Is there any package that automatically fits a curve using many simple models?
By simple models I mean:
You could also look at packages providing functions to evaluate fractional polynomials. So far, these appear to be mboost (with the function FP) and mfp (with the function mfp). Although I haven't tried the packages, the theory behind them fits what you're after.
The mfp package was described in R-News in 2005.
Two references that might be of interest are
Royston P, Altman D (1994) Regression using fractional polynomials of continuous covariates. Appl Stat. 3: 429–467.
Sauerbrei W, Royston P (1999) Building multivariable prognostic and diagnostic models: transformation of the predictors by using fractional polynomials. Journal of the Royal Statistical Society (Series A) 162: 71–94.