Using the quantum string Bethe ansatz we derive the one-loop energy of a folded string rotating with angular momenta (S, J) in AdS 3 × S 1 ⊂ AdS 5 × S 5 in the limit 1 ≪ J ≪ S, z = √ λ log(S/J)/(πJ) fixed. The one-loop energy is a sum of two contributions, one originating from the Hernandez-Lopez phase and another one being due to spin chain finite size effects. We find a result which at the functional level exactly matches the result of a string theory computation. Expanding the result for large z we obtain the strong coupling limit of the scaling function for low twist, high spin operators of the SL(2) sector of N = 4 SYM. In particular we recover the famous − 3 log(2) π . Its appearance is a result of non-trivial cancellations between the finite size effects and the Hernandez-Lopez correction.