In microcanonical molecular dynamics simulations, fast-folding proteins CLN0251 and Trp-cage2 can autonomously fold to conformations with Cα root mean square deviations (RMSDs) of 1.0−1.4 Å from the experimentally determined native conformations3. However, the folding times of CLN025 and Trp-cage predicted from the simulations3 are more than 4−10 times longer than the experimental values4,5, indicating an accuracy gap between experiment and simulation for folding speed. Here I report how combining a new protein simulation method6 and a revised AMBER forcefield7 results in accurate folding of CLN025 and Trp-cage in 40 distinct, independent, unrestricted, unbiased, and isobaric−isothermal molecular dynamics simulations. According to a survival analysis of these simulations using a Cα-and-Cβ RMSD cutoff of 0.98 Å, the simulated folding times of CLN025 at 293 and 300 K and Trp-cage at 280 and 300 K are 279 ns (95% CI: 204−380 ns), 198 ns (95% CI: 146−270 ns), 2.4 μs (95% CI: 1.8−3.3 μs), and 0.8 μs (95% CI: 0.6−1.0 μs), respectively. The corresponding experimental values are 261 ns, 137 ns, 2.4 μs, and 1.4 μs, respectively4,5. These results show that CLN025 and Trp-cage now can autonomously fold in silico as fast as they do in experiments, indicating that the accuracy of folding simulations begins to overlap with the accuracy of folding experiments. This represents a step forward in combining simulation with experiment to develop algorithms that predict structure and dynamics of a globular protein from its sequence for artificial intelligence of biomedical research.