# Timofeev Integration Test Suite

## Summary of Test Results

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.