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.
This chart summarizes the performance of Rubi and several computer algebra systems on these problems.

The following table shows the total score given each of the systems for the problems in each of the 9 chapters of Timofeev's book:

Chapter

Perfect score

Rubi 4.8

Mathematica 10

Maple 18

Maxima 5.28

Derive 6.1

1

172

172

165

165

162

162

2

198

198

198

188

192

192

3

44

44

42

40

40

40

4

244

236

211

203

144

182

5

256

247

214

207

182

213

6

50

50

50

50

50

50

7

22

20

21

19

14

18

8

302

299

292

255

262

237

9

122

118

112

80

76

92

Total:

1410

1384

1305

1207

1122

1186

Percent:

100.0%

98.2%

92.6%

85.6%

79.6%

84.1%

Each result produced by the various systems is assigned a numeric grade based on a comparison with the optimal antiderivative as follows:

If the system gives a result as good as the optimal antiderivative, 2 points are earned.

If the system gives a mathematically correct result (i.e. its derivative equals the integrand) but is substantially more
complex than the optimal antiderivative (e.g. significantly larger or involves the imaginary unit), 1 point is earned.

If the system is unable to integrate the expression in closed-form or times-out after 120 seconds, 0 points are earned.

If the system returns a mathematically incorrect result, 1 point is decremented.

So a perfect score on the Timofeev Test Suite would be a 1410.
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.

To view the score given each of the systems for each of the problems in a chapter of Timofeev's book, click on a chapter number:

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.