open Leibniz

let () =
  print_endline "root finding\n";

  let f = Parser.parse "x^2 - 4" in
  print_endline ("finding roots of f(x) = " ^ Expr.to_string f);

  (match Numerical.bisection f "x" 0.0 3.0 0.0001 100 with
   | Some root -> Printf.printf "bisection: root ≈ %.6f\n" root
   | None -> print_endline "bisection failed");

  (match Numerical.newton_raphson f "x" 1.0 0.0001 100 with
   | Some root -> Printf.printf "newton-raphson: root ≈ %.6f\n" root
   | None -> print_endline "newton-raphson failed");

  print_endline "\nnumerical integration\n";

  let g = Parser.parse "sin(x)" in
  print_endline ("integrating g(x) = " ^ Expr.to_string g);

  let trap = Numerical.trapezoidal g "x" 0.0 3.14159265 100 in
  Printf.printf "trapezoidal rule: %.6f\n" trap;

  let simp = Numerical.simpsons g "x" 0.0 3.14159265 100 in
  Printf.printf "simpson's rule: %.6f\n" simp