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 |     L |    M |    N |     O |
|------:|-----:|-----:|-----:|-----:|-----:|----:|-----:|----:|----:|----:|------:|-----:|-----:|------:|
| 40180 | 1775 | 1691 |  590 | 4056 |  539 |  64 |  603 |   0 |   0 |   0 |  4659 | 6181 |  316 |  6497 |
| 40187 | 2488 | 2222 |  950 | 5660 | 1547 | 128 | 1675 |   3 |   0 |   3 |  7338 | 7494 | 1254 |  8748 |
| 40194 | 3431 | 2702 | 1342 | 7475 | 1607 | 153 | 1760 |  11 |   0 |  11 |  9246 | 9030 | 1379 | 10409 |
| 40201 | 3310 | 3065 | 1552 | 7927 | 2114 | 244 | 2358 |   2 |   0 |   2 | 10287 | 7109 | 1201 |  8310 |
| 40208 | 3337 | 3124 | 1883 | 8344 | 1624 | 128 | 1752 |   7 |   0 |   7 | 10103 | 5491 | 1225 |  6716 |
| 40215 | 3267 | 2847 | 1598 | 7712 | 1852 | 325 | 2177 |   3 |   0 |   3 |  9892 | 6296 | 1351 |  7647 |
| 40222 | 3336 | 2945 | 1498 | 7779 | 1515 | 283 | 1798 |   0 |   0 |   0 |  9577 | 6404 |  859 |  7263 |
| 40229 | 3596 | 3095 | 1362 | 8053 | 1660 | 236 | 1896 |   0 |   0 |   0 |  9949 | 5871 | 1369 |  7240 |
| 40236 | 3291 | 3214 | 1374 | 7879 | 1591 | 259 | 1850 |  13 |   0 |  13 |  9742 | 5307 |  895 |  6202 |
| 40243 | 3441 | 3136 | 1357 | 7934 | 1686 | 164 | 1850 |   5 |   0 |   5 |  9789 | 4816 |  746 |  5562 |
| 40250 | 3137 | 2796 | 1536 | 7469 | 1429 | 139 | 1568 |  12 |   0 |  12 |  9049 | 4949 |  962 |  5911 |
| 40257 | 3117 | 2580 | 1080 | 6777 | 1103 |  55 | 1158 |  14 |   0 |  14 |  7949 | 4390 | 1027 |  5417 |
| 40264 | 3420 | 2687 | 1599 | 7706 | 1460 | 182 | 1642 |   0 |   0 |   0 |  9348 | 5072 | 1248 |  6320 |
| 40271 | 3407 | 2964 | 1571 | 7942 | 1286 | 100 | 1386 |   1 |   0 |   1 |  9329 | 4298 | 1125 |  5423 |
| 40278 | 2753 | 2522 | 1142 | 6417 |  815 | 166 |  981 |   6 |   0 |   6 |  7404 | 3551 |  650 |  4201 |
| 40285 | 3773 | 3101 | 1534 | 8408 | 1408 | 279 | 1687 |   0 |   0 |   0 | 10095 | 4350 | 1129 |  5479 |
| 40292 | 3648 | 3159 | 1694 | 8501 | 1218 | 371 | 1589 |   0 |   0 |   0 | 10090 | 4234 | 1045 |  5279 |
| 40299 | 3695 | 2942 | 1575 | 8212 | 1360 | 215 | 1575 |   1 |   0 |   1 |  9788 | 4835 | 1072 |  5907 |
| 40306 | 3305 | 2671 | 1253 | 7229 |  993 | 275 | 1268 |   1 |   0 |   1 |  8498 | 6249 |  971 |  7220 |
| 40313 | 3112 | 2604 | 1416 | 7132 | 1298 | 439 | 1737 |   1 |   0 |   1 |  8870 | 6196 |  934 |  7130 |
| 40320 | 3130 | 2623 | 1608 | 7361 | 1162 | 366 | 1528 |   2 |   0 |   2 |  8891 | 6991 | 1527 |  8518 |
| 40327 | 2669 | 2434 | 1417 | 6520 | 1346 | 345 | 1691 |   2 |   0 |   2 |  8213 | 7599 | 1504 |  9103 |
| 40334 | 2845 | 2505 | 1845 | 7195 |  889 | 296 | 1185 |   5 |   0 |   5 |  8385 | 6797 | 1275 |  8072 |
| 40341 | 2662 | 2432 | 1955 | 7049 | 1398 | 217 | 1615 |  10 |   0 |  10 |  8674 | 6973 | 1278 |  8251 |
| 40348 | 2706 | 2653 | 2116 | 7475 |  996 | 430 | 1426 |   0 |   0 |   0 |  8901 | 6363 |  940 |  7303 |
| 40355 | 2843 | 2416 | 2232 | 7491 | 1483 | 391 | 1874 |   1 |   0 |   1 |  9366 | 7269 | 1011 |  8280 |
| 40362 | 2482 | 2287 | 2371 | 7140 | 1688 | 533 | 2221 |  23 |   0 |  23 |  9384 | 6843 | 1142 |  7985 |
| 40369 | 2573 | 2314 | 2479 | 7366 | 1617 | 308 | 1925 |   7 |  82 |  89 |  9380 | 7217 | 1160 |  8377 |
| 40376 | 1756 | 1514 | 1523 | 4793 |  579 |  67 |  646 |   9 |   2 |  11 |  5450 | 5026 | 1059 |  6085 |
| 40383 | 2133 | 1733 | 1554 | 5420 | 1460 | 133 | 1593 |   1 | 114 | 115 |  7128 | 8088 |  921 |  9009 |
| 40390 | 2518 | 2047 | 1781 | 6346 | 1549 | 286 | 1835 |   2 | 124 | 126 |  8307 | 7461 |  944 |  8405 |
| 40397 | 2356 | 2027 | 2017 | 6400 | 1464 | 282 | 1746 |   7 |   2 |   9 |  8155 | 5503 | 1096 |  6599 |
| 40404 | 2618 | 1914 | 1646 | 6178 | 1523 | 278 | 1801 |   5 |  11 |  16 |  7995 | 5638 | 1206 |  6844 |
| 40411 | 2301 | 1958 | 1349 | 5608 | 1425 | 261 | 1686 |  11 |  99 | 110 |  7404 | 6059 | 1235 |  7294 |
| 40418 | 2846 | 2005 | 1182 | 6033 | 1253 | 182 | 1435 |  17 |  79 |  96 |  7564 | 6924 | 1202 |  8126 |
| 40425 | 3158 | 2187 | 1126 | 6471 | 1341 | 223 | 1564 |  11 | 108 | 119 |  8154 | 7696 | 1222 |  8918 |
| 40432 | 3993 | 2618 | 1242 | 7853 | 1492 | 219 | 1711 |  23 |  84 | 107 |  9671 | 7638 | 1243 |  8881 |
| 40439 | 4560 | 2268 | 1142 | 7970 | 1476 | 246 | 1722 |   1 | 136 | 137 |  9829 | 6167 | 1363 |  7530 |
| 40446 | 4468 | 2884 | 1161 | 8513 | 1600 | 286 | 1886 |   0 | 107 | 107 | 10506 | 5468 | 1564 |  7032 |
| 40453 | 4295 | 2759 | 1324 | 8378 | 1636 | 260 | 1896 |   3 | 133 | 136 | 10410 | 6033 | 1509 |  7542 |
| 40460 | 4415 | 2678 | 1225 | 8318 | 1903 | 245 | 2148 |   3 |  91 |  94 | 10560 | 5683 | 1453 |  7136 |
| 40467 | 4035 | 2552 | 1305 | 7892 | 1803 | 192 | 1995 |  10 |  74 |  84 |  9971 | 5698 | 1233 |  6931 |
| 40474 | 4252 | 2593 | 1220 | 8065 | 1973 | 179 | 2152 |   4 | 152 | 156 | 10373 | 5830 | 1320 |  7150 |
| 40481 | 4700 | 2503 | 1188 | 8391 | 1846 | 300 | 2146 |   0 | 112 | 112 | 10649 | 5719 | 1131 |  6850 |
| 40488 | 4304 | 2623 | 1190 | 8117 | 2214 | 249 | 2463 |   0 | 138 | 138 | 10718 | 5577 |  741 |  6318 |
| 40495 | 3917 | 2667 |  983 | 7567 | 2383 | 195 | 2578 |   1 |  91 |  92 | 10237 | 5114 |  869 |  5983 |
| 40502 | 3183 | 2695 | 1285 | 7163 | 2299 | 246 | 2545 |   0 | 124 | 124 |  9832 | 5082 | 1098 |  6180 |
| 40509 | 2986 | 2553 | 1088 | 6627 | 2236 | 237 | 2473 |   4 | 124 | 128 |  9228 | 4654 | 1160 |  5814 |
| 40516 | 2871 | 2468 | 1190 | 6529 | 1997 | 166 | 2163 |   4 | 118 | 122 |  8814 | 4145 | 1097 |  5242 |
| 40523 | 2789 | 2360 | 1477 | 6626 | 1187 | 175 | 1362 |   4 |  73 |  77 |  8065 | 4419 | 1095 |  5514 |
| 40530 | 3307 | 2760 | 1236 | 7303 | 2198 | 184 | 2382 |   0 | 131 | 131 |  9816 | 4992 |  713 |  5705 |
| 40537 | 2672 | 1911 | 1202 | 5785 | 1056 | 200 | 1256 |   0 |  83 |  83 |  7124 | 3896 |  832 |  4728 |
| 40544 | 2038 | 1752 |  920 | 4710 |  709 | 249 |  958 |   0 |  76 |  76 |  5744 | 3035 |  533 |  3568 |



label: H=F+G
K=I+J
O=M+N
L=E+H+K
labeled_formulas: H=F+G
K=I+J
O=M+N
L=E+H+K
output: {"Arithmetic-Relationship": ["H=F+G", "K=I+J", "O=M+N", "L=E+H+K"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_505200___xlsx_d418f34936d8532db8f608bf498911f65891f526.xlsx___line_750