| Indefinite Integration Test Suite Results | ||||||||||||||||
| 9 June 2011 | ||||||||||||||||
| Rubi 3 | Maple 13 | Mathematica 7 | ||||||||||||||
| Integrand Types | Problems | Optimal | Messy | Unable | Invalid | Optimal | Messy | Unable | Invalid | Optimal | Messy | Unable | Invalid | |||
| Rational functions | 1745 | 1744 | 0 | 1 | 0 | 1372 | 350 | 2 | 21 | 1613 | 123 | 8 | 1 | |||
| Algebraic functions | 1906 | 1890 | 7 | 9 | 0 | 1187 | 272 | 87 | 360 | 1763 | 94 | 39 | 10 | |||
| Exponential functions | 592 | 588 | 0 | 4 | 0 | 368 | 67 | 55 | 102 | 548 | 15 | 15 | 14 | |||
| Logarithm functions | 682 | 679 | 1 | 2 | 0 | 275 | 134 | 236 | 37 | 628 | 32 | 22 | 0 | |||
| Trig functions | 8871 | 8862 | 4 | 5 | 0 | 2670 | 5308 | 217 | 676 | 5401 | 2079 | 231 | 1160 | |||
| Inverse trig functions | 559 | 555 | 1 | 3 | 0 | 291 | 126 | 27 | 115 | 509 | 31 | 19 | 0 | |||
| Hyperbolic functions | 2431 | 2424 | 4 | 3 | 0 | 766 | 1120 | 389 | 156 | 2094 | 293 | 27 | 17 | |||
| Inverse hyperbolic functions | 851 | 848 | 0 | 3 | 0 | 213 | 119 | 307 | 212 | 780 | 56 | 13 | 2 | |||
| Error and Fresnel functions | 240 | 240 | 0 | 0 | 0 | 164 | 0 | 68 | 8 | 177 | 0 | 63 | 0 | |||
| Integral functions | 250 | 250 | 0 | 0 | 0 | 207 | 10 | 28 | 5 | 224 | 6 | 20 | 0 | |||
| Special functions | 449 | 449 | 0 | 0 | 0 | 188 | 10 | 140 | 111 | 290 | 0 | 159 | 0 | |||
| Contributed problems | 180 | 173 | 5 | 2 | 0 | 122 | 32 | 15 | 11 | 142 | 22 | 13 | 3 | |||
| Totals | 18756 | 18702 | 22 | 32 | 0 | 7823 | 7548 | 1571 | 1814 | 14169 | 2751 | 629 | 1207 | |||
| Percentages | 99.7% | 0.1% | 0.2% | 0.0% | 41.7% | 40.2% | 8.4% | 9.7% | 75.5% | 14.7% | 3.4% | 6.4% | ||||
| Column headings: | ||||||||||||||||
| Problems: the number of integration problems for each type of integrand. | ||||||||||||||||
| Optimal: the number of results that are optimal or no more than twice the size of the optimal antiderivative, in terms of leaf counts. | ||||||||||||||||
| Messy: the number of results that are correct but more than twice the size of the optimal antiderivative. | ||||||||||||||||
| Unable: the number of problems the system returns unintegrated or cannot integrate in 60 seconds. | ||||||||||||||||
| Invalid: the number of results that are incorrect or the system is incapable of verifying correct by differentiation. | ||||||||||||||||