# [ARBLE], 49 bytes

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    sqrt((a^2+b^2)/2)+(a+b)/2+sqrt(a*b)+(2*a*b)/(a+b)

[Try it online!][TIO-j8t7neom]

[ARBLE]: https://github.com/TehFlaminTaco/ARBLE
[TIO-j8t7neom]: https://tio.run/##SyxKykn9/7@4sKhEQyMxzkg7Kc5IU99IU1sjUTsJyNAGyyRqJQFFjLRAtD5Y5v///@b/zQA "ARBLE – Try It Online"