Monte Carlo methods: Difference between revisions

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@@ Line 1,174: / Line 1,174: @@
 =={{header|Julia}}==
+{{works with|Julia|0.6}}
-<lang julia>function montepi(n)
-    s = 0
+<lang julia>function monteπ(n)
-    for i = 1:n
-        s += rand()^2 + rand()^2 < 1
+    s = count(rand() ^ 2 + rand() ^ 2 < 1 for _ in 1:n)
-    end
+    return 4s / n
+end
-    return 4*s/n
+for n in 10 .^ (3:8)
+    p = monteπ(n)
+    println("$(lpad(n, 9)): π ≈ $(lpad(p, 10)), pct.err = ", @sprintf("%2.5f%%", abs(p - π) / π))
 end</lang>
 {{out}}
+<pre>     1000: π ≈      3.224, pct.err = 0.02623%
-<pre>
+: π ≈     3.1336, pct.err = 0.00254%
-julia> for n in 10.^(3:8)
-           p = montepi(n)
+: π ≈    3.13468, pct.err = 0.00220%
+  1000000: π ≈    3.14156, pct.err = 0.00001%
-           println("$n: π ≈ $p, |error| = $(abs(p-π))")
+ 10000000: π ≈  3.1412348, pct.err = 0.00011%
-       end
-: π ≈ 3.188, |error| = 0.04640734641020705
+100000000: π ≈ 3.14123216, pct.err = 0.00011%</pre>
-: π ≈ 3.128, |error| = 0.013592653589793002
-: π ≈ 3.1446, |error| = 0.003007346410206946
-1000000: π ≈ 3.14242, |error| = 0.000827346410206875
-10000000: π ≈ 3.1413596, |error| = 0.00023305358979319735
-100000000: π ≈ 3.1417196, |error| = 0.00012694641020694064
-</pre>
 =={{header|K}}==