Kevin Charlwood's 2008 article
*Integration on Computer Algebra Systems*
included 50 indefinite integration problems involving a variety of elementary functions.
This chart summarizes the performance of ** Rubi** and several computer algebra systems on these problems.

The following table shows the grade given each system on each of the 50 problems in the Charlwood Test Suite:

Problem # | Rubi 4.8 | Mathematica 10 | Maple 18 | FriCAS 1.2.1 | Maxima 5.28 | Derive 6.1 |

1 | 2 | 2 | 1 | 2 | 2 | 2 |

2 | 2 | 2 | 2 | 2 | 2 | 2 |

3 | 0 | 1 | 1 | 2 | -1 | 0 |

4 | 1 | 1 | 1 | 1 | 0 | 1 |

5 | 1 | 1 | 1 | 0 | 0 | 0 |

6 | 2 | 0 | 2 | 2 | 0 | 1 |

7 | 2 | 1 | 2 | 2 | 2 | 2 |

8 | 2 | 0 | 1 | 0 | 0 | 0 |

9 | 2 | 1 | 0 | 2 | 2 | 2 |

10 | 2 | 1 | 2 | 2 | 0 | 0 |

11 | 2 | 2 | 0 | 2 | 0 | 2 |

12 | 1 | 1 | 1 | 2 | 0 | 0 |

13 | 1 | 1 | 0 | 2 | 0 | 0 |

14 | 2 | 2 | 0 | 1 | 0 | 2 |

15 | 2 | 1 | 0 | 2 | 0 | 2 |

16 | 2 | 2 | 0 | 1 | 2 | 2 |

17 | 2 | 1 | 0 | 1 | 0 | 2 |

18 | 2 | 2 | 1 | 2 | 2 | 2 |

19 | 2 | 2 | 2 | 2 | 2 | 2 |

20 | 2 | 2 | 0 | 2 | 2 | 2 |

21 | 2 | 1 | 0 | 1 | 0 | 0 |

22 | 2 | 1 | 0 | 2 | 0 | 1 |

23 | 2 | 2 | 0 | 2 | 0 | 2 |

24 | 2 | 2 | 2 | 2 | 2 | 2 |

25 | 2 | 2 | 0 | 1 | 2 | 2 |

26 | 2 | 2 | 0 | 1 | 0 | 2 |

27 | 2 | 2 | 2 | 1 | 2 | 2 |

28 | 2 | 2 | 0 | 1 | 2 | 2 |

29 | 2 | 2 | 0 | 2 | 0 | 2 |

30 | 2 | 2 | 0 | 2 | 0 | 2 |

31 | 2 | 2 | 0 | 1 | 2 | 2 |

32 | 2 | 2 | 2 | 2 | 2 | 2 |

33 | 2 | 2 | 1 | 1 | 2 | 2 |

34 | 2 | 2 | 2 | 2 | 2 | 2 |

35 | 2 | 2 | 0 | 2 | 0 | 2 |

36 | 2 | 2 | 2 | 1 | 2 | 2 |

37 | 2 | 1 | 2 | 1 | 2 | 2 |

38 | 2 | 1 | 1 | 2 | 0 | 0 |

39 | 2 | 1 | 1 | 2 | 0 | 0 |

40 | 2 | 2 | 2 | 1 | 1 | 0 |

41 | 2 | 1 | 0 | 1 | 0 | 0 |

42 | 1 | 1 | 1 | 1 | 0 | 1 |

43 | 2 | 1 | 2 | 1 | 1 | 2 |

44 | 1 | 0 | 1 | 1 | 0 | 2 |

45 | 0 | 1 | 0 | 1 | 0 | 0 |

46 | 2 | 2 | 1 | 2 | 2 | 2 |

47 | 2 | 1 | 1 | 1 | 0 | 1 |

48 | 2 | 1 | 2 | 2 | 1 | 2 |

49 | 2 | 2 | 1 | 1 | 0 | 2 |

50 | 2 | 2 | 2 | 2 | 0 | 2 |

Totals: | 90 | 73 | 45 | 75 | 40 | 71 |

Percent: | 90.0% | 73.0% | 45.0% | 75.0% | 40.0% | 71.0% |

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 Charlwood Test Suite would be a 100. 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.