Midrash sa Genesis 15:10: Vayikra Rabbah, Pirkei DeRabbi Eliezer & Bereshit Rabbah

“Let the wicked forsake his way and the man of iniquity his thoughts” (Isaiah 55:7). Rav Beivai bar Aviya said: How must a person confess on the day before Yom Kippur? He must say: ‘I confess all the evil that I have performed before You. I had been standing on a path of evil. But everything that I have done, I will not do anything like it again. May it be Your will, Lord my God, that You pardon me for all my iniquities, forgive me for all my transgressions, and atone for me all my sins.’ That is what is written: “Let the wicked forsake his way and the man of iniquity his thoughts.”
Yitzḥak said: Like a person who welds two boards and attaches them to each other. Rabbi Yosei bar Ḥanina said: Like a person who welds two legs of a bed and attaches them to each other. “Let him return to the Lord and He will have mercy on him (Isaiah 55:7).”¹¹Rabbi Yitzḥak’s point is that when one wants to attach two boards, one must make sure they are straight. The process of confession and repentance restores one’s ability to connect to God, just as straightening a board allows it to be attached to another one. Thus, after the verse states “Let the wicked forsake his way and the man of iniquity his thoughts,” it states: “Let him return to the Lord.” Rabbi Yosei bar Ḥanina adds that the individual who has repented is considered to help hold up the world together with God, just like two legs of a bed (Etz Yosef).
The Rabbis and Rabbi Shimon ben Yoḥai, the Rabbis say: The Holy One blessed be He showed Abraham our patriarch of blessed memory all the atonements except for the tenth of an ephah.¹²In the Covenant of the Pieces, God showed Abraham all the offerings that bring atonement except the freewill meal offering, which is a tenth of an ephah of flour. Rabbi Shimon ben Yoḥai says: The Holy One blessed be He showed Abraham our patriarch of blessed memory even the tenth of an ephah. [The word] “these” (Leviticus 2:8)¹³“You shall bring the meal offering that is prepared of these to the Lord.” is stated here, and [the word] “these” (Genesis 15:10)¹⁴“He took all these for him.” is stated there. Just as [the word] “these” stated here refers to the tenth of an ephah, so, too, [the word] “these” stated there refers to the tenth of an ephah. “And to our God, as He abundantly forgives” (Isaiah 55:7); Rabbi Yehuda bar Simon in the name of Rabbi Ze’eira: The Holy One blessed be He, too, added one atonement of his own.¹⁵He added a form of atonement that He did not show to Abraham, in accordance with the opinion of the Rabbis. Which is that? It is the tenth of an ephah.

Rabbi Joshua said: Abraham took his sword and divided them, each one into two parts, as it is said, "And he took him all these, and he divided them in the midst" (Gen. 15:10). Were it not for the fact that he divided them, the world would not have been able to exist, but because he divided them, he weakened their strength, and he brought each part against its corresponding part, as it is said, "And he laid each half over against the other" (ibid.). And the young pigeon he left alive, as it is said, "But the bird he divided not" (ibid.). Hence thou mayest learn that there was not any other bird there except a young pigeon. The bird of prey came down upon them || to scatter them and to destroy them. "The bird of prey" is nought else but David, the son of Jesse, who is compared to a "speckled bird of prey," as it is said, "Is mine heritage unto me as a speckled bird of prey?" (Jer. 12:9).

“He said: My Lord God, how can I know that I will inherit it?” (Genesis 15:8).
“He said: My Lord God, how can I know” – Rabbi Ḥiyya ben Rabbi Ḥanina said: [Abraham said this] not like someone who is complaining, but rather, he said to Him: ‘By what merit [will I inherit it]?’ He said to him: ‘By means of the atonements that I will provide for your descendants.’
“He said to him: Take for Me three calves, and three goats, and three rams, and a dove, and a young pigeon” (Genesis 15:9).
“He said to him: Take for Me three calves” – He showed him three types [of atonement] involving bulls, three types involving goats, and three types involving rams: Three types involving bulls: the bull of Yom Kippur;⁴⁵See Leviticus 16:3. the bull that is brought for the transgression of any of the mitzvot;⁴⁶See Leviticus 4:13–21. and the beheaded calf.⁴⁷See Deuteronomy 21:1–8. Three types involving goats: the goats of the festivals;⁴⁸See Numbers 28:22–29:38. the goats of the New Moon;⁴⁹See Numbers 28:15. and the goat offered by the individual.⁵⁰See Numbers 15:27. Three types involving rams: the definite guilt offering;⁵¹See Leviticus 5:15, 5:20–25, 19:20–21. the provisional guilt offering;⁵²See Leviticus 5:17–18. and the lamb offered by the individual.⁵³See Leviticus 4:32. “And a dove, and a young pigeon.”⁵⁴See Leviticus 5:7.
“He took all these for Him. He divided them in the middle, and placed each half opposite the other; but the birds he did not divide” (Genesis 15:10).
“He took all these for him” – Rabbi Shimon bar Yoḥai and the Rabbis, Rabbi Shimon bar Yoḥai says: He showed him all the [other] types of atonement, but the tenth of an ephah [meal offering]⁵⁵See Leviticus 5:11. He did not show him. The Rabbis say: He showed him the tenth of an ephah as well. It is stated here: “He took all these [eleh] for Him” and it is stated elsewhere: “You shall bring the meal offering that is prepared of these [eleh] to the Lord” (Leviticus 2:8).⁵⁶The word eleh, found in both verses, forms the basis of a verbal analogy, suggesting that the meal offering is alluded to here as well.
“But the birds he did not divide” – the Holy One blessed be He showed him that [the head of] the bird burnt-offering is to be severed⁵⁷The bird is slaughtered so that the neck is cut all the way through, the head being almost severed. but [the head of] the bird sin-offering is not to be severed.⁵⁸The slaughter of this bird sacrifice does not pierce through the entire neck (see Leviticus 5:8). Since the birds brought by Abraham alluded to the atonement of a bird sin-offering, he did not cut it in two.