Failure fraction of our primary 3D Newton–Raphson-based con2prim method as a function of time. At every substep, we define the failure fraction as the ratio of the number of particles where 3D Newton–Raphson fails and the backup 1D Ridders’​​​​​​​ method is needed to the total number of particles. The blue line shows the average failure fraction at every time step. The red line shows the average failure fraction over every 0.1 ms of time. We find that the average failure rate of 3D Newton–Raphson is ∼0.1% in the premerger phase and ≲0.01% in the postmerger phase.