For a one-minute single-boss fight the searched build spends 0/37/14. Fire goes all the way to 
Combustion, and Frost stops after 
Piercing Ice and a point of 
Frost Channeling: on one minute the search prefers Combustion's burst to Fingers of Frost. Arcane gets nothing.
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0/1-23552020130133151-005500031Frostfire Bolt is a Fire spell and a Frost spell at once. The client's talent data names it in almost every Fire or Frost talent that adds damage, crit, cast speed or a mana saving, 
Incineration being the exception. So the build takes Fire talents for the bolt's crits and casts, and Frost talents for what those crits deal.
Why these talents
Improved Scorch is worth the most, 21.7 %. Each Scorch adds a stack of Fire Vulnerability, 3 % more Fire damage from you, up to five, and the bolt counts as Fire. The talent is worth more than the 15 % it gives, because without stacks the rotation's Scorch line never stops and Scorch takes the bolt's place.
Ignite, worth 14.8 %, turns 40 % of each Fire crit into a burn over four seconds, and the bolt's crits count. The burn copies the crit after Ice Shards has doubled it, so a bolt crit comes to 280 % of a hit.
Ice Shards is the reason to put points in Frost. It doubles the crit bonus of your Frost spells, so a bolt crit deals 200 % instead of 150 %. The bolt is the only Frost spell you cast, and the talent is worth 7.2 %.
Improved Fireball also cuts Frostfire Bolt's cast, from 3 seconds to 2.5, which is worth 8.7 %. Its tooltip says 1 second, but the talent data gives half a second at 5/5.
Combustion is the one-minute build's burst. Each Fire hit adds 10 % Fire crit until three crits spend it, and the bolt counts as a Fire hit. It goes out once, about ten seconds in, and is worth 8.2 %. On longer fights the same points buy Fingers of Frost and Shatter instead.
Heating Up and its prerequisite 
Pyroblast read the same, 8.0 %, because one doesn't work without the other. A crit from the bolt, Fire Blast or Scorch takes 25 % off your next Pyroblast, up to three stacks.
Critical Mass (5.8 %), 
Fire Power (8.9 %), 
Elemental Precision (5.8 %) and Piercing Ice (2.5 %) are flat gains that all reach the bolt. Elemental Precision's hit counts once for a spell of two schools, at 5 % in the talent data. Wowhead's tooltip prints 6 %.
Flexible points
These are the points with the least riding on them, and when each is worth moving.
Flame Throwing, 
Burning Soul and 
Blast Wave. Path points on the way to Combustion, each worth 0.0 % here. The simulator stands inside every range and never hits you, and the one-boss rotation never casts Blast Wave. In a raid, Burning Soul's 20 % less Fire threat is the useful one.- Frost Channeling and
Master of Elements. Mana savings you don't need in one minute: both score within a DPS of nothing.
What each talent is worth
Each value comes from running the build again without that talent. Talents lean on each other, so the values overlap and their total means nothing. For a single spare point, the last-point column is the one to read.
On every fight
Every fight and faction gets its own search, and three shapes come out. Two and three minutes on one boss take Fingers of Frost and Shatter. One minute takes Combustion, with Blast Wave and Flame Throwing on the way. The three-boss builds add Improved Flamestrike and Blast Wave and pay for them out of Improved Fireball on three minutes. Below, each fight's build is set against this one.