param n := 512;

var x {j in 0..n};
var y {j in 0..n} >= 0;

var dx {j in 1..n} = (x[j] - x[j-1]);
var dy {j in 1..n} = (y[j] - y[j-1]);

var f {j in 1..n} = sqrt( (dx[j]^2 + dy[j]^2)/((y[j]+y[j-1])/2) );

minimize time: sum {j in 1..n} f[j] ;

subject to x0: x[0] = 0;
subject to xn: x[n] = 1;

subject to y0: y[0] = 0;
subject to yn: y[n] = 1;

let {j in 0..n} x[j] := (j/n)^4;
let {j in 0..n} y[j] := x[j];

display time;

solve;

display time;

printf {j in 0..n}: "%10.5f %10.5f \n", x[j], -y[j] > bc.out;