Berachot 26b:
תנו רבנן טעה ולא התפלל מנחה בערב שבת מתפלל בליל שבת שתים טעה ולא התפלל מנחה בשבת מתפלל במוצאי שבת שתים של חול מבדיל בראשונה ואינו מבדיל בשניה ואם הבדיל בשניה ולא הבדיל בראשונה שניה עלתה לו ראשונה לא עלתה לו
למימרא דכיון דלא אבדיל בקמייתא כמאן דלא צלי דמי ומהדרינן ליה
ורמינהו טעה ולא הזכיר גבורות גשמים בתחיית המתים ושאלה בברכת השנים מחזירין אותו הבדלה בחונן הדעת אין מחזירין אותו מפני שיכול לאומרה על הכוס קשיא
Or, in 
English:
Our Rabbis taught: If a man erred and did not say the afternoon prayer on the eve of Sabbath, he says the [Sabbath] Tefillah1  twice on the night of the Sabbath. If he erred and did not say the afternoon Tefillah on Sabbath, he says the [weekday] Tefillah twice on the outgoing of the Sabbath; he says habdalah2  in the first but not in the second;3  and if he said habdalah in the second and not in the first, the second is counted to him, the first is not counted to him. 
This is equivalent, is it not, to saying that since he did not say habdalah in the first, it is as if he had not said theTefillah and we make him say it again. 
To this was opposed the following: If one forgot and did not mention the miracle of rain4  in the benediction for the resurrection of the dead5  and prayed for rain in the benediction of the years,6  he is turned back; if he forgot habdalah in 'who graciously grants knowledge',7  he is not turned back, because he can say it over wine! — This is indeed a difficulty.
The resolution of this difficulty may simply be one of 
context. Indeed, saying 
ata chonantanu [=
havdalah] in 
Ata Chonen is not required, and we would 
not make him go back if he accidentally skipped it. In this instance, however, by omitting it in the first one and saying it in the second one, he is thus designating the second one as his 
maariv and the first one as the additional one. And if the first one is his additional one, then it is a 
tefillat nedava rather than a 
tashlumin for the missed 
mincha.
Next in the daf:
איתמר רבי יוסי ברבי חנינא אמר תפלות אבות תקנום רבי יהושע בן לוי אמר תפלות כנגד תמידין תקנום
It has been stated: R. Jose son of R. Hanina said: The Tefillahs were instituted by the Patriarchs. R. Joshua b. Levi says: The Tefillahs were instituted8  to replace the daily sacrifices.
As the gemara continues to point out, and as is obvious anyway, the 
tefillot do correspond to the daily sacrifices. Thus Mussaf corresponds to the Mussaf offering, and Mincha to the Mincha offering, etc., in time and perhaps in function.
But these are two differing 
philosophical stands. In the patriarchal period, prior to the Mishkan, yes, there were 
korbanot, but the relationship between the 
avot and Hashem was of a very personal nature. Forget about the specific 
derashot. Hashem spoke to them, and they spoke to Hashem. For instance, for Avraham, at the end of 
Lech Lecha:
| א  אַחַר הַדְּבָרִים הָאֵלֶּה, הָיָה דְבַר-יְהוָה אֶל-אַבְרָם, בַּמַּחֲזֶה, לֵאמֹר:  אַל-תִּירָא אַבְרָם, אָנֹכִי מָגֵן לָךְ--שְׂכָרְךָ, הַרְבֵּה מְאֹד. | 1 After these things the word of the LORD came unto Abram in a vision, saying: 'Fear not, Abram, I am thy shield, thy reward shall be exceeding great.' | 
| ב  וַיֹּאמֶר אַבְרָם, אֲדֹנָי יְהוִה מַה-תִּתֶּן-לִי, וְאָנֹכִי, הוֹלֵךְ עֲרִירִי; וּבֶן-מֶשֶׁק בֵּיתִי, הוּא דַּמֶּשֶׂק אֱלִיעֶזֶר. | 2 And Abram said: 'O Lord GOD, what wilt Thou give me, seeing I go hence childless, and he that shall be possessor of my house is Eliezer of Damascus?' | 
| ג  וַיֹּאמֶר אַבְרָם--הֵן לִי, לֹא נָתַתָּה זָרַע; וְהִנֵּה בֶן-בֵּיתִי, יוֹרֵשׁ אֹתִי. | 3 And Abram said: 'Behold, to me Thou hast given no seed, and, lo, one born in my house is to be mine heir.' | 
And as for Yitzchak, in 
Toledot:
| כא  וַיֶּעְתַּר יִצְחָק לַיהוָה לְנֹכַח אִשְׁתּוֹ, כִּי עֲקָרָה הִוא; וַיֵּעָתֶר לוֹ יְהוָה, וַתַּהַר רִבְקָה אִשְׁתּוֹ. | 21 And Isaac entreated the LORD for his wife, because she was barren; and the LORD let Himself be entreated of him, and Rebekah his wife conceived. | 
and Yaakov, in 
Vayishlach:
| י  וַיֹּאמֶר, יַעֲקֹב, אֱלֹהֵי אָבִי אַבְרָהָם, וֵאלֹהֵי אָבִי יִצְחָק:  יְהוָה הָאֹמֵר אֵלַי, שׁוּב לְאַרְצְךָ וּלְמוֹלַדְתְּךָ--וְאֵיטִיבָה עִמָּךְ. | 10 And Jacob said: 'O God of my father Abraham, and God of my father Isaac, O LORD, who saidst unto me: Return unto thy country, and to thy kindred, and I will do thee good; | 
| יא  קָטֹנְתִּי מִכֹּל הַחֲסָדִים, וּמִכָּל-הָאֱמֶת, אֲשֶׁר עָשִׂיתָ, אֶת-עַבְדֶּךָ:  כִּי בְמַקְלִי, עָבַרְתִּי אֶת-הַיַּרְדֵּן הַזֶּה, וְעַתָּה הָיִיתִי, לִשְׁנֵי מַחֲנוֹת. | 11 I am not worthy of all the mercies, and of all the truth, which Thou hast shown unto Thy servant; for with my staff I passed over this Jordan; and now I am become two camps. | 
| יב  הַצִּילֵנִי נָא מִיַּד אָחִי, מִיַּד עֵשָׂו:  כִּי-יָרֵא אָנֹכִי, אֹתוֹ--פֶּן-יָבוֹא וְהִכַּנִי, אֵם עַל-בָּנִים. | 12 Deliver me, I pray Thee, from the hand of my brother, from the hand of Esau; for I fear him, lest he come and smite me, the mother with the children. | 
The 
avos had a personal relationship to Hashem, and if they needed something, they asked Hashem for it; and if they received it, they thanked Hashem for it.
The 
korbanot can be personal, but they were part of a larger, more impersonal, and structured, system. And the particular 
korbanot that the 
tefillot are patterned after are the 
korbanot of the 
tzibbur. Are we trying to recreate the national worship in our 
batei knisayot to give Hashem his daily due?
I think that at the end of the day, both approaches are true, to different levels, and in different ways.
Next:
איבעיא להו עד ועד בכלל או דלמא עד ולא עד בכלל תא שמע ר' יהודה אומר עד פלג המנחה אי אמרת בשלמא עד ולא עד בכלל היינו דאיכא בין ר' יהודה לרבנן אלא אי אמרת עד ועד בכלל ר' יהודה היינו רבנן
R. JUDAH SAYS: TILL THE FOURTH HOUR. It was asked: Is the point mentioned itself included in the UNTIL or is it not included?27  — Come and hear: R. JUDAH SAYS, UNTIL THE MIDDLE OF THE AFTERNOON. If you say that the point mentioned is included in the UNTIL, then there is no difficulty; this is where the difference lies between R. Judah and the Rabbis.28  O But if you say that the point mentioned is not included,29  then R. Judah says the same thing as the Rabbis?
If Rabbi Yehuda's 
ad is 
ad ve'ad bichlal, wouldn't the 
ad of the 
Rabbanan also be 
ad vead bechlal? If so, wouldn't 
ad ha-erev be inclusive of a later time, going into the evening as well?
Maybe they treat 
erev like 
chatzot, as a fixed instant. Still, I am not convinced of the strength of the question here.
On 
27b:
א"ר חייא בר אבין רב צלי של שבת בערב שבת רבי יאשיה מצלי של מוצאי שבת בשבת רב צלי של שבת בערב שבת
R. Hiyya b. Abin said: Rab used to say the Sabbath Tefillah on the eve of Sabbath;13  R. Josiah said the Tefillah of the outgoing of Sabbath on Sabbath.
This is in fact related to the idea that 
maariv ain lo keva. Since it has no 
keva, any approximate time is good for it, and it may indeed intersect the 
zman of 
mincha. And therefore, contrary to those who say one must choose a time and be consistent in terms of end of 
mincha time and beginning of 
maariv time, they may even "conflict" on a single day, or be inconsistent from week to week.
This is the meaning of:
תפלת הערב אין לה קבע:
מאי אין לה קבע אילימא דאי בעי מצלי כוליה ליליא ליתני תפלת הערב כל הלילה אלא מאי אין לה קבע כמאן דאמר תפלת ערבית רשות
THE EVENING PRAYER HAS NO FIXED LIMIT. What is the meaning of HAS NO FIXED LIMIT? Shall I say it means that if a man wants he can say the Tefillah any time in the night? Then let it state, 'The time for the evening Tefillah is the 'whole night'! — But what in fact is the meaning of HAS NO FIXED LIMIT? It is equivalent to saying, The evening Tefillah is optional.
Tomorrow, considering the difference between the Bavli and Yerushalmi accounts of the conflict involving Rabban Gamliel and Rabbi Yehoshua. (See 
here for parallel Yerushalmi, and chech our gemara carefully for the switch from Hebrew into Aramaic.)