// ---------- begin input macro ---------- // reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { (source = $s:expr, $($r:tt)*) => { let mut iter = $s.split_whitespace(); input_inner!{iter, $($r)*} }; ($($r:tt)*) => { let s = { use std::io::Read; let mut s = String::new(); std::io::stdin().read_to_string(&mut s).unwrap(); s }; let mut iter = s.split_whitespace(); input_inner!{iter, $($r)*} }; } macro_rules! input_inner { ($iter:expr) => {}; ($iter:expr, ) => {}; ($iter:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($iter, $t); input_inner!{$iter $($r)*} }; } macro_rules! read_value { ($iter:expr, ( $($t:tt),* )) => { ( $(read_value!($iter, $t)),* ) }; ($iter:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($iter, $t)).collect::>() }; ($iter:expr, chars) => { read_value!($iter, String).chars().collect::>() }; ($iter:expr, bytes) => { read_value!($iter, String).bytes().collect::>() }; ($iter:expr, usize1) => { read_value!($iter, usize) - 1 }; ($iter:expr, $t:ty) => { $iter.next().unwrap().parse::<$t>().expect("Parse error") }; } // ---------- end input macro ---------- fn calc(d: f64) -> f64 { let mut sum = 0f64; let mut c = 0f64; let n = 1 << 25; let f = 1f64 / n as f64; for i in (0..n).rev() { let r = (n - i - 1) as f64 * f; if 2.0 * r < d { continue; } let p = (d / 2.0 / r).acos() * 2.0; // ans += r * r * (p - p.sin()); let mut v = 0f64; let m = 17; let mut de = -1.0 / (1..=m).fold(1f64, |s, a| s * a as f64); for i in 0..=7 { v = v * p * p + de; de = -de * (m - 2 * i) as f64 * (m - 2 * i - 1) as f64; } v *= r * r * p * p * p; // sum += v; let y = v - c; let t = sum + y; c = (t - sum) - y; sum = t; } sum * f } fn run() { input! { r: f64, h: f64, d: f64, } let ans = r * r * h * calc(d / r); println!("{:.7}", ans); } fn main() { run(); }