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TL;DR
Farm the Ancient Claw with the 
Slicing Winds build right after you finish 100 
Volcanic Caves.
Introduction
Ancient Claw is largely the best melee weapon that does not require late-game content to obtain.
The Ancient Claw is assembled from the 
fragments that drop only from the 
Pegasus. You need to kill 3333 Pegasi on average to get enough fragments.
The question is when to farm it and what combat style is the best for that. The main point of contention is whether to farm it before or after the Volcanic Cave because this dungeon is farmed with a Melee build and is vital for idling the 
Air God Dungeon.
To answer these questions, we will consider the following builds:
These builds were chosen to show the changes that the various drops bring into farming the Pegasus. The ranged builds were not considered because the Pegasus is 
Melee and has the highest evasion against 
Ranged in addition to the Combat Triangle.
In the considered situations, no prayers, potions, or other buffs are enabled unless specified.
The skill levels are given so that you can replicate the simulations in the Combat Simulator.
The 
Auto Eat - Tier III is used.
The 
Whale (Perfect) was used as a food of choice because it was considered a middle ground between starting out and being fully leveled out in Firemaking, Fishing, Farming, and Cooking.
The ring slot is always occupied with 
Magical Ring.
Builds
The simulations were done for 
Hardcore with all skills on level 75.
All intermediate steps can be found in this spreadsheet (link).
The grind time with this build is 141 hour.
However, pay attention that it would be more than 331 hours without the Slayer gear.
The grind time with this build is 67 hours.
If you don't use the Slayer gear, the grind time with this build will be 142 hours.
You need 
Level 88 for this build.
With the following setup, you should have a bit more than 20k accuracy on Slicing Winds, which means they won't miss at all.
Warning: Swapping 
Miolite Shield to 
Book of Eli will only increase the clear time because your melee defence would plummet, resulting in much more food eaten.
Overall, you want to put as much DR and Melee defence as possible when maintaining the 20k accuracy.
For instance, if you have higher Magic, you might be able to swap 
Enchanted Cape with 
Fire Cape and reduce the food consumption even further.
The grind time with this build is 48 hours. The slayer gear doesn't add to the clear speed in this case.
The grind time with this build is 44 hours.
However, this build implies that you go through the Air God Dungeon with 
Sunset Rapier, which is a sizeable loss of DPS that will cost you more than 4 hours of the difference between this build and the Slicing Winds build.
Analysis
Essentially, we want to know which of two sequences is faster:
- Rapier > Claw > Volcano,
- Rapier > Volcano > Claw.
Full-Sunset Volcano vs Full-Claw Volcano
Let's consider the builds Rapier and Slicing Winds.
The difference between their timings of completing the claw is 19 hours.
The Volcano grind of the full 
ancient set is longer with the with Sunset Rapier than it is with the Claw.
The question is then if the difference between the rapier and the claw in the Volcanic grind is bigger than 19 hours.
We know the length of "Raper > Claw" and "Volcano > Claw", but we need the data on "Rapier > Volcano" and "Claw > Volcano".
We take this data from Volcanic Cave/Guide#Weapon choice.
The goal of clearing the Volcanic Cave is to get the ancient set.
As specified on in the Volcanic Cave/Guide, you need 1350 clears to almost certainly get a full set of Ancient armor or 832 clears to have a 75% chance. The median (50% or results) is 564 clears.
| Item
|
Adjusted clears per hour
|
564 clears (h)
|
832 clears (h)
|
1350 clears (h)
|
| Sunset Rapier
|
5.204
|
108.4
|
160
|
259.4
|
| Ancient Claw
|
5.412
|
104.2
|
153.7
|
249.5
|
| Difference (h)
|
|
4.2
|
6.3
|
10.1
|
The biggest difference is 10 hours. It means that Rapier>Volcano>Claw is faster than Rapier>Claw>Volcano by at least 9 hours.
However, what if we were to use the Ancient Magicks as soon as we unlock it?
Sunset/Ancient Volcano vs Claw/Ancient Volcano
It is possible to clear the Volcano using the Ancient Magicks with the build from Volcanic Cave/Guide#100-Volcanoes Magic. Pay attention that you need 37% DR with 920 
HP to idle it. That amount of DR is reached either through the 
Stone Skin prayer or through the 
DR potion II.
If we consider that we clear only 100 Volcanoes as a melee build and the rest as the 100-Volcanoes Magic build, then we compare the two sequences:
- Claw farm with Rapier + 100 Claw Volcanoes,
- 100 Rapier Volcanoes + Claw farm with Ancient Magicks.
In other words, the advantage of farming 100 Volcanic Caves with the Claw when compared to the Sunset Rapier is less than 5 hours.
If we consider the rearranged sum of what we compare
- Claw farm with Rapier + 100 Claw Volcanoes,
- Claw farm with Ancient Magicks + 100 Rapier Volcanoes.
and then subtract the second row from the first one, then we would get
[math]\displaystyle{ 17 - 4.87 = 12.13 }[/math]
In other words the sequence where we farm the Claw after the Volcano is faster than the sequence of farming the claw with Rapier by 12 hours.
Conclusion
Farm the Ancient Claw with the Ancient Magicks build right after you finish 100 Volcanic Caves.
If you cannot get the Ancient Magick build for some reason, then use the Rapier melee build with Slayer gear.
Surge magic,
Glacia magic.
Slayer Wizard Hat (Strong)
Slayer Wizard Robes (Strong)
Fire Expert Wizard Bottoms
Fire Expert Wizard Boots
Amulet of Magic
Paladin Gloves
Magic Wand (Powerful)
Slayer Helmet (Strong)
Slayer Platebody (Strong)
(G) Dragon Platelegs
(G) Dragon Boots
(G) Dragon Shield
Promotion or 
Glory
Ancient Wizard Hat
Ancient Wizard Robes
Ancient Wizard Bottoms
Ancient Wizard Boots
Elite Amulet of Magic
Elementalist Gloves
Glacia God Platebody
Glacia God Platelegs
Glacia God Boots
Glacia God Gloves
Infernal Cape
Combat:
