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 |
|------:|:---------------------|----:|----:|----:|----:|------:|----:|------:|
| 43203 | NIFTY  10400 CE      |  75 | 145 | 149 |   0 |   300 |   0 |   300 |
| 43202 | BANK NIFTY 24900 CE  |  40 | 245 | 285 |   0 |  1600 |   0 |  1600 |
| 43201 | BANK NIFTY 24900 CE  |  40 | 165 | 205 |   0 |  1600 |   0 |  1600 |
| 43200 | NIFTY 10300 CE       |  75 | 180 | 190 |   0 |   750 |   0 |   750 |
| 43199 | NIFTY 10400 CE       |  75 | 110 | 125 |   0 |  1125 |   0 |  1125 |
| 43196 | BANK NIFTY 25000 PE  |  40 | 310 | 350 |   0 |  1600 |   0 |  1600 |
| 43195 | BANK NIFTY 24400 CE  |  40 | 125 | 165 |   0 |  1600 |   0 |  1600 |
| 43194 | BANK NIFTY  24000 CE |  40 | 250 | 285 |   0 |  1400 |   0 |  1400 |
| 43193 | NIFTY 10300 PE       |  75 | 175 | 155 |   0 | -1500 |   0 | -1500 |
| 43192 | NIFTY 10300 CE       |  75 | 110 | 125 | 145 |  1125 |   0 |  1125 |
| 43187 | NIFTY 10300 PE       |  75 | 160 | 175 |   0 |  1125 |   0 |  1125 |
| 43186 | BANK NIFTY  24200 CE |  40 | 250 | 285 |   0 |  1400 |   0 |  1400 |
| 43182 | NIFTY  10000 PE      |  75 |  75 |  90 |   0 |  1125 |   0 |  1125 |
| 43182 | BANK NIFTY 23700 PE  |  40 | 175 | 215 |   0 |  1600 |   0 |  1600 |
| 43181 | NIFTY  10000 CE      |  75 | 186 | 201 |   0 |  1125 |   0 |  1125 |
| 43181 | BANK NIFTY 24000 CE  |  40 | 165 | 205 |   0 |  1600 |   0 |  1600 |
| 43180 | NIFTY  10200 CE      |  75 |  95 |  75 |   0 | -1500 |   0 | -1500 |
| 43175 | NIFTY  10200 CE      |  75 | 160 | 140 |   0 | -1500 |   0 | -1500 |
| 43174 | BANK NIFTY 24500 CE  |  40 | 300 | 340 |   0 |  1600 |   0 |  1600 |
| 43173 | NIFTY  10500 PE      |  75 | 175 | 150 |   0 | -1875 |   0 | -1875 |
| 43172 | BANK NIFTY  24800 CE |  40 | 260 | 300 |   0 |  1600 |   0 |  1600 |
| 43172 | NIFTY 10500 CE       |  75 |  90 |  97 |   0 |   525 |   0 |   525 |
| 43168 | NIFTY  10200 CE      |  75 | 158 | 135 |   0 | -1725 |   0 | -1725 |
| 43167 | NIFTY  10200 PE      |  75 | 120 |  95 |   0 | -1875 |   0 | -1875 |
| 43165 | NIFTY  10200 CE      |  75 | 270 | 250 |   0 | -1500 |   0 | -1500 |
| 43164 | NIFTY  10200 CE      |  75 | 240 | 255 | 275 |  1125 |   0 |  1125 |
| 43160 | BANK NIFTY 25000 CE  |  40 | 100 | 140 |   0 |  1600 |   0 |  1600 |
| 43159 | BANK NIFTY  24800 CE |  40 | 210 | 260 | 300 |  2000 |   0 |  2000 |
| 43158 | BANK NIFTY  25200 CE |  40 | 310 | 350 |   0 |  1600 |   0 |  1600 |
| 43157 | NIFTY  10500 CE      |  75 | 200 | 210 |   0 |   750 |   0 |   750 |
| 43154 | NIFTY  10500 CE      |  75 | 158 | 165 |   0 |   525 |   0 |   525 |
| 43153 | NIFTY  10200 CE      |  75 | 150 | 165 |   0 |  1125 |   0 |  1125 |
| 43152 | NIFTY  10200 CE      |  75 | 160 | 175 | 200 |  1125 |   0 |  1125 |
| 43151 | NIFTY  10300 CE      |  75 | 108 | 123 |   0 |  1125 |   0 |  1125 |
| 43150 | NIFTY  10300 CE      |  75 | 300 | 275 |   0 | -1875 |   0 | -1875 |
| 43147 | NIFTY  10500 CE      |  75 | 100 |  75 |   0 | -1875 |   0 | -1875 |
| 43145 | NIFTY  10500 CE      |  75 | 135 | 150 | 170 |  1125 |   0 |  1125 |
| 43143 | BANK NIFTY  25500 CE |  40 | 301 | 340 |   0 |  1560 |   0 |  1560 |
| 43140 | NIFTY  10500 CE      |  75 | 120 | 135 |   0 |  1125 |   0 |  1125 |
| 43138 | NIFTY  10500 CE      |  75 | 155 | 169 |   0 |  1050 |   0 |  1050 |
| 43138 | NIFTY  10600 CE      |  75 | 105 | 110 |   0 |   375 |   0 |   375 |
| 43136 | NIFTY  10500 CE      |  75 | 255 | 270 |   0 |  1125 |   0 |  1125 |
| 43133 | NIFTY  10800 CE      |  75 | 170 | 185 |   0 |  1125 |   0 |  1125 |
| 43130 | NIFTY  11200 CE      |  75 | 130 | 110 |   0 | -1500 |   0 | -1500 |
| 43129 | NIFTY  11200 CE      |  75 | 180 | 160 |   0 | -1500 |   0 | -1500 |
| 43125 | BANK NIFTY  27300 CE |  40 | 130 | 170 |   0 |  1600 |   0 |  1600 |
| 43124 | BANK NIFTY  27300 CE |  40 | 175 | 215 |   0 |  1600 |   0 |  1600 |
| 43124 | NIFTY 11000 CE       |  75 |  95 | 105 |   0 |   750 |   0 |   750 |
| 43123 | NIFTY 11000 CE       |  75 | 100 |  80 |   0 | -1500 |   0 | -1500 |
| 43118 | NIFTY 10700 CE       |  75 | 160 | 140 |   0 | -1500 |   0 | -1500 |
| 43116 | NIFTY 10500 CE       |  75 | 225 | 241 |   0 |  1200 |   0 |  1200 |
| 43115 | NIFTY 10500 CE       |  75 | 265 | 275 |   0 |   750 |   0 |   750 |
| 43112 | NIFTY 10800 PE       |  75 | 180 | 160 |   0 | -1500 |   0 | -1500 |
| 43111 | NIFTY 10500 CE       |  75 | 195 | 210 |   0 |  1125 |   0 |  1125 |
| 43108 | NIFTY 10500 CE       |  75 | 180 | 186 |   0 |   450 |   0 |   450 |
| 43105 | NIFTY 10300 CE       |  75 | 286 | 301 |   0 |  1125 |   0 |  1125 |
| 43104 | BANK NIFTY  25300 CE |  40 | 150 | 150 |   0 |     0 |   0 |     0 |
| 43103 | NIFTY 10300 CE       |  75 | 245 | 225 |   0 | -1500 |   0 | -1500 |
| 43102 | NIFTY 10500 CE       |  75 |  99 | 114 |   0 |  1125 |   0 |  1125 |
| 43101 | BANK NIFTY  25400 CE |  40 | 185 | 135 |   0 | -2000 |   0 | -2000 |



label: G=(E-D)*C
labeled_formulas: G=(E-D)*C
I=(A*H)+G
I=(E-D)*C
I=(C*H)+G
I=(D*H)+G
I=(E*H)+G
I=(F*H)+G
output: {"Arithmetic-Relationship": ["G=(E-D)*C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_152980___xlsx_4e967b3a4ccc787f442d53a2088699382b3bc133.xlsx___line_250