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==code(python) |

while abs(c - lo * lo * lo) < 1e-3:

while abs(c - lo * lo * lo) > 1e-3:

==
This doesn't work. For large numbers like 1e37 the code goes into an infinite loop. Try to figure out why. Discuss it in the comment section. Let’s try using the *relative error* (|(a - b) / b| < eps). There are some weird cases when a and b are close or equal to 0. Can the code be cleaner?

notes:
* Thanks Tomek for pointing out the iteration problem and possible efficient solutions.

* When c is large, mid * mid * mid will overflow but the algorithm still works.

* We’ve addressed negative numbers, numbers in (0, 1), overflow problems, absolute and relative error problems.
* Some tests for your own code -1, 0, 1, 2, 8, 0.001, 1e30, 1e60
* In practice faster methods like Newton Rapson method are used.

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