vm.fail
symbolic mathematics engine in OCaml with differentiation, integration, simplification, and numerical methods
1open Leibniz
2
3let time_operation name f =
4 let start = Unix.gettimeofday () in
5 let result = f () in
6 let elapsed = Unix.gettimeofday () -. start in
7 Printf.printf "%-40s: %.6f seconds\n" name elapsed;
8 result
9
10let () =
11 print_endline "leibniz benchmark suite\n";
12
13 print_endline "parsing performance:";
14 let _ = time_operation "parse simple expression" (fun () ->
15 Parser.parse "x + 1"
16 ) in
17 let _ = time_operation "parse complex expression" (fun () ->
18 Parser.parse "sin(x^2) * cos(y) + exp(z) / sqrt(w)"
19 ) in
20
21 print_endline "\nsimplification performance:";
22 let simple_expr = Parser.parse "(x + 0) * 1" in
23 let _ = time_operation "simplify simple" (fun () ->
24 Simplify.simplify simple_expr
25 ) in
26
27 let complex_expr = Parser.parse "(x + 0) * (y + 0) + (x * 0) + (x * 1)" in
28 let _ = time_operation "simplify complex" (fun () ->
29 Simplify.simplify complex_expr
30 ) in
31
32 let nested = Parser.parse "((x + 0) * (y + 0)) * ((z + 0) * (w + 0))" in
33 let _ = time_operation "simplify deeply nested" (fun () ->
34 Simplify.simplify nested
35 ) in
36
37 print_endline "\ndifferentiation performance:";
38 let poly = Parser.parse "x^5 + x^4 + x^3 + x^2 + x + 1" in
39 let _ = time_operation "diff polynomial" (fun () ->
40 Diff.diff "x" poly
41 ) in
42
43 let trig = Parser.parse "sin(x) * cos(x) * tan(x)" in
44 let _ = time_operation "diff trigonometric" (fun () ->
45 Diff.diff "x" trig
46 ) in
47
48 let composite = Parser.parse "sin(cos(sin(x)))" in
49 let _ = time_operation "diff nested functions" (fun () ->
50 Diff.diff "x" composite
51 ) in
52
53 print_endline "\nintegration performance:";
54 let int_expr = Parser.parse "x^3" in
55 let _ = time_operation "integrate polynomial" (fun () ->
56 Integrate.integrate "x" int_expr
57 ) in
58
59 let int_trig = Parser.parse "sin(x)" in
60 let _ = time_operation "integrate sin(x)" (fun () ->
61 Integrate.integrate "x" int_trig
62 ) in
63
64 print_endline "\nnumerical methods performance:";
65 let root_expr = Parser.parse "x^2 - 4" in
66 let _ = time_operation "newton-raphson root finding" (fun () ->
67 Numerical.newton_raphson root_expr "x" 1.0 0.0001 100
68 ) in
69
70 let _ = time_operation "bisection root finding" (fun () ->
71 Numerical.bisection root_expr "x" 0.0 3.0 0.0001 100
72 ) in
73
74 let quad_expr = Parser.parse "x^2" in
75 let _ = time_operation "trapezoidal integration" (fun () ->
76 Numerical.trapezoidal quad_expr "x" 0.0 1.0 1000
77 ) in
78
79 let _ = time_operation "simpson's integration" (fun () ->
80 Numerical.simpsons quad_expr "x" 0.0 1.0 1000
81 ) in
82
83 print_endline "\nmultivariate operations:";
84 let mv_expr = Parser.parse "x^2 + y^2 + z^2" in
85 let _ = time_operation "compute gradient (3 vars)" (fun () ->
86 Multivariate.gradient ["x"; "y"; "z"] mv_expr
87 ) in
88
89 let _ = time_operation "compute hessian (3 vars)" (fun () ->
90 Multivariate.hessian ["x"; "y"; "z"] mv_expr
91 ) in
92
93 print_endline "\nformatting performance:";
94 let fmt_expr = Parser.parse "sin(x^2) + cos(y^2)" in
95 let _ = time_operation "to_string" (fun () ->
96 Expr.to_string fmt_expr
97 ) in
98
99 let _ = time_operation "to_latex" (fun () ->
100 Format.to_latex fmt_expr
101 ) in
102
103 let _ = time_operation "to_graphviz" (fun () ->
104 Format.to_graphviz fmt_expr
105 ) in
106
107 print_endline "\nbenchmark complete."