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 |
|:--------|-------:|-------:|----------:|---------:|---------:|----------:|---------:|---------:|---------:|-------:|------:|-------:|-----:|-------:|-----:|-----:|
| TS91-54 |  56.9  |  97.37 | 0.584369  | 0.057489 | 0.001403 |  0.740197 | 0.018486 | 0.094357 | 0.001195 |  509.3 |  53.7 |  562.5 | 10.8 |  581.3 |  7   | 0.96 |
| TS91-65 | 102.43 | 200.86 | 0.509957  | 0.056803 | 0.000991 |  0.752331 | 0.014408 | 0.096265 | 0.000955 |  483.4 |  32.4 |  569.6 |  8.4 |  592.5 |  5.6 | 0.96 |
| TS91-69 | 187.39 | 277.37 | 0.675596  | 0.060373 | 0.000827 |  0.842685 | 0.012768 | 0.101269 | 0.000883 |  616.7 |  34.3 |  620.6 |  7   |  621.8 |  5.2 | 0.99 |
| TS91-10 | 161.78 | 164.81 | 0.981615  | 0.063687 | 0.005211 |  0.886509 | 0.069385 | 0.101438 | 0.000836 |  731.5 | 174.8 |  644.5 | 37.3 |  622.8 |  4.9 | 0.96 |
| TS91-14 |  26    | 115.11 | 0.225871  | 0.060704 | 0.000842 |  0.848492 | 0.011449 | 0.101815 | 0.000811 |  627.8 |  29.6 |  623.8 |  6.3 |  625   |  4.8 | 0.99 |
| TS91-43 |  90.24 | 198.4  | 0.454839  | 0.061351 | 0.000972 |  0.869352 | 0.014917 | 0.102749 | 0.000962 |  650   |  35.2 |  635.2 |  8.1 |  630.5 |  5.6 | 0.99 |
| TS91-22 | 689.25 | 274.66 | 2.50947   | 0.059975 | 0.000752 |  0.85634  | 0.012845 | 0.103456 | 0.001038 |  611.1 |  26.7 |  628.1 |  7   |  634.6 |  6.1 | 0.98 |
| TS91-46 | 120.88 | 190.45 | 0.634707  | 0.059475 | 0.001001 |  0.858516 | 0.015973 | 0.10462  | 0.001017 |  583.4 |  37   |  629.3 |  8.7 |  641.4 |  5.9 | 0.98 |
| TS91-77 | 211.58 | 273.68 | 0.773093  | 0.062239 | 0.000862 |  0.907877 | 0.01334  | 0.105864 | 0.000854 |  683.3 |  34.3 |  655.9 |  7.1 |  648.7 |  5   | 0.98 |
| TS91-55 | 211.45 | 254.17 | 0.831924  | 0.062001 | 0.000872 |  0.910283 | 0.01416  | 0.106708 | 0.001104 |  675.9 |  31.5 |  657.2 |  7.5 |  653.6 |  6.4 | 0.99 |
| TS91-30 | 197.93 | 442.85 | 0.446946  | 0.062711 | 0.000819 |  0.927633 | 0.013322 | 0.107346 | 0.000988 |  698.2 |  28.9 |  666.4 |  7   |  657.3 |  5.8 | 0.98 |
| TS91-73 |  36.51 |  73.04 | 0.499863  | 0.060076 | 0.001634 |  0.885419 | 0.023734 | 0.10842  | 0.001275 |  605.6 |  59.3 |  643.9 | 12.8 |  663.6 |  7.4 | 0.96 |
| TS91-61 | 159.89 | 210.94 | 0.757988  | 0.060988 | 0.000927 |  0.916483 | 0.015382 | 0.108955 | 0.001061 |  638.9 |  33.3 |  660.5 |  8.2 |  666.7 |  6.2 | 0.99 |
| TS91-40 |  27.87 |  26.97 | 1.03337   | 0.060169 | 0.002828 |  0.884066 | 0.041723 | 0.109466 | 0.001795 |  609.3 | 101.8 |  643.2 | 22.5 |  669.6 | 10.4 | 0.95 |
| TS91-79 |  73.79 | 159.16 | 0.463622  | 0.061155 | 0.00104  |  0.920859 | 0.016887 | 0.109512 | 0.001073 |  655.6 |  35.2 |  662.8 |  8.9 |  669.9 |  6.2 | 0.98 |
| TS91-07 | 112.57 | 243.98 | 0.46139   | 0.060268 | 0.000769 |  0.912204 | 0.012564 | 0.109912 | 0.000847 |  613   |  25.9 |  658.2 |  6.7 |  672.2 |  4.9 | 0.97 |
| TS91-02 | 143.1  | 394.88 | 0.362389  | 0.060755 | 0.000627 |  0.931482 | 0.012601 | 0.110919 | 0.000945 |  631.5 |  22.2 |  668.4 |  6.6 |  678.1 |  5.5 | 0.98 |
| TS91-49 | 161.99 | 145.3  | 1.11487   | 0.064692 | 0.001108 |  0.999701 | 0.018952 | 0.111937 | 0.001125 |  764.8 |  36   |  703.7 |  9.6 |  684   |  6.5 | 0.97 |
| TS91-01 |  57.14 |  73.33 | 0.779217  | 0.067486 | 0.001937 |  1.04557  | 0.04308  | 0.112015 | 0.002806 |  853.7 |  65.7 |  726.7 | 21.4 |  684.4 | 16.3 | 0.94 |
| TS91-68 |  72.96 |  76.27 | 0.956602  | 0.060411 | 0.001573 |  0.963569 | 0.027276 | 0.116184 | 0.00126  |  616.7 |  55.5 |  685.1 | 14.1 |  708.6 |  7.3 | 0.96 |
| TS91-06 | 101.49 | 108.32 | 0.936946  | 0.060343 | 0.00107  |  0.972553 | 0.020331 | 0.116919 | 0.001413 |  616.7 |  38.9 |  689.8 | 10.5 |  712.8 |  8.2 | 0.96 |
| TS91-13 | 264.34 | 210.33 | 1.25679   | 0.061594 | 0.000816 |  1.01565  | 0.015217 | 0.119741 | 0.001113 |  661.1 |  27.8 |  711.7 |  7.7 |  729.1 |  6.4 | 0.97 |
| TS91-05 | 261.24 | 213.49 | 1.22366   | 0.06459  | 0.001079 |  1.06652  | 0.018656 | 0.119821 | 0.000811 |  761.1 |  36   |  737   |  9.2 |  729.5 |  4.7 | 0.98 |
| TS91-15 | 130.65 | 167.67 | 0.779209  | 0.066012 | 0.001017 |  1.14157  | 0.01925  | 0.125401 | 0.001194 |  805.6 |  31.5 |  773.3 |  9.1 |  761.6 |  6.9 | 0.98 |
| TS91-47 |  79.92 | 107.98 | 0.740137  | 0.065913 | 0.001344 |  1.13649  | 0.023689 | 0.125575 | 0.001226 |  803.4 |  47.2 |  770.8 | 11.3 |  762.6 |  7   | 0.98 |
| TS91-75 | 733.08 | 478.84 | 1.53095   | 0.065338 | 0.000683 |  1.13785  | 0.014246 | 0.126137 | 0.001056 |  787   |  21.1 |  771.5 |  6.8 |  765.8 |  6.1 | 0.99 |
| TS91-80 | 237.52 | 216.19 | 1.09866   | 0.066634 | 0.001614 |  1.21044  | 0.03021  | 0.132766 | 0.001341 |  827.8 |  50   |  805.4 | 13.9 |  803.6 |  7.6 | 0.99 |
| TS91-11 | 120.23 |  78    | 1.54141   | 0.064731 | 0.00125  |  1.19263  | 0.025265 | 0.133819 | 0.001385 |  764.8 |  40.7 |  797.2 | 11.7 |  809.6 |  7.9 | 0.98 |
| TS91-17 | 328.78 | 235.62 | 1.39538   | 0.066003 | 0.000882 |  1.2183   | 0.01883  | 0.134051 | 0.001406 |  805.6 |  23.1 |  809   |  8.6 |  810.9 |  8   | 0.99 |
| TS91-03 |  97.23 |  71.63 | 1.35739   | 0.062862 | 0.001236 |  1.1602   | 0.022835 | 0.13482  | 0.001147 |  703.4 |  42.6 |  782   | 10.7 |  815.3 |  6.5 | 0.95 |
| TS91-39 |  94.51 | 102.26 | 0.924213  | 0.063654 | 0.00125  |  1.18547  | 0.02573  | 0.134893 | 0.001439 |  731.5 |  42.6 |  793.9 | 12   |  815.7 |  8.2 | 0.97 |
| TS91-38 |  86.8  |  98.09 | 0.884902  | 0.066122 | 0.0012   |  1.24712  | 0.023739 | 0.137042 | 0.001252 |  809.3 |  37.8 |  822.1 | 10.7 |  827.9 |  7.1 | 0.99 |
| TS91-04 | 349.98 | 464.5  | 0.753455  | 0.064531 | 0.000594 |  1.2261   | 0.015935 | 0.137544 | 0.001327 |  759   |  25   |  812.6 |  7.3 |  830.8 |  7.5 | 0.97 |
| TS91-37 |  43.45 |  58.86 | 0.738192  | 0.070101 | 0.001801 |  1.32468  | 0.034397 | 0.138092 | 0.00148  |  931.5 |  52.9 |  856.6 | 15   |  833.9 |  8.4 | 0.97 |
| TS91-12 |  65.81 | 100.18 | 0.656918  | 0.065781 | 0.001068 |  1.25393  | 0.021869 | 0.138395 | 0.001248 |  798.2 |  34.1 |  825.2 |  9.9 |  835.6 |  7.1 | 0.98 |
| TS91-26 | 308.2  | 138.28 | 2.22881   | 0.065342 | 0.001025 |  1.25173  | 0.022201 | 0.138953 | 0.001449 |  787   |  31.5 |  824.2 | 10   |  838.7 |  8.2 | 0.98 |
| TS91-25 | 180.08 | 196.16 | 0.918026  | 0.065098 | 0.000907 |  1.25194  | 0.025053 | 0.138956 | 0.002021 |  777.5 |  28.9 |  824.3 | 11.3 |  838.8 | 11.4 | 0.98 |
| TS91-09 |  93.46 | 122.19 | 0.764874  | 0.06282  | 0.000997 |  1.20834  | 0.022056 | 0.139155 | 0.001245 |  701.9 |   5.6 |  804.4 | 10.2 |  839.9 |  7.1 | 0.95 |
| TS91-41 | 148.3  | 115.67 | 1.2821    | 0.065017 | 0.001219 |  1.24538  | 0.024267 | 0.13946  | 0.001418 |  775.9 |  34.3 |  821.3 | 11   |  841.6 |  8   | 0.97 |
| TS91-74 |  95.43 | 169.59 | 0.56271   | 0.066861 | 0.000959 |  1.28244  | 0.018507 | 0.139734 | 0.00122  |  835.2 |  30.7 |  837.9 |  8.3 |  843.2 |  6.9 | 0.99 |
| TS91-16 |  81.09 |  87.37 | 0.928122  | 0.066965 | 0.001343 |  1.30438  | 0.026605 | 0.142462 | 0.001542 |  836.7 |  42.6 |  847.7 | 11.7 |  858.6 |  8.7 | 0.98 |
| TS91-62 |  60.74 |  63.19 | 0.961228  | 0.067518 | 0.001522 |  1.31193  | 0.028791 | 0.142949 | 0.001629 |  853.7 |  47.1 |  851   | 12.7 |  861.3 |  9.2 | 0.98 |
| TS91-63 |  79.26 |  88.49 | 0.895694  | 0.066964 | 0.001364 |  1.316    | 0.027366 | 0.143325 | 0.001462 |  836.7 |  42.6 |  852.8 | 12   |  863.4 |  8.3 | 0.98 |
| TS91-60 | 157.92 | 133.42 | 1.18363   | 0.066741 | 0.001043 |  1.34556  | 0.02291  | 0.146436 | 0.001408 |  831.5 |  31.5 |  865.6 |  9.9 |  881   |  7.9 | 0.98 |
| TS91-23 |  20.57 |  36.44 | 0.56449   | 0.072103 | 0.002113 |  1.42786  | 0.041549 | 0.146726 | 0.001835 |  988.6 |  59.7 |  900.7 | 17.4 |  882.6 | 10.3 | 0.97 |
| TS91-29 | 339.58 | 366.76 | 0.925892  | 0.070718 | 0.001646 |  1.47729  | 0.042604 | 0.150522 | 0.001378 |  950   |  47.1 |  921.1 | 17.5 |  903.9 |  7.7 | 0.98 |
| TS91-67 | 253.1  | 221.94 | 1.1404    | 0.068197 | 0.00086  |  1.41722  | 0.019285 | 0.150755 | 0.001219 |  875.9 |  25.9 |  896.2 |  8.1 |  905.2 |  6.8 | 0.99 |
| TS91-50 | 162.19 | 200.93 | 0.807197  | 0.067255 | 0.000858 |  1.40274  | 0.020969 | 0.151172 | 0.001541 |  855.6 |  25.9 |  890.1 |  8.9 |  907.5 |  8.6 | 0.98 |
| TS91-51 | 161.34 | 233.55 | 0.690816  | 0.067112 | 0.000809 |  1.41647  | 0.02031  | 0.152637 | 0.001408 |  842.6 |  24.8 |  895.9 |  8.6 |  915.7 |  7.9 | 0.97 |
| TS91-53 |  73.23 |  82.33 | 0.889469  | 0.067229 | 0.001241 |  1.40815  | 0.026732 | 0.152878 | 0.001512 |  855.6 |  38.9 |  892.4 | 11.3 |  917.1 |  8.5 | 0.97 |
| TS91-64 | 169.96 | 125.75 | 1.35157   | 0.067344 | 0.001023 |  1.43352  | 0.024742 | 0.154163 | 0.001479 |  850   |  31.5 |  903   | 10.3 |  924.3 |  8.3 | 0.97 |
| TS91-71 |  75.7  |  88.8  | 0.852477  | 0.067281 | 0.001329 |  1.43073  | 0.029673 | 0.154819 | 0.001556 |  855.6 |  40.7 |  901.9 | 12.4 |  927.9 |  8.7 | 0.97 |
| TS91-21 |  15.43 |  33.76 | 0.45705   | 0.067876 | 0.00241  |  1.43822  | 0.050906 | 0.15615  | 0.002393 |  864.8 |  73   |  905   | 21.2 |  935.3 | 13.4 | 0.96 |
| TS91-76 | 229.7  | 187.6  | 1.22441   | 0.068408 | 0.000849 |  1.48236  | 0.026447 | 0.156595 | 0.001978 |  881.2 |  25.2 |  923.2 | 10.8 |  937.8 | 11   | 0.98 |
| TS91-81 | 202.6  | 223.18 | 0.907787  | 0.077941 | 0.001079 |  1.68571  | 0.023409 | 0.158852 | 0.001856 | 1146.3 |  27.3 | 1003.1 |  8.9 |  950.4 | 10.3 | 0.94 |
| TS91-42 |  31.19 |  44.95 | 0.693882  | 0.070051 | 0.001561 |  1.52718  | 0.03524  | 0.158882 | 0.001748 |  931.5 |  46.3 |  941.4 | 14.2 |  950.6 |  9.7 | 0.99 |
| TS91-36 | 111.69 | 150.73 | 0.740994  | 0.067552 | 0.000914 |  1.47585  | 0.02096  | 0.159    | 0.001473 |  853.7 |  27.8 |  920.5 |  8.6 |  951.2 |  8.2 | 0.96 |
| TS91-44 | 111.37 | 172.16 | 0.646898  | 0.070787 | 0.000931 |  1.57404  | 0.026149 | 0.160822 | 0.001687 |  951.5 |  32.4 |  960   | 10.3 |  961.3 |  9.4 | 0.99 |
| TS91-31 | 128.95 | 111.66 | 1.15485   | 0.069877 | 0.001056 |  1.60372  | 0.025985 | 0.166802 | 0.001702 |  924.1 |  30.4 |  971.7 | 10.2 |  994.5 |  9.4 | 0.97 |
| TS91-28 | 138.86 | 121.18 | 1.1459    | 0.072801 | 0.001064 |  1.71396  | 0.02653  | 0.17144  | 0.001678 | 1009.3 |  25   | 1013.8 |  9.9 | 1020   |  9.2 | 1.01 |
| TS91-32 |  28.02 |  85.53 | 0.327604  | 0.074036 | 0.001277 |  1.7411   | 0.033153 | 0.171491 | 0.002149 | 1042.6 |  34.9 | 1023.9 | 12.3 | 1020.3 | 11.8 | 0.98 |
| TS91-45 | 158.36 | 162.95 | 0.971832  | 0.073835 | 0.001022 |  1.76844  | 0.028674 | 0.173174 | 0.001612 | 1036.7 |  27.8 | 1033.9 | 10.5 | 1029.6 |  8.9 | 0.99 |
| TS91-56 |  61.13 | 123.76 | 0.49394   | 0.071682 | 0.001099 |  1.70899  | 0.028537 | 0.173396 | 0.001778 |  975.9 |  31.5 | 1011.9 | 10.7 | 1030.8 |  9.8 | 1.06 |
| TS91-59 |  14.23 |  38.7  | 0.3677    | 0.073628 | 0.00141  |  1.79401  | 0.034393 | 0.17787  | 0.001613 | 1031.5 |  38.6 | 1043.3 | 12.5 | 1055.3 |  8.8 | 1.02 |
| TS91-34 | 173.35 | 205.83 | 0.8422    | 0.072221 | 0.000867 |  1.80248  | 0.025821 | 0.180472 | 0.001641 |  992.3 |  24.1 | 1046.4 |  9.4 | 1069.6 |  9   | 1.08 |
| TS91-35 | 130.37 | 209.91 | 0.621076  | 0.073058 | 0.000835 |  1.84973  | 0.025811 | 0.183225 | 0.001747 | 1016.7 |  23.3 | 1063.3 |  9.2 | 1084.6 |  9.5 | 1.07 |
| TS91-19 | 382.24 | 360.02 | 1.06172   | 0.077514 | 0.000701 |  2.14173  | 0.023501 | 0.200745 | 0.001912 | 1144.5 |  18.5 | 1162.4 |  7.6 | 1179.3 | 10.3 | 1.03 |
| TS91-58 | 545.08 | 478.8  | 1.13843   | 0.077381 | 0.000666 |  2.15804  | 0.023255 | 0.202018 | 0.001714 | 1131.5 |  17   | 1167.6 |  7.5 | 1186.2 |  9.2 | 1.05 |
| TS91-52 |  63.16 | 360.03 | 0.17543   | 0.114049 | 0.000869 |  5.47718  | 0.061925 | 0.347406 | 0.003389 | 1865.1 |  14.4 | 1897   |  9.8 | 1922.2 | 16.2 | 1.03 |
| TS91-72 | 195.75 | 387.05 | 0.505749  | 0.12117  | 0.000958 |  6.15301  | 0.059976 | 0.368371 | 0.003147 | 1973.8 |  13.1 | 1997.8 |  8.6 | 2021.7 | 14.9 | 1.02 |
| TS91-08 | 126.4  | 283.24 | 0.446265  | 0.153792 | 0.001141 |  8.90698  | 0.093318 | 0.419663 | 0.003621 | 2388.6 |  12.7 | 2328.5 |  9.7 | 2259   | 16.5 | 0.95 |
| TS91-78 | 296.67 | 219.96 | 1.34875   | 0.164533 | 0.001187 | 10.6613   | 0.103823 | 0.468852 | 0.003638 | 2502.8 |  13.1 | 2494.1 |  9.2 | 2478.5 | 16   | 0.99 |
| TS91-24 |  68.84 | 167.6  | 0.41074   | 0.162536 | 0.001349 | 10.555    | 0.10924  | 0.470387 | 0.004039 | 2483.3 |  13.9 | 2484.8 |  9.7 | 2485.3 | 17.8 | 1    |
| TS91-20 | 308.23 | 303.3  | 1.01625   | 0.165479 | 0.001295 | 10.7308   | 0.101991 | 0.470403 | 0.004025 | 2512.7 |  13.3 | 2500.1 |  9   | 2485.3 | 17.7 | 0.99 |
| TS91-18 |  69.5  | 117.43 | 0.591842  | 0.163802 | 0.00132  | 10.8262   | 0.132475 | 0.478808 | 0.005134 | 2495.4 |  12.8 | 2508.3 | 11.5 | 2522.1 | 22.4 | 1.01 |
| TS91-66 | 128.66 | 225.84 | 0.569695  | 0.165137 | 0.001228 | 10.9655   | 0.110293 | 0.480985 | 0.004099 | 2509   |  11.6 | 2520.2 |  9.5 | 2531.6 | 17.9 | 1.01 |
| TS91-57 |  26.58 | 479.92 | 0.0553842 | 0.169935 | 0.001242 | 11.3669   | 0.117265 | 0.483885 | 0.004213 | 2557.1 |  11.6 | 2553.7 |  9.8 | 2544.2 | 18.4 | 0.99 |
| TS91-33 | 107.91 | 106.87 | 1.00973   | 0.166635 | 0.001472 | 11.6429   | 0.129317 | 0.505772 | 0.004478 | 2524.4 |  14.8 | 2576.1 | 10.5 | 2638.6 | 19.2 | 1.05 |
| TS91-70 | 177.9  | 191.1  | 0.930926  | 0.179972 | 0.001326 | 12.8869   | 0.120857 | 0.519251 | 0.004287 | 2653.7 |  12   | 2671.4 |  9   | 2696   | 18.2 | 1.02 |



label: D=B/C
labeled_formulas: D=B/C
output: {"Arithmetic-Relationship": ["D=B/C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_172663___xlsx_59831fa647fabf46223f2b8b91b5950c6cc0355c.xlsx___line_356