[math-fun] algebraic fcn simplification

I just spent hours simplifying (64 t^2 - 16 Sqrt[-32 t^2 + t^2/Sqrt[1 - t] + 31 Sqrt[1 - t] t^2 + 32 t^3 - 17 Sqrt[1 - t] t^3 + 10 t^4 + Sqrt[1 - t] t^4])/(128 t^2) to 1/2 + (4 - 5 t)/(8 (1 - t)^(1/4) t) - ((1 - t)^(1/4) (4 + t))/(8 t) using Corey's denester on numeric special cases. How should I have done this? Plotting the difference shows they only agree when arg t lies within π/4 of the real axis. Elsewhere it seems to be -1. Mma gives 0 for Limit t->0, but Plot3D rather consistently spikes at the origin. I don't know how to elicit that spike value except by plotting. Bug? --rwg