How to make faster approximation of data by sinusoids - r

Question

I have a function that generates a sine wave
my.sin <- function(vec,a,f,p) a*sin(f*vec+p)
vec = vector indices
a = amplitude
f = frequency
p = phase
I also have some data my_var that I want to approximate with several sinusoids
set.seed(22)
my_var <- rnorm(100)
plot(my_var,t="l")
There is also a fitness function that calculates the approximation error of the sum of two sinusoids,but there can be any number of sinusoids
fit <- function(x,test=F){
vec <- 1:length(my_var)
s1 <- my.sin(vec = vec,a = x[1],f = x[2],p = x[3])
s2 <- my.sin(vec = vec,a = x[4],f = x[5],p = x[6])
res_sin <- s1+s2
err <- sqrt(sum((res_sin - my_var) ^ 2))
if(test) return(res_sin)
return( err/-1 )
}
Next, I use a genetic algorithm to find the best solution.
library(GA)
GA <- ga("real-valued",
fit,
lower = rep(-5,6),
upper = rep( 5,6),
maxiter = 300,
popSize = 300)
sol <- tail(GA#solution,1)[1,]
ga_sin <- fit(sol,test = T)
lines(ga_sin,col=4,lwd=2)
best_sin_comb <- matrix(sol,ncol = 3,byrow = T)
colnames(best_sin_comb) <- c("amplitude","frequency","phase")
print(best_sin_comb)
result
amplitude frequency phase
[1,] -0.3435402 1.5458888 1.8904578
[2,] -0.4326791 -0.4886035 0.5606401
My question is: can the approximation be made more efficient in terms of time spent. Perhaps a different search algorithm or something else ..
Also I would like to keep compatibility with the function my.sin