n <- 10000

res <- numeric(0)
while (length(res) < n) {
  X <- runif(1, -1, +1)
  p <- sqrt(1 - X^2)
  U <- runif(1)
  if (U <= p) {
    res <- c(res, X)
    # cat("accept", X, "\n")
  } else {
    # cat("reject", X, "\n")
  }
}

hist(res, probability = TRUE)
x <- seq(-1, +1, by=0.01)
lines(x, 2/pi*sqrt(1-x^2), col="red", lwd = 2)