Forty Items Two Halves

You have 40 weights and a target sum, and you must decide whether some subset hits the target exactly. Enumerating all subsets is $2^{40} \approx 1.10 \cdot 10^{12}$, far too slow.

You split the 40 into two halves of 20, enumerate all $2^{20} = 1,048,576$ subset sums of each half, sort the left list, and for every right-half sum binary search the left list for the complement.

Roughly how many elementary operations does that plan cost?