Sum the means of the two integers There are quite a few means in mathematics, such as the arithmetic mean, the geometric mean, and many others...

Definitions and Task

Note that these are the definitions for two positive integers*:


The root mean square is the square root of the sum of their squares halved ().
The arithmetic mean is their sum, halved ().
The geometric mean is the square root of their product ().
The harmonic mean is 2 divided by the sum of their inverses ( = ).


Given two integers a and b  such that a, b ∈ [1, +∞), sum the means mentioned above of a and b. Your answers must be accurate to at least 3 decimal places, but you do not have to worry about rounding or floating-point precision errors.

Test Cases


a, b -> Output

7, 6 -> 25.961481565148972
10, 10 -> 40
23, 1 -> 34.99131878607909
2, 4 -> 11.657371451581236
345, 192 -> 1051.7606599443843


You can see the correct results for more test cases using this program. This is code-golf, so the shortest valid submissions that follows the standard rules wins. 


* There are many other means, but for the purposes of this challenge we'll use the ones mentioned in the "Definitions" section.
Haskell, 48 bytes



a%b=sum[((a**p+b**p)/2)**(1/p)|p&lt;-[2,1,-1,1e-9]]


Try it online!

This uses the fact that the root-square, arithmetic, harmonic, and geometric means are all special cases of the generalized mean ((a**p+b**p)/2)**(1/p) for p=2,1,-1,0. The geometric mean uses the limit p-&gt;0+, approximated as p=1e-9 which suffices for precision.