[Header]
let test_approx y e =
  let y' = calculate e in
  Float.abs (y' -. y) < 0.01

[Test]
(* test 1 - simple arithmetic *)
S(A(I(3),M(R(4.),I(5))),R(6.7))
|> test_approx 16.3

[Value]
true

[Test]
(* test 2 - division *)
D(I(32), I(7))
|> test_approx 4.57142857142857

[Value]
true

[Test]
(* test 3 - simple sigma *)
C(I(1),I(10),D(M(X,X),R(2.)))
|> test_approx 192.5

[Value]
true

[Test]
(* test 4 - simple integral *)
L(I(0),R(17.18),D(I(1),A(X,I(10))))
|> test_approx 1.

[Value]
true

[Test]
(* test 5 - sigma index *)
A(M(I(100), C(I(5),I(2),X)), C(I(3),A(I(1),I(2)),X))
|> test_approx 3.

[Value]
true

[Test]
(* test 6 - reversed integral *)
L(R(17.18),I(0),D(I(1),A(X,I(10))))
|> test_approx (-1.)

[Value]
true

[Test]
(* test 7 - nested sigma *)
C(I(1),I(5),M(X,C(S(M(X,X),X),M(X,X),M(X,I(2)))))
|> test_approx 2128.

[Value]
true

[Test]
(* test 8 - nested integral *)
C(I(3),I(5),M(L(M(X,I(2)),M(X,R(3.001)),S(M(X,I(2)),I(1))),X))
|> test_approx 1053.8

[Value]
true

[Test]
(* test 9 - error 1 *)
A(X,I(3))
|> calculate

[Exception]
Unbound

[Test]
(* test 10 - error 2 *)
M(C(I(1),I(5),X),X)
|> calculate

[Exception]
Unbound