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 |
|----:|------------:|-------:|----------------:|----------------:|-----------------:|
|   1 | 0.000432152 |    0.3 |      2.6773e+06 |      2.6773e+06 |      2.6773e+06  |
|   2 | 0.00172861  |    1.2 | 669324          | 669326          |      1.33865e+06 |
|   3 | 0.00388933  |    2.7 | 297478          | 297480          | 892441           |
|   4 | 0.00691424  |    4.8 | 167331          | 167336          | 669344           |
|   5 | 0.010803    |    7.5 | 107092          | 107099          | 535497           |
|   6 | 0.0155552   |   10.8 |  74369.4        |  74380.2        | 446281           |
|   7 | 0.0211698   |   14.7 |  54638.7        |  54653.4        | 382574           |
|   8 | 0.027645    |   19.2 |  41832.8        |  41852          | 334816           |
|   9 | 0.0349786   |   24.3 |  33053.1        |  33077.4        | 297696           |
|  10 | 0.0431668   |   30   |  26773          |  26803          | 268030           |
|  11 | 0.0522048   |   36.3 |  22126.4        |  22162.7        | 243790           |
|  12 | 0.0620856   |   43.2 |  18592.3        |  18635.5        | 223627           |
|  13 | 0.0728007   |   50.7 |  15842          |  15892.7        | 206605           |
|  14 | 0.0843388   |   58.8 |  13659.7        |  13718.5        | 192059           |
|  15 | 0.0966858   |   67.5 |  11899.1        |  11966.6        | 179499           |
|  16 | 0.109824    |   76.8 |  10458.2        |  10535          | 168560           |
|  17 | 0.123734    |   86.7 |   9264.01       |   9350.71       | 158962           |
|  18 | 0.138389    |   97.2 |   8263.27       |   8360.47       | 150488           |
|  19 | 0.153762    |  108.3 |   7416.34       |   7524.64       | 142968           |
|  20 | 0.169816    |  120   |   6693.24       |   6813.24       | 136265           |
|  21 | 0.186515    |  132.3 |   6070.97       |   6203.27       | 130269           |
|  22 | 0.203812    |  145.2 |   5531.61       |   5676.81       | 124890           |
|  23 | 0.221658    |  158.7 |   5061.05       |   5219.75       | 120054           |
|  24 | 0.239997    |  172.8 |   4648.09       |   4820.89       | 115701           |
|  25 | 0.258769    |  187.5 |   4283.68       |   4471.18       | 111779           |
|  26 | 0.277905    |  202.8 |   3960.5        |   4163.3        | 108246           |
|  27 | 0.297333    |  218.7 |   3672.56       |   3891.26       | 105064           |
|  28 | 0.316976    |  235.2 |   3414.92       |   3650.12       | 102203           |
|  29 | 0.336751    |  252.3 |   3183.47       |   3435.77       |  99637.3         |
|  30 | 0.356573    |  270   |   2974.78       |   3244.78       |  97343.3         |
|  31 | 0.376352    |  288.3 |   2785.95       |   3074.25       |  95301.8         |
|  32 | 0.395996    |  307.2 |   2614.55       |   2921.75       |  93496           |
|  33 | 0.415411    |  326.7 |   2458.49       |   2785.19       |  91911.3         |
|  34 | 0.434505    |  346.8 |   2316          |   2662.8        |  90535.3         |
|  35 | 0.453184    |  367.5 |   2185.55       |   2553.05       |  89356.7         |
|  36 | 0.471357    |  388.8 |   2065.82       |   2454.62       |  88366.2         |
|  37 | 0.488937    |  410.7 |   1955.66       |   2366.36       |  87555.3         |
|  38 | 0.50584     |  433.2 |   1854.08       |   2287.28       |  86916.8         |
|  39 | 0.521989    |  456.3 |   1760.22       |   2216.52       |  86444.4         |
|  40 | 0.537312    |  480   |   1673.31       |   2153.31       |  86132.4         |
|  41 | 0.551745    |  504.3 |   1592.68       |   2096.98       |  85976.3         |
|  42 | 0.565233    |  529.2 |   1517.74       |   2046.94       |  85971.6         |
|  43 | 0.577729    |  554.7 |   1447.97       |   2002.67       |  86114.8         |
|  44 | 0.589193    |  580.8 |   1382.9        |   1963.7        |  86402.9         |
|  45 | 0.599599    |  607.5 |   1322.12       |   1929.62       |  86833           |
|  46 | 0.608927    |  634.8 |   1265.26       |   1900.06       |  87402.9         |
|  47 | 0.617167    |  662.7 |   1212          |   1874.7        |  88110.7         |
|  48 | 0.624318    |  691.2 |   1162.02       |   1853.22       |  88954.6         |
|  49 | 0.630388    |  720.3 |   1115.08       |   1835.38       |  89933.4         |
|  50 | 0.635393    |  750   |   1070.92       |   1820.92       |  91046           |
|  51 | 0.639356    |  780.3 |   1029.33       |   1809.63       |  92291.3         |
|  52 | 0.642305    |  811.2 |    990.125      |   1801.32       |  93668.9         |
|  53 | 0.644276    |  842.7 |    953.114      |   1795.81       |  95178.2         |
|  54 | 0.645309    |  874.8 |    918.141      |   1792.94       |  96818.8         |
|  55 | 0.645447    |  907.5 |    885.057      |   1792.56       |  98590.6         |
|  56 | 0.644737    |  940.8 |    853.73       |   1794.53       | 100494           |
|  57 | 0.643229    |  974.7 |    824.038      |   1798.74       | 102528           |
|  58 | 0.640973    | 1009.2 |    795.867      |   1805.07       | 104694           |
|  59 | 0.638022    | 1044.3 |    769.117      |   1813.42       | 106992           |
|  60 | 0.634427    | 1080   |    743.694      |   1823.69       | 109422           |
|  61 | 0.630239    | 1116.3 |    719.51       |   1835.81       | 111984           |
|  62 | 0.625511    | 1153.2 |    696.488      |   1849.69       | 114681           |
|  63 | 0.620291    | 1190.7 |    674.552      |   1865.25       | 117511           |
|  64 | 0.614629    | 1228.8 |    653.637      |   1882.44       | 120476           |
|  65 | 0.608569    | 1267.5 |    633.68       |   1901.18       | 123577           |
|  66 | 0.602158    | 1306.8 |    614.623      |   1921.42       | 126814           |
|  67 | 0.595436    | 1346.7 |    596.413      |   1943.11       | 130189           |
|  68 | 0.588445    | 1387.2 |    579          |   1966.2        | 133702           |
|  69 | 0.58122     | 1428.3 |    562.339      |   1990.64       | 137354           |
|  70 | 0.573798    | 1470   |    546.387      |   2016.39       | 141147           |
|  71 | 0.566212    | 1512.3 |    531.105      |   2043.4        | 145082           |
|  72 | 0.558491    | 1555.2 |    516.454      |   2071.65       | 149159           |
|  73 | 0.550664    | 1598.7 |    502.402      |   2101.1        | 153380           |
|  74 | 0.542756    | 1642.8 |    488.915      |   2131.71       | 157747           |
|  75 | 0.53479     | 1687.5 |    475.964      |   2163.46       | 162260           |
|  76 | 0.52679     | 1732.8 |    463.521      |   2196.32       | 166920           |
|  77 | 0.518774    | 1778.7 |    451.56       |   2230.26       | 171730           |
|  78 | 0.510759    | 1825.2 |    440.056      |   2265.26       | 176690           |
|  79 | 0.502762    | 1872.3 |    428.985      |   2301.29       | 181802           |
|  80 | 0.494798    | 1920   |    418.328      |   2338.33       | 187066           |
|  81 | 0.486879    | 1968.3 |    408.062      |   2376.36       | 192485           |
|  82 | 0.479016    | 2017.2 |    398.17       |   2415.37       | 198060           |
|  83 | 0.471219    | 2066.7 |    388.634      |   2455.33       | 203793           |
|  84 | 0.463498    | 2116.8 |    379.436      |   2496.24       | 209684           |
|  85 | 0.45586     | 2167.5 |    370.56       |   2538.06       | 215735           |
|  86 | 0.448312    | 2218.8 |    361.993      |   2580.79       | 221948           |
|  87 | 0.44086     | 2270.7 |    353.719      |   2624.42       | 228324           |
|  88 | 0.433508    | 2323.2 |    345.725      |   2668.93       | 234865           |
|  89 | 0.426261    | 2376.3 |    338          |   2714.3        | 241573           |
|  90 | 0.419122    | 2430   |    330.531      |   2760.53       | 248448           |
|  91 | 0.412095    | 2484.3 |    323.306      |   2807.61       | 255492           |
|  92 | 0.405181    | 2539.2 |    316.316      |   2855.52       | 262707           |
|  93 | 0.398382    | 2594.7 |    309.55       |   2904.25       | 270095           |
|  94 | 0.391699    | 2650.8 |    302.999      |   2953.8        | 277657           |
|  95 | 0.385133    | 2707.5 |    296.654      |   3004.15       | 285395           |
|  96 | 0.378686    | 2764.8 |    290.505      |   3055.31       | 293309           |
|  97 | 0.372355    | 2822.7 |    284.546      |   3107.25       | 301403           |
|  98 | 0.366143    | 2881.2 |    278.769      |   3159.97       | 309677           |
|  99 | 0.360047    | 2940.3 |    273.166      |   3213.47       | 318133           |
| 100 | 0.354068    | 3000   |    267.73       |   3267.73       | 326773           |
| 101 | 0.348205    | 3060.3 |    262.454      |   3322.75       | 335598           |
| 102 | 0.342456    | 3121.2 |    257.334      |   3378.53       | 344610           |
| 103 | 0.336821    | 3182.7 |    252.361      |   3435.06       | 353811           |
| 104 | 0.331297    | 3244.8 |    247.531      |   3492.33       | 363202           |
| 105 | 0.325884    | 3307.5 |    242.839      |   3550.34       | 372786           |
| 106 | 0.32058     | 3370.8 |    238.279      |   3609.08       | 382562           |
| 107 | 0.315384    | 3434.7 |    233.846      |   3668.55       | 392534           |
| 108 | 0.310293    | 3499.2 |    229.535      |   3728.74       | 402703           |
| 109 | 0.305306    | 3564.3 |    225.343      |   3789.64       | 413071           |
| 110 | 0.300421    | 3630   |    221.264      |   3851.26       | 423639           |
| 111 | 0.295636    | 3696.3 |    217.296      |   3913.6        | 434409           |
| 112 | 0.29095     | 3763.2 |    213.433      |   3976.63       | 445383           |
| 113 | 0.28636     | 3830.7 |    209.672      |   4040.37       | 456562           |
| 114 | 0.281864    | 3898.8 |    206.009      |   4104.81       | 467948           |
| 115 | 0.277462    | 3967.5 |    202.442      |   4169.94       | 479543           |
| 116 | 0.27315     | 4036.8 |    198.967      |   4235.77       | 491349           |
| 117 | 0.268927    | 4106.7 |    195.58       |   4302.28       | 503367           |
| 118 | 0.264791    | 4177.2 |    192.279      |   4369.48       | 515599           |
| 119 | 0.260741    | 4248.3 |    189.061      |   4437.36       | 528046           |
| 120 | 0.256773    | 4320   |    185.923      |   4505.92       | 540711           |
| 121 | 0.252887    | 4392.3 |    182.863      |   4575.16       | 553595           |
| 122 | 0.249081    | 4465.2 |    179.878      |   4645.08       | 566699           |
| 123 | 0.245352    | 4538.7 |    176.965      |   4715.66       | 580027           |
| 124 | 0.2417      | 4612.8 |    174.122      |   4786.92       | 593578           |
| 125 | 0.238122    | 4687.5 |    171.347      |   4858.85       | 607356           |
| 126 | 0.234617    | 4762.8 |    168.638      |   4931.44       | 621361           |
| 127 | 0.231183    | 4838.7 |    165.993      |   5004.69       | 635596           |
| 128 | 0.227818    | 4915.2 |    163.409      |   5078.61       | 650062           |
| 129 | 0.224521    | 4992.3 |    160.886      |   5153.19       | 664761           |
| 130 | 0.221291    | 5070   |    158.42       |   5228.42       | 679695           |
| 131 | 0.218124    | 5148.3 |    156.011      |   5304.31       | 694865           |
| 132 | 0.215022    | 5227.2 |    153.656      |   5380.86       | 710273           |
| 133 | 0.21198     | 5306.7 |    151.354      |   5458.05       | 725921           |
| 134 | 0.208999    | 5386.8 |    149.103      |   5535.9        | 741811           |
| 135 | 0.206077    | 5467.5 |    146.902      |   5614.4        | 757944           |
| 136 | 0.203212    | 5548.8 |    144.75       |   5693.55       | 774323           |
| 137 | 0.200404    | 5630.7 |    142.645      |   5773.34       | 790948           |
| 138 | 0.19765     | 5713.2 |    140.585      |   5853.78       | 807822           |
| 139 | 0.19495     | 5796.3 |    138.569      |   5934.87       | 824947           |
| 140 | 0.192301    | 5880   |    136.597      |   6016.6        | 842324           |
| 141 | 0.189704    | 5964.3 |    134.666      |   6098.97       | 859954           |
| 142 | 0.187157    | 6049.2 |    132.776      |   6181.98       | 877841           |
| 143 | 0.184658    | 6134.7 |    130.926      |   6265.63       | 895984           |
| 144 | 0.182207    | 6220.8 |    129.114      |   6349.91       | 914388           |
| 145 | 0.179802    | 6307.5 |    127.339      |   6434.84       | 933052           |
| 146 | 0.177443    | 6394.8 |    125.6        |   6520.4        | 951978           |
| 147 | 0.175128    | 6482.7 |    123.897      |   6606.6        | 971170           |
| 148 | 0.172856    | 6571.2 |    122.229      |   6693.43       | 990627           |
| 149 | 0.170626    | 6660.3 |    120.594      |   6780.89       |      1.01035e+06 |
| 150 | 0.168438    | 6750   |    118.991      |   6868.99       |      1.03035e+06 |
| 151 | 0.16629     | 6840.3 |    117.42       |   6957.72       |      1.05062e+06 |
| 152 | 0.164181    | 6931.2 |    115.88       |   7047.08       |      1.07116e+06 |
| 153 | 0.162111    | 7022.7 |    114.37       |   7137.07       |      1.09197e+06 |
| 154 | 0.160079    | 7114.8 |    112.89       |   7227.69       |      1.11306e+06 |
| 155 | 0.158083    | 7207.5 |    111.438      |   7318.94       |      1.13444e+06 |
| 156 | 0.156123    | 7300.8 |    110.014      |   7410.81       |      1.15609e+06 |
| 157 | 0.154198    | 7394.7 |    108.617      |   7503.32       |      1.17802e+06 |
| 158 | 0.152308    | 7489.2 |    107.246      |   7596.45       |      1.20024e+06 |
| 159 | 0.150451    | 7584.3 |    105.902      |   7690.2        |      1.22274e+06 |
| 160 | 0.148627    | 7680   |    104.582      |   7784.58       |      1.24553e+06 |
| 161 | 0.146835    | 7776.3 |    103.287      |   7879.59       |      1.26861e+06 |
| 162 | 0.145074    | 7873.2 |    102.016      |   7975.22       |      1.29198e+06 |
| 163 | 0.143344    | 7970.7 |    100.768      |   8071.47       |      1.31565e+06 |



label: E=D+C
F=E*A
labeled_formulas: E=D+C
F=E*A
output: {"Arithmetic-Relationship": ["E=D+C", "F=E*A"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_90259___xlsx_cbf3ce12191d09a3fe0f07ad0afa721f17b88c91.xlsx___line_468