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 |   K |
|:----|:------|:----|:-----|----:|----:|-----:|:----|----:|----:|----:|
| f   | HS+HE | yes | high | 180 | 300 |  120 | yes |   5 |   4 |  -1 |
| m   | HS+HE | yes | high | 140 | 160 |   20 | no  |   2 |   4 |   2 |
| f   | HS+HE | yes | high | 300 | 300 |    0 | yes |   4 |   7 |   3 |
| f   | HS+HE | yes | high | 260 | 250 |  -10 | no  |   5 |   4 |  -1 |
| f   | HS+HE | yes | high | 120 | 230 |  110 | no  |   7 |   4 |  -3 |
| m   | HS+HE | yes | high | 300 | 300 |    0 | yes |   3 |   7 |   4 |
| f   | HS+HE | yes | high | 270 | 220 |  -50 | no  |   4 |   6 |   2 |
| f   | HS+HE | yes | high | 180 | 300 |  120 | yes |   7 |   4 |  -3 |
| m   | HS+HE | yes | high | 280 | 300 |   20 | yes |   6 |   5 |  -1 |
| f   | HS+HE | yes | high | 220 | 160 |  -60 | no  |   3 |   5 |   2 |
| f   | HS+HE | yes | high | 180 | 260 |   80 | no  |   4 |   3 |  -1 |
| f   | HS+HE | yes | high |  70 | 225 |  155 | no  |   3 |   4 |   1 |
| m   | HS+HE | yes | high | 280 | 300 |   20 | yes |   4 |   2 |  -2 |
| f   | HS+HE | yes | high | 180 | 300 |  120 | yes |   6 |   1 |  -5 |
| f   | HS+HE | yes | high | 283 | 220 |  -63 | no  |   2 |   5 |   3 |
| f   | HS+HE | yes | high | 200 | 220 |   20 | no  |   4 |   6 |   2 |
| f   | HS+HE | yes | high | 180 | 300 |  120 | yes |   7 |   7 |   0 |
| f   | HS+HE | yes | high |  73 |  70 |   -3 | no  |   7 |   7 |   0 |
| m   | HS+HE | yes | high | 280 | 290 |   10 | no  |   2 |   1 |  -1 |
| f   | HS+HE | yes | high | 160 | 280 |  120 | no  |   7 |   5 |  -2 |
| f   | HS+HE | yes | high | 300 | 300 |    0 | yes |   4 |   3 |  -1 |
| m   | HS+HE | yes | high | 300 | 300 |    0 | yes |   3 |   7 |   4 |
| f   | HS+HE | yes | high | 180 | 280 |  100 | no  |   6 |   5 |  -1 |
| f   | HS+HE | yes | high |  70 | 110 |   40 | no  |   3 |   4 |   1 |
| f   | HS+HE | yes | high | 220 | 280 |   60 | no  |   7 |   7 |   0 |
| m   | HS+HE | yes | high | 160 | 200 |   40 | no  |   5 |   7 |   2 |
| f   | HS+HE | yes | high | 162 | 245 |   83 | no  |   7 |   4 |  -3 |
| m   | HS+HE | yes | high | 210 | 210 |    0 | no  |   7 |   4 |  -3 |
| f   | HS+HE | yes | high |  90 | 130 |   40 | no  |   6 |   6 |   0 |
| f   | HS+HE | yes | high | 270 | 300 |   30 | yes |   7 |   6 |  -1 |
| m   | HS+HE | yes | high | 180 | 160 |  -20 | no  |   5 |   7 |   2 |
| f   | HS+HE | yes | high | 100 | 190 |   90 | no  |   7 |   7 |   0 |
| m   | HS+HE | yes | high | 152 | 230 |   78 | no  |   6 |   6 |   0 |
| m   | HS+HE | yes | high | 240 | 270 |   30 | no  |   4 |   5 |   1 |
| f   | HS+HE | yes | high |  30 |  90 |   60 | no  |   4 |   6 |   2 |
| f   | HS+HE | yes | high | 193 | 290 |   97 | no  |   5 |   6 |   1 |
| f   | HS+HE | yes | high | 150 | 280 |  130 | no  |   3 |   2 |  -1 |
| m   | HS+HE | yes | high | 300 | 300 |    0 | yes |   6 |   5 |  -1 |
| f   | HS+HE | yes | high |  73 | 129 |   56 | no  |   4 |   6 |   2 |
| f   | HS+HE | yes | high | 280 | 220 |  -60 | no  |   6 |   7 |   1 |
| f   | HS+HE | yes | high | 120 | 300 |  180 | yes |   6 |   4 |  -2 |
| f   | HS+HE | yes | high | 180 | 240 |   60 | no  |   6 |   6 |   0 |
| f   | HS+HE | yes | high | 200 | 240 |   40 | no  |   7 |   7 |   0 |
| f   | HS+HE | yes | high | 120 | 180 |   60 | no  |   6 |   6 |   0 |
| f   | HS+HE | yes | high | 138 | 197 |   59 | no  |   5 |   5 |   0 |
| m   | HS+HE | yes | high | 120 | 100 |  -20 | no  |   6 |   6 |   0 |
| f   | HS+HE | yes | high | 190 | 220 |   30 | no  |   5 |   3 |  -2 |
| f   | HS+HE | yes | high | 257 | 297 |   40 | no  |   4 |   7 |   3 |
| f   | HS+HE | yes | high | 160 | 180 |   20 | no  |   7 |   7 |   0 |
| m   | HS+HE | yes | high | 180 | 240 |   60 | no  |   5 |   6 |   1 |
| f   | HS+HE | yes | high | 210 | 300 |   90 | yes |   6 |   7 |   1 |
| m   | HS+HE | yes | high | 100 | 100 |    0 | no  |   6 |   7 |   1 |
| f   | HS+HE | yes | high | 260 | 300 |   40 | yes |   4 |   7 |   3 |
| m   | HS+HE | yes | high | 270 | 300 |   30 | yes |   4 |   5 |   1 |
| f   | HS+HE | yes | high | 140 | 150 |   10 | no  |   3 |   4 |   1 |
| f   | HS+HE | yes | high | 210 | 180 |  -30 | no  |   4 |   7 |   3 |
| f   | HS+HE | yes | high | 300 | 300 |    0 | yes |   7 |   7 |   0 |
| f   | HS+HE | yes | high |  90 | 100 |   10 | no  |   6 |   5 |  -1 |
| f   | HS+HE | yes | high | 100 | 240 |  140 | no  |   5 |   5 |   0 |
| m   | HS+HE | yes | high | 180 | 270 |   90 | no  |   5 |   6 |   1 |
| m   | HS+HE | yes | high | 280 | 300 |   20 | yes |   3 |   2 |  -1 |
| m   | HS+HE | yes | high | 200 | 300 |  100 | yes |   5 |   4 |  -1 |
| m   | HS+HE | yes | high | 300 | 300 |    0 | yes |   2 |   5 |   3 |
| m   | HS+HE | yes | high | 220 | 240 |   20 | no  |   7 |   7 |   0 |
| f   | HS+HE | yes | high | 200 | 300 |  100 | yes |   7 |   7 |   0 |
| f   | HS+HE | yes | high | 260 | 300 |   40 | yes |   5 |   7 |   2 |
| f   | HS+HE | yes | high | 210 | 150 |  -60 | no  |   4 |   3 |  -1 |
| m   | HS+HE | yes | high | 200 | 300 |  100 | yes |   1 |   1 |   0 |
| f   | HS+HE | yes | high | 300 | 300 |    0 | yes |   2 |   3 |   1 |
| m   | HS+HE | yes | high | 280 | 140 | -140 | no  |   2 |   2 |   0 |
| f   | HS+HE | yes | high | 250 | 300 |   50 | yes |   1 |   6 |   5 |
| f   | HS+HE | yes | high | 300 | 300 |    0 | yes |   5 |   6 |   1 |
| m   | LS+HE | no  | high | 300 | 300 |    0 | yes |   4 |   4 |   0 |
| f   | LS+HE | no  | high | 190 | 260 |   70 | no  |   2 |   7 |   5 |
| m   | LS+HE | no  | high | 300 | 300 |    0 | yes |   5 |   5 |   0 |
| m   | LS+HE | no  | high | 230 | 190 |  -40 | no  |   5 |   5 |   0 |
| f   | LS+HE | no  | high |  50 |  60 |   10 | no  |   7 |   7 |   0 |
| f   | LS+HE | no  | high | 300 | 240 |  -60 | no  |   1 |   4 |   3 |
| m   | LS+HE | no  | high | 260 | 250 |  -10 | no  |   1 |   4 |   3 |
| f   | LS+HE | no  | high | 173 | 230 |   57 | no  |   5 |   7 |   2 |
| f   | LS+HE | no  | high | 300 | 300 |    0 | yes |   2 |   1 |  -1 |
| m   | LS+HE | no  | high | 120 |  60 |  -60 | no  |   4 |   2 |  -2 |
| m   | LS+HE | no  | high | 120 | 110 |  -10 | no  |   7 |   7 |   0 |
| f   | LS+HE | no  | high | 240 | 160 |  -80 | no  |   7 |   3 |  -4 |
| m   | LS+HE | no  | high | 300 | 230 |  -70 | no  |   6 |   5 |  -1 |
| m   | LS+HE | no  | high | 110 | 110 |    0 | no  |   1 |   1 |   0 |
| f   | LS+HE | no  | high | 190 | 223 |   33 | no  |   2 |   1 |  -1 |
| f   | LS+HE | no  | high | 200 | 120 |  -80 | no  |   6 |   5 |  -1 |
| f   | LS+HE | no  | high | 300 | 240 |  -60 | no  |   4 |   4 |   0 |
| m   | LS+HE | no  | high | 150 | 160 |   10 | no  |   4 |   1 |  -3 |
| f   | LS+HE | no  | high | 230 | 230 |    0 | no  |   5 |   6 |   1 |
| m   | LS+HE | no  | high | 300 | 130 | -170 | no  |   2 |   2 |   0 |
| f   | LS+HE | no  | high | 120 | 230 |  110 | no  |   5 |   7 |   2 |
| f   | LS+HE | no  | high | 300 | 230 |  -70 | no  |   4 |   7 |   3 |
| f   | LS+HE | no  | high | 300 | 300 |    0 | yes |   4 |   7 |   3 |
| m   | LS+HE | no  | high | 300 | 300 |    0 | yes |   2 |   1 |  -1 |
| f   | LS+HE | no  | high | 160 |  80 |  -80 | no  |   7 |   7 |   0 |
| f   | LS+HE | no  | high |  50 |  40 |  -10 | no  |   4 |   4 |   0 |
| f   | LS+HE | no  | high |  80 |  90 |   10 | no  |   4 |   5 |   1 |
| f   | LS+HE | no  | high | 260 | 220 |  -40 | no  |   7 |   7 |   0 |
| f   | LS+HE | no  | high | 140 | 130 |  -10 | no  |   7 |   7 |   0 |
| f   | LS+HE | no  | high | 160 | 283 |  123 | no  |   5 |   6 |   1 |
| f   | LS+HE | no  | high | 150 | 220 |   70 | no  |   7 |   7 |   0 |
| m   | LS+HE | no  | high | 130 | 120 |  -10 | no  |   4 |   5 |   1 |
| f   | LS+HE | no  | high |  93 |  95 |    2 | no  |   7 |   7 |   0 |
| m   | LS+HE | no  | high | 240 | 240 |    0 | no  |   6 |   7 |   1 |
| m   | LS+HE | no  | high | 120 |  90 |  -30 | no  |   3 |   4 |   1 |
| f   | LS+HE | no  | high | 189 | 193 |    4 | no  |   7 |   7 |   0 |
| m   | LS+HE | no  | high | 300 | 300 |    0 | yes |   2 |   3 |   1 |
| m   | LS+HE | no  | high | 280 | 280 |    0 | no  |   1 |   7 |   6 |
| m   | LS+HE | no  | high | 140 | 300 |  160 | yes |   4 |   4 |   0 |
| f   | LS+HE | no  | high | 120 | 100 |  -20 | no  |   4 |   6 |   2 |
| f   | LS+HE | no  | high | 280 | 300 |   20 | yes |   1 |   7 |   6 |
| f   | LS+HE | no  | high | 300 | 300 |    0 | yes |   2 |   4 |   2 |
| f   | LS+HE | no  | high | 160 | 120 |  -40 | no  |   6 |   6 |   0 |
| m   | LS+HE | no  | high | 110 | 110 |    0 | no  |   6 |   5 |  -1 |
| m   | LS+HE | no  | high | 260 | 300 |   40 | yes |   2 |   3 |   1 |
| f   | LS+HE | no  | high | 100 | 160 |   60 | no  |   7 |   6 |  -1 |
| m   | LS+HE | no  | high | 300 | 290 |  -10 | no  |   5 |   5 |   0 |
| f   | LS+HE | no  | high | 300 | 300 |    0 | yes |   7 |   7 |   0 |
| f   | LS+HE | no  | high | 260 | 200 |  -60 | no  |   5 |   4 |  -1 |
| m   | LS+HE | no  | high | 300 | 300 |    0 | yes |   5 |   1 |  -4 |
| m   | LS+HE | no  | high | 130 | 230 |  100 | no  |   5 |   5 |   0 |
| f   | LS+HE | no  | high | 130 | 140 |   10 | no  |   4 |   5 |   1 |
| f   | LS+HE | no  | high | 280 | 300 |   20 | yes |   7 |   7 |   0 |
| f   | LS+HE | no  | high | 200 | 240 |   40 | no  |   7 |   7 |   0 |
| f   | LS+HE | no  | high | 185 | 210 |   25 | no  |   3 |   3 |   0 |
| f   | LS+HE | no  | high | 200 | 140 |  -60 | no  |   7 |   5 |  -2 |
| f   | LS+HE | no  | high | 280 | 300 |   20 | yes |   4 |   6 |   2 |
| f   | LS+HE | no  | high | 180 |  90 |  -90 | no  |   7 |   7 |   0 |
| m   | LS+HE | no  | high | 300 | 300 |    0 | yes |   3 |   1 |  -2 |
| f   | LS+HE | no  | high | 120 | 263 |  143 | no  |   2 |   1 |  -1 |
| f   | LS+HE | no  | high | 240 | 260 |   20 | no  |   5 |   6 |   1 |
| f   | LS+HE | no  | high | 100 | 230 |  130 | no  |   3 |   5 |   2 |
| m   | LS+HE | no  | high | 241 | 300 |   59 | yes |   4 |   4 |   0 |
| f   | LS+HE | no  | high | 140 | 120 |  -20 | no  |   4 |   4 |   0 |
| f   | LS+HE | no  | high | 300 | 300 |    0 | yes |   4 |   4 |   0 |
| f   | LS+HE | no  | high | 150 | 220 |   70 | no  |   6 |   6 |   0 |
| m   | HS+LE | yes | low  | 300 | 300 |    0 | yes |   4 |   4 |   0 |
| f   | HS+LE | yes | low  | 170 | 180 |   10 | no  |   3 |   5 |   2 |
| m   | HS+LE | yes | low  | 270 | 290 |   20 | no  |   7 |   7 |   0 |
| m   | HS+LE | yes | low  | 150 | 150 |    0 | no  |   5 |   3 |  -2 |
| m   | HS+LE | yes | low  | 250 | 200 |  -50 | no  |   7 |   5 |  -2 |
| f   | HS+LE | yes | low  | 240 | 280 |   40 | no  |   4 |   4 |   0 |
| f   | HS+LE | yes | low  | 280 | 240 |  -40 | no  |   7 |   7 |   0 |
| m   | HS+LE | yes | low  | 120 | 160 |   40 | no  |   5 |   7 |   2 |
| f   | HS+LE | yes | low  | 190 | 180 |  -10 | no  |   5 |   4 |  -1 |
| f   | HS+LE | yes | low  | 220 | 200 |  -20 | no  |   3 |   7 |   4 |
| m   | HS+LE | yes | low  | 300 | 300 |    0 | yes |   5 |   2 |  -3 |
| f   | HS+LE | yes | low  | 300 | 300 |    0 | yes |   5 |   4 |  -1 |
| m   | HS+LE | yes | low  | 160 | 300 |  140 | yes |   7 |   4 |  -3 |
| f   | HS+LE | yes | low  | 224 | 260 |   36 | no  |   3 |   5 |   2 |
| m   | HS+LE | yes | low  | 300 | 300 |    0 | yes |   6 |   6 |   0 |
| m   | HS+LE | yes | low  | 160 | 150 |  -10 | no  |   1 |   4 |   3 |
| f   | HS+LE | yes | low  | 210 | 170 |  -40 | no  |   7 |   7 |   0 |
| m   | HS+LE | yes | low  |  45 |  90 |   45 | no  |   7 |   4 |  -3 |
| f   | HS+LE | yes | low  | 250 | 240 |  -10 | no  |   5 |   5 |   0 |
| f   | HS+LE | yes | low  | 160 | 180 |   20 | no  |   4 |   4 |   0 |
| m   | HS+LE | yes | low  | 300 | 300 |    0 | yes |   4 |   3 |  -1 |
| f   | HS+LE | yes | low  | 180 | 200 |   20 | no  |   4 |   6 |   2 |
| m   | HS+LE | yes | low  | 300 | 300 |    0 | yes |   4 |   7 |   3 |
| f   | HS+LE | yes | low  | 300 | 300 |    0 | yes |   3 |   3 |   0 |
| f   | HS+LE | yes | low  | 180 | 210 |   30 | no  |   7 |   7 |   0 |
| f   | HS+LE | yes | low  | 180 | 180 |    0 | no  |   6 |   5 |  -1 |
| m   | HS+LE | yes | low  | 110 | 180 |   70 | no  |   7 |   7 |   0 |
| f   | HS+LE | yes | low  | 120 | 160 |   40 | no  |   7 |   7 |   0 |
| m   | HS+LE | yes | low  | 220 | 210 |  -10 | no  |   7 |   7 |   0 |
| f   | HS+LE | yes | low  | 180 | 170 |  -10 | no  |   7 |   7 |   0 |
| f   | HS+LE | yes | low  | 280 | 260 |  -20 | no  |   4 |   6 |   2 |
| m   | HS+LE | yes | low  |  70 | 100 |   30 | no  |   6 |   6 |   0 |
| m   | HS+LE | yes | low  | 130 | 290 |  160 | no  |   7 |   5 |  -2 |



label: K=J-I
labeled_formulas: K=J-I
output: {"Arithmetic-Relationship": ["K=J-I"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_45970___xlsx_e2a81c96a73f8eec6f9502ca06642297046aefb7.xlsx___line_1007