A. F. Timofeev's 1948 book Integration of Functions includes numerous indefinite integration problems involving a wide variety of rational, algebraic and elementary function integrands. The following table shows the score given Rubi and a variety of computer algebra systems for each of the problems in Chapter 3 of Timofeev's book:
Problem # | Rubi 4.8 | Mathematica 10 | Maple 18 | Maxima 5.28 | Derive 6.1 |
1 | 2 | 2 | 2 | 2 | 2 |
2 | 2 | 2 | 2 | 2 | 2 |
3 | 2 | 2 | 2 | 2 | 2 |
4.1 | 2 | 2 | 2 | 2 | 2 |
4.2 | 2 | 2 | 2 | 2 | 2 |
4.3 | 2 | 2 | 2 | 2 | 2 |
4.4 | 2 | 2 | 2 | 2 | 2 |
4.n | 2 | 1 | 0 | x | x |
5.1 | 2 | 2 | 2 | 2 | 2 |
5.2 | 2 | 2 | 2 | 2 | 2 |
5.3 | 2 | 2 | 2 | 2 | 2 |
5.4 | 2 | 2 | 2 | 2 | 2 |
5.n | 2 | 1 | 0 | x | x |
6 | 2 | 2 | 2 | 2 | 2 |
7 | 2 | 2 | 2 | 2 | 2 |
8 | 2 | 2 | 2 | 2 | 2 |
9 | 2 | 2 | 2 | 2 | 2 |
10 | 2 | 2 | 2 | 2 | 2 |
11 | 2 | 2 | 2 | 2 | 2 |
12 | 2 | 2 | 2 | 2 | 2 |
13 | 2 | 2 | 2 | 2 | 2 |
14 | 2 | 2 | 2 | 2 | 2 |
Totals: | 44 | 42 | 40 | 40 | 40 |
Percent: | 100.0% | 95.5% | 90.9% | 90.9% | 90.9% |
The result produced by the various systems on each problem is assigned a numeric grade based on a comparison with the optimal antiderivative as follows:
Note that simplification of results using functions and/or domain restrictions on variables was not done. In other words, the comparisons are based on the results a novice user would see.
The raw test results generated by running Rubi, Mathematica and Maple on the Timofeev Test Suite are available for viewing or downloading by clicking on the Test Results menu option on the Rubi homepage.