how to run for loops in parallel in R

library(foreach)
library(doParallel)

library(ggplot2)

# Set up parallel backend
n.cores <- detectCores() - 1
registerDoParallel(cores = n.cores)

nsim <- 9
n_values <- c(1, 10, 100, 1000, 10000, 100000,2e5,3e5, 1000000, 10000000, 1e8)
results <- data.frame(n = integer(), method = character(), time = numeric(), stringsAsFactors = FALSE)

for (n in n_values) {
  # Parallel run
  tic_parallel <- Sys.time()
  foreach(i = 1:nsim, .combine = 'c') %dopar% {
    mean(runif(n) ^ 2)
  }
  toc_parallel <- Sys.time()
  parallel_time <- as.numeric(toc_parallel - tic_parallel, units = "secs")
  
  # Sequential run
  tic_sequential <- Sys.time()
  foreach(i = 1:nsim, .combine = 'c') %do% {
    mean(runif(n) ^ 2)
  }
  toc_sequential <- Sys.time()
  sequential_time <- as.numeric(toc_sequential - tic_sequential, units = "secs")
  
  # Store results
  results <- rbind(results, data.frame(n = n, method = "Parallel", time = parallel_time))
  results <- rbind(results, data.frame(n = n, method = "Sequential", time = sequential_time))
}

# Plot results
ggplot(results, aes(x = n, y = time, color = method)) +
  geom_line() +
  scale_x_log10() +
#  scale_y_log10() +
  geom_point() +
  labs(x = "Number of samples (n)", y = "Time (seconds)", title = "Comparison of Parallel and Sequential Run Times") +
  theme_minimal()

# Plot results
ggplot(results, aes(x = n, y = time, color = method)) +
  geom_line() +
  scale_x_log10() +
  scale_y_log10() +
  geom_point() +
  labs(x = "Number of samples (n)", y = "log10 Time (seconds)", title = "Log Log scale Comparison of Parallel and Sequential Run Times") +
  theme_minimal()