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 |      P |         Q |         R |         S |         T |      U |      V |      W |      X |
|----:|-----:|:----------|-------:|-------:|-------:|-------:|-------:|-------:|-------:|-------:|-------:|-------:|-------:|----------:|-------:|----------:|----------:|----------:|----------:|-------:|-------:|-------:|-------:|
|   1 | 2015 | April     | 0.0402 | 0.0441 | 0.0512 | 0.052  | 0.0536 | 0.0639 | 0.0647 | 0.0656 | 0.0663 | 0.0766 | 0.0774 | 0.0783    | 0.079  | 0.0893    | 0.0893    | 0.0893    | 0.0893    | 0.102  | 0.1028 | 0.1036 | 0.1044 |
|   1 | 2015 | May       | 0.0296 | 0.0325 | 0.0378 | 0.0384 | 0.0395 | 0.0471 | 0.0477 | 0.0483 | 0.0489 | 0.0565 | 0.0571 | 0.0577    | 0.0582 | 0.0658    | 0.0658    | 0.0658    | 0.0658    | 0.0752 | 0.0758 | 0.0763 | 0.0769 |
|   1 | 2015 | June      | 0.0405 | 0.0445 | 0.0517 | 0.0525 | 0.0541 | 0.0645 | 0.0653 | 0.0661 | 0.0669 | 0.0773 | 0.0781 | 0.078894  | 0.0797 | 0.090072  | 0.090072  | 0.090072  | 0.090072  | 0.1029 | 0.1037 | 0.1045 | 0.1053 |
|   1 | 2015 | July      | 0.0306 | 0.0336 | 0.0391 | 0.0397 | 0.0409 | 0.0488 | 0.0494 | 0.0499 | 0.0506 | 0.0584 | 0.059  | 0.0596088 | 0.0603 | 0.0680544 | 0.0680544 | 0.0680544 | 0.0680544 | 0.0778 | 0.0784 | 0.079  | 0.0796 |
|   1 | 2015 | August    | 0.0304 | 0.0333 | 0.0387 | 0.0393 | 0.0406 | 0.0483 | 0.0489 | 0.0495 | 0.0501 | 0.0579 | 0.0585 | 0.0592    | 0.0597 | 0.0676    | 0.0676    | 0.0676    | 0.0676    | 0.0771 | 0.0777 | 0.0783 | 0.0789 |
|   1 | 2015 | September | 0.028  | 0.0307 | 0.0357 | 0.0363 | 0.0374 | 0.0445 | 0.0451 | 0.0457 | 0.0462 | 0.0534 | 0.0539 | 0.054544  | 0.0551 | 0.0622173 | 0.0622173 | 0.0622173 | 0.0622173 | 0.0711 | 0.0716 | 0.0722 | 0.0727 |
|   1 | 2015 | October   | 0.04   | 0.044  | 0.0511 | 0.0519 | 0.0535 | 0.0637 | 0.0645 | 0.0653 | 0.0661 | 0.0764 | 0.0772 | 0.07792   | 0.0788 | 0.08896   | 0.08896   | 0.08896   | 0.08896   | 0.1017 | 0.1025 | 0.1033 | 0.1041 |
|   1 | 2015 | November  | 0.025  | 0.0275 | 0.032  | 0.0325 | 0.0335 | 0.0399 | 0.0404 | 0.0408 | 0.0414 | 0.0478 | 0.0483 | 0.0487    | 0.0493 | 0.0556    | 0.0556    | 0.0556    | 0.0556    | 0.0636 | 0.0641 | 0.0646 | 0.0651 |
|   1 | 2015 | December  | 0.0251 | 0.0276 | 0.032  | 0.0325 | 0.0336 | 0.04   | 0.0405 | 0.041  | 0.0415 | 0.0479 | 0.0484 | 0.0489    | 0.0494 | 0.0558    | 0.0558    | 0.0558    | 0.0558    | 0.0638 | 0.0643 | 0.0648 | 0.0653 |
|   1 | 2016 | January   | 0.025  | 0.0274 | 0.0318 | 0.0323 | 0.0333 | 0.0397 | 0.0402 | 0.0408 | 0.0412 | 0.0476 | 0.0481 | 0.0487    | 0.0491 | 0.0556    | 0.0556    | 0.0556    | 0.0556    | 0.0634 | 0.0639 | 0.0644 | 0.0649 |
|   1 | 2016 | February  | 0.025  | 0.0275 | 0.032  | 0.0325 | 0.0335 | 0.0399 | 0.0404 | 0.0408 | 0.0414 | 0.0478 | 0.0483 | 0.0487    | 0.0493 | 0.0556    | 0.0556    | 0.0556    | 0.0556    | 0.0636 | 0.0641 | 0.0646 | 0.0651 |
|   1 | 2016 | March     | 0.0251 | 0.0275 | 0.032  | 0.0325 | 0.0335 | 0.0399 | 0.0404 | 0.041  | 0.0414 | 0.0478 | 0.0483 | 0.0489    | 0.0493 | 0.0558    | 0.0558    | 0.0558    | 0.0558    | 0.0636 | 0.0641 | 0.0646 | 0.0651 |
|   1 | 2016 | April     | 0.025  | 0.0274 | 0.0319 | 0.0324 | 0.0334 | 0.0398 | 0.0403 | 0.0408 | 0.0413 | 0.0477 | 0.0482 | 0.0487    | 0.0492 | 0.0556    | 0.0556    | 0.0556    | 0.0556    | 0.0634 | 0.0639 | 0.0644 | 0.0649 |
|   1 | 2016 | May       | 0.039  | 0.0428 | 0.0497 | 0.0505 | 0.052  | 0.062  | 0.0628 | 0.0636 | 0.0644 | 0.0743 | 0.0751 | 0.076     | 0.0767 | 0.0867    | 0.0867    | 0.0867    | 0.0867    | 0.099  | 0.0997 | 0.1005 | 0.1013 |
|   1 | 2016 | June      | 0.0252 | 0.0276 | 0.0321 | 0.0326 | 0.0336 | 0.0401 | 0.0406 | 0.0411 | 0.0416 | 0.048  | 0.0485 | 0.0491    | 0.0496 | 0.056     | 0.056     | 0.056     | 0.056     | 0.064  | 0.0645 | 0.065  | 0.0655 |
|   1 | 2016 | July      | 0.0251 | 0.0275 | 0.032  | 0.0325 | 0.0335 | 0.0399 | 0.0404 | 0.041  | 0.0414 | 0.0478 | 0.0483 | 0.0489    | 0.0493 | 0.0558    | 0.0558    | 0.0558    | 0.0558    | 0.0637 | 0.0642 | 0.0647 | 0.0652 |
|   1 | 2016 | August    | 0.0256 | 0.0282 | 0.0327 | 0.0332 | 0.0343 | 0.0408 | 0.0413 | 0.0418 | 0.0424 | 0.0489 | 0.0494 | 0.0499    | 0.0505 | 0.0569    | 0.0569    | 0.0569    | 0.0569    | 0.0651 | 0.0656 | 0.0661 | 0.0667 |
|   1 | 2016 | September | 0.0259 | 0.0285 | 0.0331 | 0.0336 | 0.0347 | 0.0413 | 0.0418 | 0.0423 | 0.0429 | 0.0495 | 0.05   | 0.0505    | 0.0511 | 0.0576    | 0.0576    | 0.0576    | 0.0576    | 0.0659 | 0.0664 | 0.0669 | 0.0675 |
|   1 | 2016 | October   | 0.0253 | 0.0278 | 0.0323 | 0.0328 | 0.0338 | 0.0403 | 0.0408 | 0.0413 | 0.0418 | 0.0482 | 0.0488 | 0.0492844 | 0.0498 | 0.0562672 | 0.0562672 | 0.0562672 | 0.0562672 | 0.0642 | 0.0647 | 0.0652 | 0.0657 |
|   1 | 2016 | November  | 0.0253 | 0.0278 | 0.0323 | 0.0328 | 0.0338 | 0.0402 | 0.0407 | 0.0413 | 0.0418 | 0.0482 | 0.0487 | 0.0493    | 0.0497 | 0.0563    | 0.0563    | 0.0563    | 0.0563    | 0.0642 | 0.0647 | 0.0652 | 0.0657 |
|   1 | 2016 | December  | 0.0258 | 0.0283 | 0.0329 | 0.0334 | 0.0344 | 0.041  | 0.0415 | 0.0421 | 0.0426 | 0.0492 | 0.0497 | 0.0503    | 0.0507 | 0.0574    | 0.0574    | 0.0574    | 0.0574    | 0.0654 | 0.066  | 0.0665 | 0.067  |
|   1 | 2017 | January   | 0.025  | 0.0274 | 0.0318 | 0.0323 | 0.0333 | 0.0397 | 0.0402 | 0.0408 | 0.0412 | 0.0476 | 0.0481 | 0.0487    | 0.0491 | 0.0556    | 0.0556    | 0.0556    | 0.0556    | 0.0634 | 0.0639 | 0.0644 | 0.0649 |
|   1 | 2017 | February  | 0.025  | 0.0274 | 0.0319 | 0.0324 | 0.0334 | 0.0398 | 0.0402 | 0.0408 | 0.0412 | 0.0476 | 0.0481 | 0.0487    | 0.0491 | 0.0556    | 0.0556    | 0.0556    | 0.0556    | 0.0634 | 0.0639 | 0.0644 | 0.0649 |
|   1 | 2017 | March     | 0.025  | 0.0274 | 0.0319 | 0.0324 | 0.0334 | 0.0397 | 0.0402 | 0.0408 | 0.0412 | 0.0476 | 0.0481 | 0.0487    | 0.0491 | 0.0556    | 0.0556    | 0.0556    | 0.0556    | 0.0634 | 0.0639 | 0.0644 | 0.0649 |
|   1 | 2017 | April     | 0.0305 | 0.0335 | 0.0389 | 0.0395 | 0.0407 | 0.0485 | 0.0491 | 0.0498 | 0.0504 | 0.0582 | 0.0588 | 0.0594    | 0.06   | 0.0678    | 0.0678    | 0.0678    | 0.0678    | 0.0774 | 0.078  | 0.0787 | 0.0793 |
|   1 | 2017 | May       | 0.0234 | 0.0249 | 0.0268 | 0.0273 | 0.0282 | 0.0311 | 0.0316 | 0.032  | 0.0325 | 0.0354 | 0.0359 | 0.0363    | 0.0368 | 0.0397    | 0.0397    | 0.0397    | 0.0397    | 0.044  | 0.0445 | 0.045  | 0.0455 |
|   1 | 2017 | June      | 0.0252 | 0.0268 | 0.0289 | 0.0294 | 0.0304 | 0.0335 | 0.034  | 0.0345 | 0.035  | 0.0382 | 0.0387 | 0.0391    | 0.0397 | 0.0427    | 0.0427    | 0.0427    | 0.0427    | 0.0475 | 0.048  | 0.0485 | 0.049  |
|   1 | 2017 | July      | 0.0256 | 0.0272 | 0.0293 | 0.0298 | 0.0308 | 0.034  | 0.0345 | 0.035  | 0.0355 | 0.0387 | 0.0392 | 0.0397    | 0.0402 | 0.0434    | 0.0434    | 0.0434    | 0.0434    | 0.0481 | 0.0486 | 0.0491 | 0.0497 |
|   1 | 2017 | August    | 0.0235 | 0.025  | 0.0269 | 0.0274 | 0.0283 | 0.0313 | 0.0317 | 0.0321 | 0.0327 | 0.0356 | 0.0361 | 0.0365    | 0.037  | 0.0399    | 0.0399    | 0.0399    | 0.0399    | 0.0442 | 0.0447 | 0.0452 | 0.0457 |
|   1 | 2017 | September | 0.0432 | 0.0459 | 0.0495 | 0.0503 | 0.0521 | 0.0574 | 0.0583 | 0.0591 | 0.06   | 0.0654 | 0.0663 | 0.067     | 0.068  | 0.0733    | 0.0733    | 0.0733    | 0.0733    | 0.0813 | 0.0822 | 0.083  | 0.0839 |
|   1 | 2017 | October   | 0.0307 | 0.0326 | 0.0351 | 0.0357 | 0.037  | 0.0408 | 0.0414 | 0.042  | 0.0426 | 0.0464 | 0.047  | 0.0476    | 0.0483 | 0.0521    | 0.0521    | 0.0521    | 0.0521    | 0.0577 | 0.0583 | 0.059  | 0.0596 |
|   1 | 2017 | November  | 0.0267 | 0.0283 | 0.0305 | 0.031  | 0.0321 | 0.0354 | 0.036  | 0.0365 | 0.037  | 0.0403 | 0.0409 | 0.0414    | 0.0419 | 0.0453    | 0.0453    | 0.0453    | 0.0453    | 0.0501 | 0.0507 | 0.0512 | 0.0517 |
|   1 | 2017 | December  | 0.0339 | 0.036  | 0.0388 | 0.0395 | 0.0409 | 0.0451 | 0.0457 | 0.0464 | 0.0471 | 0.0513 | 0.052  | 0.0526    | 0.0533 | 0.0575    | 0.0575    | 0.0575    | 0.0575    | 0.0638 | 0.0645 | 0.0651 | 0.0658 |
|   1 | 2018 | January   | 0.025  | 0.0265 | 0.0286 | 0.0291 | 0.0301 | 0.0332 | 0.0337 | 0.0342 | 0.0347 | 0.0378 | 0.0383 | 0.0388    | 0.0393 | 0.0424    | 0.0424    | 0.0424    | 0.0424    | 0.047  | 0.0475 | 0.048  | 0.0485 |
|   1 | 2018 | February  | 0.025  | 0.0266 | 0.0287 | 0.0292 | 0.0302 | 0.0333 | 0.0338 | 0.0342 | 0.0348 | 0.0379 | 0.0384 | 0.0388    | 0.0394 | 0.0424    | 0.0424    | 0.0424    | 0.0424    | 0.0471 | 0.0476 | 0.0481 | 0.0486 |
|   1 | 2018 | March     | 0.025  | 0.0266 | 0.0286 | 0.0291 | 0.0301 | 0.0332 | 0.0337 | 0.0342 | 0.0347 | 0.0378 | 0.0383 | 0.0388    | 0.0393 | 0.0424    | 0.0424    | 0.0424    | 0.0424    | 0.047  | 0.0475 | 0.048  | 0.0485 |
|   1 | 2018 | April     | 0.026  | 0.0276 | 0.0297 | 0.0302 | 0.0313 | 0.0345 | 0.035  | 0.0356 | 0.036  | 0.0393 | 0.0398 | 0.0404    | 0.0408 | 0.0441    | 0.0441    | 0.0441    | 0.0441    | 0.0488 | 0.0493 | 0.0498 | 0.0504 |
|   1 | 2018 | May       | 0.0271 | 0.0287 | 0.031  | 0.0315 | 0.0326 | 0.0359 | 0.0365 | 0.0371 | 0.0376 | 0.0409 | 0.0415 | 0.0421    | 0.0426 | 0.046     | 0.046     | 0.046     | 0.046     | 0.0509 | 0.0514 | 0.052  | 0.0525 |
|   1 | 2018 | June      | 0.0303 | 0.0322 | 0.0346 | 0.0352 | 0.0365 | 0.0402 | 0.0408 | 0.0415 | 0.042  | 0.0458 | 0.0464 | 0.047     | 0.0476 | 0.0514    | 0.0514    | 0.0514    | 0.0514    | 0.0569 | 0.0575 | 0.0581 | 0.0587 |
|   1 | 2018 | July      | 0.0305 | 0.0324 | 0.0349 | 0.0355 | 0.0368 | 0.0406 | 0.0412 | 0.0417 | 0.0424 | 0.0462 | 0.0468 | 0.0473    | 0.048  | 0.0517    | 0.0517    | 0.0517    | 0.0517    | 0.0574 | 0.058  | 0.0586 | 0.0592 |
|   1 | 2018 | August    | 0.0283 | 0.03   | 0.0324 | 0.0329 | 0.0341 | 0.0376 | 0.0381 | 0.0387 | 0.0393 | 0.0428 | 0.0433 | 0.0439    | 0.0445 | 0.048     | 0.048     | 0.048     | 0.048     | 0.0532 | 0.0537 | 0.0543 | 0.0549 |
|   1 | 2018 | September | 0.0311 | 0.033  | 0.0355 | 0.0362 | 0.0374 | 0.0413 | 0.0419 | 0.0425 | 0.0431 | 0.047  | 0.0476 | 0.0483    | 0.0488 | 0.0527    | 0.0527    | 0.0527    | 0.0527    | 0.0584 | 0.059  | 0.0596 | 0.0603 |
|   1 | 2018 | October   | 0.038  | 0.0404 | 0.0435 | 0.0443 | 0.0458 | 0.0505 | 0.0513 | 0.052  | 0.0528 | 0.0575 | 0.0583 | 0.059     | 0.0598 | 0.0644    | 0.0644    | 0.0644    | 0.0644    | 0.0715 | 0.0722 | 0.073  | 0.0738 |
|   1 | 2018 | November  | 0.0365 | 0.0388 | 0.0417 | 0.0425 | 0.0439 | 0.0485 | 0.0492 | 0.0499 | 0.0507 | 0.0552 | 0.0559 | 0.0566    | 0.0574 | 0.0619    | 0.0619    | 0.0619    | 0.0619    | 0.0686 | 0.0693 | 0.0701 | 0.0708 |
|   1 | 2018 | December  | 0.0707 | 0.0751 | 0.0809 | 0.0823 | 0.0852 | 0.0939 | 0.0953 | 0.0967 | 0.0982 | 0.1069 | 0.1083 | 0.1097    | 0.1111 | 0.1199    | 0.1199    | 0.1199    | 0.1199    | 0.1329 | 0.1343 | 0.1357 | 0.1377 |
|   1 | 2019 | January   | 0.061  | 0.0647 | 0.0697 | 0.071  | 0.0734 | 0.081  | 0.0822 | 0.0834 | 0.0846 | 0.0922 | 0.0934 | 0.0947    | 0.0958 | 0.1035    | 0.1035    | 0.1035    | 0.1035    | 0.1146 | 0.1158 | 0.1171 | 0.1183 |
|   1 | 2019 | February  | 0.0665 | 0.0706 | 0.0761 | 0.0774 | 0.0801 | 0.0883 | 0.0896 | 0.091  | 0.0923 | 0.1005 | 0.1019 | 0.1032    | 0.1045 | 0.1128    | 0.1128    | 0.1128    | 0.1128    | 0.125  | 0.1263 | 0.1277 | 0.129  |
|   1 | 2019 | March     | 0.07   | 0.0743 | 0.0801 | 0.0815 | 0.0843 | 0.0929 | 0.0943 | 0.0958 | 0.0971 | 0.1058 | 0.1072 | 0.1086    | 0.11   | 0.1187    | 0.1187    | 0.1187    | 0.1187    | 0.1316 | 0.133  | 0.1344 | 0.1358 |
|   1 | 2019 | April     | 0.075  | 0.0796 | 0.0857 | 0.0872 | 0.0902 | 0.0995 | 0.101  | 0.1026 | 0.104  | 0.1133 | 0.1148 | 0.1164    | 0.1178 | 0.1272    | 0.1272    | 0.1272    | 0.1272    | 0.1409 | 0.1424 | 0.1439 | 0.1454 |
|   1 | 2019 | May       | 0.0719 | 0.0764 | 0.0823 | 0.0837 | 0.0866 | 0.0955 | 0.097  | 0.0984 | 0.0998 | 0.1087 | 0.1102 | 0.1116    | 0.1131 | 0.1219    | 0.1219    | 0.1219    | 0.1219    | 0.1352 | 0.1367 | 0.1381 | 0.1395 |
|   1 | 2019 | June      | 0.072  | 0.0764 | 0.0823 | 0.0838 | 0.0866 | 0.0956 | 0.097  | 0.0985 | 0.0999 | 0.1088 | 0.1102 | 0.1117    | 0.1131 | 0.1221    | 0.1221    | 0.1221    | 0.1221    | 0.1353 | 0.1367 | 0.1382 | 0.1396 |
|   1 | 2019 | July      | 0.0843 | 0.0895 | 0.0964 | 0.0981 | 0.1015 | 0.1119 | 0.1136 | 0.1153 | 0.117  | 0.1274 | 0.1291 | 0.1308    | 0.1325 | 0.143     | 0.143     | 0.143     | 0.143     | 0.1584 | 0.1601 | 0.1618 | 0.1635 |
|   1 | 2019 | August    | 0.078  | 0.0828 | 0.0892 | 0.0908 | 0.0939 | 0.1036 | 0.1051 | 0.1067 | 0.1083 | 0.1179 | 0.1195 | 0.1211    | 0.1226 | 0.1323    | 0.1323    | 0.1323    | 0.1323    | 0.1466 | 0.1482 | 0.1498 | 0.1513 |
|   1 | 2019 | September | 0.0868 | 0.0922 | 0.0993 | 0.101  | 0.1045 | 0.1153 | 0.117  | 0.1187 | 0.1205 | 0.1313 | 0.133  | 0.1347    | 0.1365 | 0.1472    | 0.1472    | 0.1472    | 0.1472    | 0.1632 | 0.1649 | 0.1667 | 0.1684 |
|   1 | 2019 | October   | 0.0868 | 0.0922 | 0.0993 | 0.101  | 0.1045 | 0.1153 | 0.117  | 0.1187 | 0.1205 | 0.1313 | 0.133  | 0.1347    | 0.1365 | 0.1472    | 0.1472    | 0.1472    | 0.1472    | 0.1632 | 0.1649 | 0.1667 | 0.1684 |
|   1 | 2019 | November  | 0.0866 | 0.092  | 0.0991 | 0.1009 | 0.1043 | 0.1151 | 0.1168 | 0.1185 | 0.1203 | 0.131  | 0.1327 | 0.1344    | 0.1362 | 0.1469    | 0.1469    | 0.1469    | 0.1469    | 0.1629 | 0.1646 | 0.1664 | 0.1681 |
|   1 | 2019 | December  | 0.085  | 0.0902 | 0.0972 | 0.0989 | 0.1023 | 0.1128 | 0.1145 | 0.1163 | 0.1179 | 0.1285 | 0.1302 | 0.1319    | 0.1336 | 0.1442    | 0.1442    | 0.1442    | 0.1442    | 0.1597 | 0.1614 | 0.1631 | 0.1648 |



labeled_formulas: R=A*Q
S=A*Q
T=A*Q
S=A*R
T=A*R
T=A*S
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_779932___xlsx_e6b889bac6029f64fac662c0b76b735ffa0a858c.xlsx___line_645