Genesis 18:15

And Sarah denied and said, I wondered not; for she was afraid. And the Angel said, Fear not: yet in truth thou didst laugh.

AND SARAH DENIED, SAYING. I wonder about the righteous prophetess: How did she deny that which G-d had said to the prophet, and also, why did she not believe in the words of G-d’s angels?
The answer appears to me to be that these angels who appeared as men came to Abraham, and he, in his wisdom, recognized them. They announced to him, “I will certainly return unto thee, and Sarah shall have a son.” And Sarah heard it, but she did not know that they were angels of the Supreme One, as was the case with the wife of Manoah. It is even possible that she did not see them at all. Therefore she laughed within herself in derision, just [as the word “laugh” is used in the verse]: He that sitteth in heaven laugheth, the Eternal hath them in derision. For joyous laughter is [expressed in Hebrew as originating] in the mouth — Then was our mouth filled with laughter, 126:2. — but laughter originating in the heart is not spoken of as joyous. Now the Holy One, blessed be He, accused her before Abraham as to why the matter appeared to her to be impossible. It was fitting for her to believe, or she should have said, “Amen, G-d do so!” Now Abraham said to her, “Why did you laugh? Is anything too hard for the Eternal?” He did not explain to her that G-d had revealed her secret to him. And she, because of Abraham’s fear of G-d, denied it for she thought that Abraham had said so through recognition of the expressions on her face or because she had kept quiet and gave no expression of praise and thanksgiving or joy. And he said to her, Nay, but thou didst laugh. Then she understood that it was told to him in a prophecy, and so she remained quiet and did not answer a word.
It is proper that we also say that Abraham had not revealed to her what had originally been told to him: Indeed, Sarah, thy wife shall bear thee a son. Perhaps he waited until G-d would send her the announcement on the following day for he knew that the Eternal G-d will do nothing, but He revealed His counsel unto His servants the prophets. It may be that due to his great diligence in fulfilling commandments, he was occupied with his circumcision and the circumcision of the many people in his house. Afterward, on account of his weakness, he sat at the doorway of the tent, and the angels came before he had told her anything.

כי צחקת. “but you did laugh.” On most occasions when we encounter the word כי after the word לא, it means “but.” Actually, the word כי can have four different meanings, depending on the context in which it appears (Rashi). The meanings are: if, maybe, but, for. Examples of כי meaning “but,” are Exodus 23,24 לא תשתחוה להם כי הרוס תהרסם, “do not bow down to them but destroy them utterly.” Or, Deut. 15,7-8: לא תקפוץ את ידך כי פתוח תפתח, “do not ball your hand into a fist, but open it wide, etc.”

כי יראה, to say “I have sinned;” but she repented the lie in her heart.

!ויאמר לא, for the angel knew that as Bileam said (Numbers 23,19) “seeing than man is not G’d, he lies and deceives,” לא איש א-ל ויכזב. He did not believe her at all.

ותכחש...כי יראה, seeing that she was afraid she denied having laughed;

!ויאמר לא, not as you say, for you truly did laugh.