Question:
Did Eve say those things (changing God’s word) to the serpent purposely or by accident?

Answer:
The Scriptures say that she sinned: “Adam was not deceived, but the woman being deceived was in the transgression” (1 Timothy 2:14), so she purposely changed what God said.
Contrast Genesis 2:16, 17 with Genesis 3:2, 3 and you will see that she changed God’s Word:
Genesis 2:16, 17: “And the LORD God commanded the man, saying, Of every tree of the garden thou mayest freely eat: but of the tree of the knowledge of good and evil, thou shalt not eat of it: for in the day that thou eatest thereof thou shalt surely die.”
Genesis 3:2, 3:  “And the woman said unto the serpent, We may eat of the fruit of the trees of the garden: but of the fruit of the tree which is in the midst of the garden, God hath said, Ye shall not eat of it, neither shall ye touch it, lest ye die.” and you will see that she changed God’s Word.
God had said that “the tree of life” was “in the midst of the garden”  (Genesis 2:9), instead of the tree of the knowledge of good and evil, which Eve said was in the midst of the garden! The expression “in the midst” in Scripture indicates what is most important. Christ is “in the midst” of His people (the most important Person) when they are gathered unto His name (Matthew 18:20). So evidently to Eve “knowledge” was more important to her than “life”! Men today would rather try to understand God than trust Him and receive eternal life. Though it is only “through faith we [can] understand” the truth of God, what He has done and His blessings (Hebrews 11:3).
God also said that “in the day that thou eatest thereof thou shalt surely die” and Eve said that “God hath said, ‘Ye shall not eat of it, neither shall ye touch it, lest ye die.’” God had told this to Adam and evidently Eve heard what God said from Adam, but even so—even though she was deceived—she still transgressed the one commandment God gave them—not to eat of the tree of knowledge of good and evil!