 1011.43   | 2.895    | 2928.09  |
| PID221 | Widget 221 | 31 X 1 | 1019.82   | 3.10233  | 3163.83  |
| PID222 | Widget 222 | 31 X 2 | 1028.21   | 4.15417  | 4271.37  |
| PID223 | Widget 223 | 32 X 1 | 1036.61   | 3.206    | 3323.36  |
| PID224 | Widget 224 | 32 X 2 | 1045      | 3.25783  | 3404.44  |
| PID225 | Widget 225 | 32 X 1 | 1053.39   | 3.30967  | 3486.38  |
| PID226 | Widget 226 | 32 X 2 | 1061.79   | 3.2615   | 3463.01  |
| PID227 | Widget 227 | 33 X 1 | 1070.18   | 3.21333  | 3438.84  |
| PID228 | Widget 228 | 33 X 2 | 1078.57   | 3.16517  | 3413.86  |
| PID229 | Widget 229 | 33 X 1 | 1086.96   | 3.117    | 3388.07  |
| PID230 | Widget 230 | 33 X 2 | 1095.36   | 3.06883  | 3361.47  |
| PID231 | Widget 231 | 34 X 1 | 1103.75   | 3.02067  | 3334.06  |
| PID232 | Widget 232 | 34 X 2 | 1112.14   | 2.9725   | 3305.84  |
| PID233 | Widget 233 | 34 X 1 | 1120.54   | 2.92433  | 3276.82  |
| PID234 | Widget 234 | 34 X 2 | 1128.93   | 2.87617  | 3246.99  |
| PID235 | Widget 235 | 35 X 1 | 1137.32   | 4.15417  | 4724.62  |
| PID236 | Widget 236 | 35 X 2 | 1145.71   | 3.206    | 3673.16  |
| PID237 | Widget 237 | 35 X 1 | 1154.11   | 3.25783  | 3759.89  |
| PID238 | Widget 238 | 35 X 2 | 1162.5    | 3.30967  | 3847.49  |
| PID239 | Widget 239 | 36 X 1 | 1170.89   | 3.3615   | 3935.96  |
| PID240 | Widget 240 | 36 X 2 | 1179.29   | 5.41333  | 6383.87  |
| PID241 | Widget 241 | 36 X 1 | 1187.68   | 4.46517  | 5303.18  |
| PID242 | Widget 242 | 36 X 2 | 1196.07   | 4.65986  | 5573.52  |
| PID243 | Widget 243 | 37 X 1 | 1204.46   | 3.59     | 4324.03  |
| PID244 | Widget 244 | 37 X 2 | 1212.86   | 2.29     | 2777.44  |
| PID245 | Widget 245 | 37 X 1 | 1221.25   | 3.29     | 4017.91  |
| PID246 | Widget 246 | 37 X 2 | 1229.64   | 1.95     | 2397.8   |
| PID247 | Widget 247 | 38 X 1 | 1238.04   | 5.43862  | 6733.2   |
| PID248 | Widget 248 | 38 X 2 | 1246.43   | 5.63331  | 7021.52  |
| PID249 | Widget 249 | 38 X 1 | 1254.82   | 5.828    | 7313.1   |
| PID250 | Widget 250 | 38 X 2 | 1263.21   | 6.02269  | 7607.95  |
| PID251 | Widget 251 | 39 X 1 | 1271.61   | 6.21738  | 7906.07  |
| PID252 | Widget 252 | 39 X 2 | 1280      | 6.41207  | 8207.45  |
| PID253 | Widget 253 | 39 X 1 | 1288.39   | 6.60676  | 8512.1   |
| PID254 | Widget 254 | 39 X 2 | 1296.79   | 6.80145  | 8820.03  |
| PID255 | Widget 255 | 40 X 1 | 1305.18   | 5.95     | 7765.81  |
| PID256 | Widget 256 | 40 X 2 | 1313.57   | 2.895    | 3802.79  |
| PID257 | Widget 257 | 40 X 1 | 1321.96   | 3.10233  | 4101.17  |
| PID258 | Widget 258 | 40 X 2 | 1330.36   | 4.15417  | 5526.53  |
| PID259 | Widget 259 | 41 X 1 | 1338.75   | 3.206    | 4292.03  |
| PID260 | Widget 260 | 41 X 2 | 1347.14   | 3.25783  | 4388.77  |
| PID261 | Widget 261 | 41 X 1 | 1355.54   | 3.30967  | 4486.37  |
| PID262 | Widget 262 | 41 X 2 | 1363.93   | 3.2615   | 4448.45  |
| PID263 | Widget 263 | 42 X 1 | 1372.32   | 3.21333  | 4409.73  |
| PID264 | Widget 264 | 42 X 2 | 1380.71   | 3.16517  | 4370.19  |
| PID265 | Widget 265 | 42 X 1 | 1389.11   | 3.117    | 4329.85  |
| PID266 | Widget 266 | 42 X 2 | 1397.5    | 3.06883  | 4288.69  |
| PID267 | Widget 267 | 43 X 1 | 1405.89   | 3.02067  | 4246.73  |
| PID268 | Widget 268 | 43 X 2 | 1414.29   | 2.9725   | 4203.96  |
| PID269 | Widget 269 | 43 X 1 | 1422.68   | 2.92433  | 4160.39  |
| PID270 | Widget 270 | 43 X 2 | 1431.07   | 2.87617  | 4116     |
| PID271 | Widget 271 | 44 X 1 | 1439.46   | 4.15417  | 5979.77  |
| PID272 | Widget 272 | 44 X 2 | 1447.86   | 3.206    | 4641.83  |
| PID273 | Widget 273 | 44 X 1 | 1456.25   | 3.25783  | 4744.22  |
| PID274 | Widget 274 | 44 X 2 | 1464.64   | 3.30967  | 4847.48  |
| PID275 | Widget 275 | 45 X 1 | 1473.04   | 3.3615   | 4951.61  |
| PID276 | Widget 276 | 45 X 2 | 1481.43   | 5.41333  | 8019.47  |
| PID277 | Widget 277 | 45 X 1 | 1489.82   | 4.46517  | 6652.3   |
| PID278 | Widget 278 | 45 X 2 | 1498.21   | 4.65986  | 6981.46  |
| PID279 | Widget 279 | 46 X 1 | 1506.61   | 3.59     | 5408.72  |
| PID280 | Widget 280 | 46 X 2 | 1515      | 2.29     | 3469.35  |
| PID281 | Widget 281 | 46 X 1 | 1523.39   | 3.29     | 5011.96  |
| PID282 | Widget 282 | 46 X 2 | 1531.79   | 1.95     | 2986.98  |
| PID283 | Widget 283 | 47 X 1 | 1540.18   | 2.29     | 3527.01  |
| PID284 | Widget 284 | 47 X 2 | 1548.57   | 3.29     | 5094.8   |
| PID285 | Widget 285 | 47 X 1 | 1556.96   | 1.95     | 3036.08  |
| PID286 | Widget 286 | 47 X 2 | 1565.36   | 1.8      | 2817.64  |
| PID287 | Widget 287 | 48 X 1 | 1573.75   | 1.408    | 2215.84  |
| PID288 | Widget 288 | 48 X 2 | 1582.14   | 1.016    | 1607.46  |
| PID289 | Widget 289 | 48 X 1 | 1590.54   | 5.95     | 9463.69  |
| PID290 | Widget 290 | 48 X 2 | 1598.93   | 2.895    | 4628.9   |
| PID291 | Widget 291 | 49 X 1 | 1607.32   | 3.10233  | 4986.45  |
| PID292 | Widget 292 | 49 X 2 | 1615.71   | 4.15417  | 6711.95  |
| PID293 | Widget 293 | 49 X 1 | 1624.11   | 3.86044  | 6269.78  |



label: G=E*F
labeled_formulas: G=E*F
output: {"Arithmetic-Relationship": ["G=E*F"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_293716___xlsx_22a739207f465a6e7b35a878bdcf63b99b52b28c.xlsx___line_132