  A new algorithm is developed allowing the Monte Carlo study of a 1 + 1
dimensional theory in real time. The main algorithmic development is to avoid
the explicit calculation of the Jacobian matrix and its determinant in the
update process. This improvement has a wide applicability and reduces the cost
of the update in thimble-inspired calculations from O(N^3) to less than O(N^2).
As an additional feature, the algorithm leads to improved Monte Carlo
proposals. We exemplify the use of the algorithm to the real time dynamics of a
scalar {\phi}^4 theory with weak and strong couplings.
