First, note @MrLemon's comment, which points out that you'll have no 3rd-level slots if you greater magic fang all of your Eidolon's claw attacks. That means you aren't casting haste yourself if you want that extra +2 to attack and damage. That shaves off either an attack, or +2 damage per claw (since you can still just greater magic fang in the other mode to give +1 to all claws).
Second, one of the designers allegedly said during a playtest that eidolon's rend being different from the universal monster rules was an oversight. Reference: http://paizo.com/threads/rzs2ro3f?Yet-another-Summonereidolon-question#8. That shaves off 2d6 + 15 + (power attack).
Third, for rend and power attack, I can't find a definitive reference. But there is a large amount of consensus that rend is worded as extra damage to an attack (similarly to the way that freezing weapons add damage), and is not "melee damage" for the purposes of power attack. If you take that for granted, there goes the power attack bonus for rend.
Later edit: There appears to be a Pathfinder Society ruling on this (here, but strangely, even though that's the link to the material, it actually takes you to the Pathfinder FAQ, not the society one, so it'll probably have to be Googled for anyone reading this later):
How does Rend work with power Attack in Pathfinder Society Organized Play?
Damage is rolled once per attack. If it's a longsword attack, the roll is 1d8, to which you add other modifiers, like Strength bonus, Weapon Specialization, and enhancement bonuses. If it's a short sword with sneak attack, the damage roll is 1d6+1d6 sneak attack. It's two dice, but it's a single damage roll. If it's a confirmed critical hit on a sneak attack while employing Power Attack with a flaming greataxe, the single damage roll is 3d12+3xStrength+2xPower Attack+1d6 sneak attack+1d6 fire. A full attack, you add Power Attack once to each attack that hits, even if each of those attacks also has other effects added to its final damage value. The rend universal monster rule grants the creature an additional damage roll after successfully making two different attacks. Since it's a melee damage roll from a different attack than the first two, it gets Power Attack as well. Thus, a GM applying Power Attack to a rend damage roll is operating completely within the rules.
Fourth, don't forget to account for base attack bonus. A fighter at the same level will have the benefits of a full BaB, weapon focus, weapon training, and all the glorious things that come with loads of combat feats. A relatively quick mockup of a fighter using about half the gp budget for items, and assuming (n+1)/2 hp, gives me this
# con 16 st 18 (20 with level bonuses, 22 with belt) dx 16
# HP 13 + 8*11 = 101
# AC adamantine full plate + 1, amulet natural armor + 2, ring of protection +2 = 10 + 9 + 1 + 3 + 2 + 2 = 28
# DR 3/adamantine
# greatsword +3
# belt str +2
# BaB 11/6/1
# 6 fighter feats, 6 reg feats
# weapon training 2 (heavy blades): +2/+2
# 1,2: weapon focus, weapon specialization (greatsword): +1/+2
# 3: power attack (-3/+6 (9 with 2-hander))
# 4: improved critical (greatsword)
# 5: cleave
# 6: dodge
# <six more feats to work with>
# Attacks (greatsword): 11 + 6 + 3 + 1 + 2 = +23/+18/+13 (1d10+15 17-20/x2)
# Attacks (greatsword, PA): +20/+15/+10 (1d10+23 17-20/x2)
# Attacks (greatsword, *enlarged*, *hasted*): above + 1 (haste) + 1 (str bonus from enlarge) - 1 (size penalty) = +24/+19/+14/+24 (2d6 + 15 17-20/x2)
# Attacks (greatsword, PA, *enlarged*, *hasted*): +21/+16/+11/+21 (2d6 + 24 17-20/x2)
Fully buffed, hit with every attack, do average damage, and it's (7 + 24) * 4 = 124 damage. A fifth of those are critical threats, and again assume we confirm all criticals (a lot of assumptions, but no different than assuming your eidolon hits every attack), and we effectively add another 40% for ~173 damage. The higher BaB means the fighter will achieve a higher percentage of this against a given opponents, so the numbers are very comparable to your (revised) eidolon, with a slightly better AC and HP to boot. And I'm sure you haven't forgotten that you are a target if someone wants to remove the eidolon from the conflict, and you're a bit squishier.
There's a lot more room in that fighter--I didn't bother choosing a race (just assumed it was something with +2 str), I didn't have time to go fully into the rabbit hole with feats, and using more of the gp budget has a lot of room to improve these numbers across the board (the total for above was only 48k out of 82k from here, which leaves plenty of room for, say, a +4 or +6 strength belt, or more weapon bonuses), but this should give the idea. I think the moral of the story is that the eidolon can definitely be built to unleash a ton of damage, and while it may edge into pretty high territory, it's not necessarily completely breaking the game. As long as you're not being a jerk about it, you should be fine.