I used the word "bug" to adress any failure in the software chain to do it shorter, I hope you will accept that word generalization inside that part of that thread.
Testing software is never a cheap operation, it is at contrary the most expensive part of building a software (1>100 is not unusual). And we have to repeat that testing some times in critical designs connected to human life or strategic aims.
That amount of work to debug really softwares is not abnormal if we accept that rule well known from the begin of software use by engineers and managers : a software is not chosen for fashion or modernity reason but to get money ! If you use your software only a little number of time it is much cheaper to do it by hand ! You have to calculate the benefit of the long, expensive, hard work creating and using software's. A sort software is used millions of times, which is much more than FADECs use. Our traditional Aeronautics ingineers had a very safe score, thank you to them.
Arrival of Personal computer induced a image of toy to the computer and the idea that everything gets magic like a play and everybody could rebuild the world in the secrecy of his office without to need acceptance by others or at least to listen their opinion about your Ptoleme's fantasma.
That experience from Airbus with DOD and some other companies is interesting but not more than that : Testing must be done by the team who elaborated the software. It is nearly impossible to debug a software yourself were not the conceiver.
Testing is a long chain of logic, with the same level of logic you used in the software conception. So you may use statistics only if you used statistics inside the software, ie theory of games to solve a great amount of equations, and respecting strticly the rules of statistics (ie if you are not sure of the distribution law, don't use tests adapted to Gaussian law).
Bug free software exists ie bootstraps and the multiple layers above the bootstrap to build operating systems or nets like the web (despite you may find some bugs in some OS...)