# How to find possible closed-form-formula for a given decimal expansion online?

What mathematical program or library can guess formula for decimal fraction? For example, for number 2.414213562373095 right guess is 1 + $\sqrt 2$. Are there such tools online? I cannot find one.

• Wolfram alpha is very good for this : Just enter a decimal expansion to get various possible closed forms! Feb 26, 2017 at 13:46
• @S.C.B. But 2.414213562373095 is. Feb 26, 2017 at 13:49
• But do not expect miracles! If you enter the decimal expansion of $\large \frac{\pi^3+e^3-\sqrt{7}}{\pi^5-e^7+\sqrt{11}}$ , you won't get your expression as a closed form. But for numbers satisfying linear or algebraic dependences with great accuracy , such as in the example, it will work very well. Feb 26, 2017 at 13:50
• For the case, you also accept offline tools, I suggest the free PARI/GP-calculator. It can determine algebraic and linear dependencies. Feb 26, 2017 at 14:04
• Using continued fractions, you can find very good rational approximations even with a table calculator. For example , $\pi$ is very close to $\frac{355}{113}$ Feb 26, 2017 at 14:09