Grisu is also proven to be always correct. As mentioned in another comment: you have to define "correct". Grisu is always accurate, but may bail out if you need the shortest or closest result.
Basically: Grisu will always print a number that reads back to the input. However, it may not be able to print the shortest or closest number (when two decimal outputs have the same shortest length). In that case, it knows this, though, and can tell the user.
I would say that the combination of Grisu and Errol is currently the state of the art.
Errol is not the fastest, nor is it (afaik) proven to always return the closest result.
However, combining Grisu with Errol (as fallback) would probably yield the fastest complete algorithm.
Grisu is also proven to be always correct. As mentioned in another comment: you have to define "correct". Grisu is always accurate, but may bail out if you need the shortest or closest result.
Basically: Grisu will always print a number that reads back to the input. However, it may not be able to print the shortest or closest number (when two decimal outputs have the same shortest length). In that case, it knows this, though, and can tell the user.
I would say that the combination of Grisu and Errol is currently the state of the art.
Errol is not the fastest, nor is it (afaik) proven to always return the closest result.
However, combining Grisu with Errol (as fallback) would probably yield the fastest complete algorithm.