YOU SAID:
I sleep with my eyes open
INTO JAPANESE
私は私の目を開いて寝る
BACK INTO ENGLISH
I open my eyes and sleep
INTO JAPANESE
私は私の目と睡眠を開く
BACK INTO ENGLISH
I sleep with my eyes open
INTO JAPANESE
私は私の目を開いて寝る
BACK INTO ENGLISH
I open my eyes and sleep
INTO JAPANESE
私は私の目と睡眠を開く
it is unlikely that this phrase will ever reach equilibrium