BURN_IN = 10000
DRAWS   = 100000

f = function(x) exp(sin(x))

chain = numeric(BURN_IN + DRAWS)

x = 1/2

for (i in 1:(BURN_IN + DRAWS)) {
    y = runif(1) # proposal
    if (runif(1) < min(1, f(y)/f(x))) x = y
    chain[i] = x
}

x_min = median(chain[BURN_IN : (BURN_IN + DRAWS)])

cat("Metropolis minimum found at", x_min, "nn")

# MONTE CARLO ENDS HERE. The integrations bellow are just to check the results.

A = integrate(f, 0, 1)$value

F = function(x) (abs(integrate(f, 0, x)$value - A/2))

cat("Optimize minimum found at", optimize(F, c(0, 1))$minimum, "n")

Metropolis minimum found at 0.6005409
Optimize minimum found at 0.601365