This whimsical Python script takes a single integer as input, and expands it to an equivalent arithmetic expression of a size corresponding to the specified depth ("de-solving it"). The output expression, which simplifies to the input number, is returned in a standard format that can be plugged into a calculator program, as well as in TeX formatting.
Note that the expression tree will not always reach the maximum depth specified due to limitations regarding keeping every operand an integer, as well as avoiding huge numbers that would make the program hang.
python desolver.py <Input integer> <Max depth of expression tree>
Example output for python desolver.py 42 8:
Standard Format:
(((2 + 2) + (((1694400 / ((224296565760 / (6 * 54386)) / ((78044 * 4) / (208 + 228)))) - ((((10 / 2) + (17 * 2)) * 101) / (3 * ((18876 / 132) / (21 - 10))))) / (2 * ((((190 + 365) + (319 - 130)) / ((244992 / 464) / (132 / 6))) - (((35 / 5) - 2) + (2 + (7 + 1))))))) - (((((11 + (2 * (7 - 2))) * (((14 + 1) / 3) - 2)) / ((((550 / 22) - (9 - 4)) / ((13 - 6) - 3)) - 2)) * (((((19 * 11) / 11) * 2) + 2) / ((((16 - 4) - (20 / 4)) + 2) - (((4 * 10) / (3 + 2)) / 2)))) / ((((((399289 - 186631) / (120 + 81)) + ((7611 + 16899) / (126 + 3))) - (((88 * 3) + (4 * 31)) - (2 * (34 + 22)))) / ((5 - 2) * (((9 + 15) / 3) + 1))) / ((((13 - 2) - 2) - (2 + 1)) / 2))))
TeX Format:
(((2 + 2) + \frac{(\frac{1694400}{\frac{\frac{224296565760}{6 \times 54386}}{\frac{78044 \times 4}{(208 + 228)}}} - \frac{(\frac{10}{2} + 17 \times 2) \times 101}{3 \times \frac{\frac{18876}{132}}{(21 - 10)}})}{2 \times (\frac{((190 + 365) + (319 - 130))}{\frac{\frac{244992}{464}}{\frac{132}{6}}} - ((\frac{35}{5} - 2) + (2 + (7 + 1))))}) - \frac{\frac{(11 + 2 \times (7 - 2)) \times (\frac{(14 + 1)}{3} - 2)}{(\frac{(\frac{550}{22} - (9 - 4))}{((13 - 6) - 3)} - 2)} \times \frac{(\frac{19 \times 11}{11} \times 2 + 2)}{((((16 - 4) - \frac{20}{4}) + 2) - \frac{\frac{4 \times 10}{(3 + 2)}}{2})}}{\frac{\frac{((\frac{(399289 - 186631)}{(120 + 81)} + \frac{(7611 + 16899)}{(126 + 3)}) - ((88 \times 3 + 4 \times 31) - 2 \times (34 + 22)))}{(5 - 2) \times (\frac{(9 + 15)}{3} + 1)}}{\frac{(((13 - 2) - 2) - (2 + 1))}{2}}})
The output expression simplified to 42. The corresponding TeX:
As a more extreme example, by increasing the depth you can create even further comically large expressions, such as this result from running python desolver.py 88 16 (zoom and scrolling required for full effect)
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