![]() Try a math problem of your own with the pad and the input box. You can click see more in order to see more examples. Selecting an example will take you to the Solutions page. In order to identify how much sampling resolution to have (instead of a guess of 0.001), you need to introduce the field of statistics into the problem.The examples section contains some examples to see the flow of the site. Thankfully some functions like sin repeat periodically, so you often only need a small sampling domain. A good number to begin with is 0.001 increments. ![]() Nonetheless, you'll probably want many samples along each argument's domain so that you get a wide variety of ouputs. With a derivative stored for each function's arguments, along with the output, you can produce very high accuracy interpolations of unknown points. This process of comparing an output to a slightly offset input is actually a simple form of calculating a derivative. By now you should have much greater accuracy of guesses. Using the slope of the nearest sample, you can move the terms of the predicted input in such a way that approximates how far they need to move to hit the queried output. This produces a line segment with a particular slope which approximates the function as you change that term in the expression! For every argument in the input expression, you can tinker with the term by slightly offsetting it, and comparing the output of the original expression and the offset expression. You can greatly improve your approximations by introducing calculus. However simple this is, it's not a close fit and tends to only work with continuous linear functions. Is it a 40:60 split? A 50:50? This ratio is then used to mix those known values together. You collect the nearest samples in each direction and identify roughly how much influence each one has on the query. This will work, but you'll want a lot of samples near points of interest like sin(pi).Ī simple method is interpolation. If query doesn't exist in your output set, you can simply take the nearest point in your output. So a simplistic approach is to approximate the data. In a database of output => input it is not possible to hold every output and every input. By associating input expressions to their output, you can produce a list for values on the real number line. The basic idea is that you collect a database you can query. Plouffe both before and during his period as an employee at CECM. The lookup tables include a substantial data set compiled by S. The Inverse Symbolic Calculator (ISC) uses a combination of lookup tables and integer relation algorithms in order to associate a closed form representation with a user-defined, truncated decimal expansion (written as a floating point expression). THIS BEING SAID, the answers you are asking is shown on your website. Using the other information you provided such as above (using cookies, or information the users would have just put), you may achieve to narrow your answers enough to have something great ! Trivially, and probably too abstractly explained : if you want to reverse "10", it will know where it most went according to the number of iterations made, and path it took to get there. This whole will be linked to the output via some neural network.Īs for the last part, it will be the "reverse engineering" problem. Save the user inputs, along with some other information (Is this science data ? Sociology ? Politics ? Stats ? Linear algebra ?). Anonymize the data so you can't trace it back to one specific user, but save a way to know it is this user specifically. Register and save the data from a bunch of calculators around the web. We have very briefly settled that we need to make a history, but as you said : How would you do it efficiently ? And that's a very different question. How would you do that ? By having a history of, either the users specifically (an individual), or a certain cluster of people, or just everyone. A number like this doesn't help because there is an infinite number of answers, and you want to narrow your answers accordingly.Ī simple example of infinite answers would be :īut now, you need to give credits to some answers more than others. If your question is "10", it will need to know where to go, and where to search. It can't think, or whatever : but it will give you an answer related to your question. The computer is dumb, but it is very fast at it. This is not a trivial question, but it is a question nonetheless. I do not have enough characters, so I am answering to the comment below the original post.Įxactly.
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