In general when under-estimating the project you can make it:
1) on time and within planned resources,
2) with all the planned functionalities and
3) without sacrificing quality.
Pick any two.
Evidence suggests otherwise. Sure you can estimate +/- 100-200% early on but that isn't what anyone is aiming for in a software project. Even detailed plans of repeatable (non-trivial) software projects do not result error bars that anyone really desires.
The problem is that most companies don't record this data. Start today!
My point was that it is the planning step that is extremely difficult, not the estimating one. With most real-world projects the project plan must follow changing requirements (based on external input or on things you have learned during development). It is extremely unlikely that the original plan will (or should) be followed to the end.