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Mh interesting question. I'm sure that I will not answer it completely satisfactory, but for the example that you have given, the following works:

f= (x* 2* pi* log(5)* 6^1.5)/(3^4*pi^2+x)
R = RR['x']


148.621271129886*x/(x + 799.437956488238)

The idea behind it is to convert the symbolic expression to the fractional field of polynomials with coefficiants in the real numbers. This however fails as soon as the expression you like to simplify is not a rational function anymore, i.e. as soon as some squareroots or trigonometric functions appear. So what else can be done?