I was wondering if exp() is faster than more general pow(). I run fast benchmark on JsPerf http://jsperf.com/pow-vs-exp and it shown interesting result
Yes, exp will be faster than pow in general.
The exp and log functions will be optimized for the target platform; many techniques can be used such as Pade approximation, linear or binary reduction followed by approximation, etc.
The pow function will generally be implemented as exp(log(a) * b) as you say, so it is obviously slower than exp alone. There are many special cases for pow such as negative exponents, integral exponents, exponents equal to 1/2 or 1/3, etc. These will slow down pow even further in the general case because these tests are expensive.
See this SO question on pow.