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