open Leibniz

let () =
  print_endline "gradient descent optimization\n";

  let f = Parser.parse "x^2 + y^2" in
  print_endline ("minimizing f(x,y) = " ^ Expr.to_string f);

  match Numerical.gradient_descent f ["x"; "y"] [5.0; 5.0] 0.1 100 with
  | Some [x; y] ->
      Printf.printf "minimum found at (%.4f, %.4f)\n" x y;
      let f_val = Eval.eval [("x", x); ("y", y)] f in
      Printf.printf "f(%.4f, %.4f) = %.4f\n" x y f_val
  | _ ->
      print_endline "optimization failed";

  print_endline "\ngradient computation\n";

  let grad = Multivariate.gradient ["x"; "y"] f in
  print_endline "∇f = [";
  List.iter (fun g -> print_endline ("  " ^ Expr.to_string g)) grad;
  print_endline "]"