Is there an online resource that lists irrationals close to given a decimal? For example, if $x=0.3740049$, a candidate solution would be $x_c = \left ( \frac{1+\sqrt{5}}{2} \right ) ^2 /7$.
This would be something akin to the OEIS (Online Encyclopedia of Integer Sequences), which is a reverse lookup for integer sequences and various properties about them. While there are an infinite number of irrationals over any fixed range, a list of "simple" (operation depth, low coefficients, etc...) would be very useful.
See inverse symbolic calculator, which I think was originally coined Plouffe's inverter. It does exactly what you want. If you enter your decimals there, it will give your candidate solution as one match, other close matches for instance being $(16+9^{2/3} \cdot 11^{2/3}) / 100 \approx 0.37400477$.