Correct me if I'm wrong, but the strategic objectives of the Egyptian HQ was to secure a bridge-head east of the cannal 4 km deep and this wasn't completely achieved.
Wrong. The Egyptian army targets were as follows:-
1- Occupying the East Canal bank with a depth ranging from 10 to 15 Kms. This should not be exceeded to employ the protection of EAAM & avoid subjecting to IAF raids.
2- Implementing the heaviest possible man losses on IDF. Knowing ythe limited man resources for IDF, the effect of such losses would be crucial to the Israeli community.
3- Elongation of the War duration as much as possible. This would keep Israel main work force held in the war fronts. Such war would crumble the Israeli economy seriously.
4- Challenging the enforced No War/ No Peace status that was enjoyed by Israel & its allies.
The above targets were mostly fulfilled to a satisfactory degree.
The IDF not only penetrated the Egyptian bridge-head but it crossed the cannal and encircled the 2nd Army.
You mean it encircled the 3rd army. Yet, Israel accepted the ceasefire on the 22nd of Oct where its troops were 50 Kms from the main supply routes of the 3rd army. In violation to its ceasefire approval, IDF developed its offensive till it succeded in cutting the 3rd army supply routes on the 24th of Oct. IDF land gains past the 22nd were never accepted by Egypt or the Superpowers. During the past war 60 days negotiations, Israel had to choose between retreating to the 22nd ceasefire lines or risking the restore of the military operations by the refreshed Egyptian army. On the 18th of Jan, Israel choose to retreat from Canal west bank to lines located 35 Kms from the canal water lines.