Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 72 | 56 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.16 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.456 | 0.024 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.252 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 59 | 40 | 40 | 66 | 32 | 119 | 152 | 9 | 0 |
N.S. |
1 | 1.02 | 0.69 | 0.69 | 1.14 | 0.55 | 2.05 | 2.62 | 0.16 | 0.00 |
time (sec) |
N/A | 0.221 | 0.020 | 0.174 | 0.042 | 0.106 | 49.824 | 0.134 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 50 | 35 | 35 | 52 | 27 | 90 | 116 | 9 | 0 |
N.S. |
1 | 1.06 | 0.74 | 0.74 | 1.11 | 0.57 | 1.91 | 2.47 | 0.19 | 0.00 |
time (sec) |
N/A | 0.208 | 0.016 | 0.113 | 0.034 | 0.111 | 16.415 | 0.141 | 0.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 39 | 28 | 28 | 38 | 20 | 61 | 80 | 7 | 0 |
N.S. |
1 | 1.08 | 0.78 | 0.78 | 1.06 | 0.56 | 1.69 | 2.22 | 0.19 | 0.00 |
time (sec) |
N/A | 0.198 | 0.014 | 0.113 | 0.035 | 0.106 | 5.434 | 0.134 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 22 | 21 | 14 | 29 | 41 | 5 | 21 |
N.S. |
1 | 1.00 | 1.00 | 1.22 | 1.17 | 0.78 | 1.61 | 2.28 | 0.28 | 1.17 |
time (sec) |
N/A | 0.165 | 0.003 | 0.105 | 0.052 | 0.105 | 2.102 | 0.128 | 0.216 | 1.281 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 62 | 54 | 63 | 0 | 0 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.11 | 0.96 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.464 | 0.018 | 0.341 | 0.000 | 0.000 | 0.000 | 0.000 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 36 | 32 | 44 | 51 | 19 | 75 | 30 | 9 | 28 |
N.S. |
1 | 0.95 | 0.84 | 1.16 | 1.34 | 0.50 | 1.97 | 0.79 | 0.24 | 0.74 |
time (sec) |
N/A | 0.203 | 0.016 | 0.118 | 0.148 | 0.119 | 11.785 | 0.129 | 0.220 | 0.824 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | C | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 57 | 55 | 57 | 80 | 29 | 144 | 44 | 9 | 0 |
N.S. |
1 | 1.06 | 1.02 | 1.06 | 1.48 | 0.54 | 2.67 | 0.81 | 0.17 | 0.00 |
time (sec) |
N/A | 0.208 | 0.024 | 0.121 | 0.116 | 0.199 | 38.071 | 0.134 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | C | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 76 | 45 | 67 | 106 | 35 | 180 | 58 | 9 | 0 |
N.S. |
1 | 1.12 | 0.66 | 0.99 | 1.56 | 0.51 | 2.65 | 0.85 | 0.13 | 0.00 |
time (sec) |
N/A | 0.218 | 0.037 | 0.118 | 0.124 | 0.121 | 108.728 | 0.390 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 62 | 42 | 56 | 54 | 39 | 51 | 47 | 12 | 0 |
N.S. |
1 | 1.11 | 0.75 | 1.00 | 0.96 | 0.70 | 0.91 | 0.84 | 0.21 | 0.00 |
time (sec) |
N/A | 0.266 | 0.025 | 0.684 | 0.126 | 0.104 | 0.213 | 0.148 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 57 | 44 | 67 | 46 | 38 | 41 | 39 | 47 | 38 |
N.S. |
1 | 1.21 | 0.94 | 1.43 | 0.98 | 0.81 | 0.87 | 0.83 | 1.00 | 0.81 |
time (sec) |
N/A | 0.231 | 0.018 | 0.644 | 0.134 | 0.105 | 0.181 | 0.124 | 0.227 | 0.699 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 28 | 24 | 27 | 22 | 28 | 21 | 24 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 0.92 | 1.04 | 0.85 | 1.08 | 0.81 | 0.92 |
time (sec) |
N/A | 0.201 | 0.008 | 0.664 | 0.032 | 0.117 | 0.148 | 0.123 | 0.218 | 0.761 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 67 | 59 | 76 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.14 | 1.00 | 1.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.368 | 0.017 | 0.844 | 0.000 | 0.000 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | C | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 93 | 30 | 52 | 107 | 29 | 61 | 12 | 29 |
N.S. |
1 | 1.00 | 3.00 | 0.97 | 1.68 | 3.45 | 0.94 | 1.97 | 0.39 | 0.94 |
time (sec) |
N/A | 0.246 | 0.089 | 0.041 | 0.034 | 0.124 | 1.304 | 0.124 | 0.208 | 0.683 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 36 | 33 | 32 | 39 | 53 | 61 | 12 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.87 | 0.84 | 1.03 | 1.39 | 1.61 | 0.32 | 0.00 |
time (sec) |
N/A | 0.221 | 0.016 | 0.647 | 0.119 | 0.122 | 0.738 | 0.130 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | C | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 61 | 69 | 54 | 64 | 142 | 100 | 80 | 12 | 0 |
N.S. |
1 | 1.02 | 1.15 | 0.90 | 1.07 | 2.37 | 1.67 | 1.33 | 0.20 | 0.00 |
time (sec) |
N/A | 0.245 | 0.028 | 0.646 | 0.110 | 0.126 | 1.679 | 0.126 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 80 | 60 | 93 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.16 | 0.87 | 1.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.492 | 0.056 | 0.795 | 0.000 | 0.000 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 206 | 173 | 329 | 0 | 152 | 0 | 412 | 12 | 0 |
N.S. |
1 | 1.05 | 0.88 | 1.67 | 0.00 | 0.77 | 0.00 | 2.09 | 0.06 | 0.00 |
time (sec) |
N/A | 0.724 | 0.115 | 0.244 | 0.000 | 0.125 | 0.000 | 0.161 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 157 | 150 | 249 | 0 | 130 | 0 | 302 | 12 | 0 |
N.S. |
1 | 1.01 | 0.97 | 1.61 | 0.00 | 0.84 | 0.00 | 1.95 | 0.08 | 0.00 |
time (sec) |
N/A | 0.536 | 0.178 | 0.170 | 0.000 | 0.122 | 0.000 | 0.153 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 116 | 131 | 190 | 0 | 117 | 0 | 207 | 12 | 0 |
N.S. |
1 | 1.00 | 1.13 | 1.64 | 0.00 | 1.01 | 0.00 | 1.78 | 0.10 | 0.00 |
time (sec) |
N/A | 0.399 | 0.118 | 0.171 | 0.000 | 0.139 | 0.000 | 0.162 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 110 | 108 | 0 | 104 | 0 | 136 | 10 | 0 |
N.S. |
1 | 1.00 | 1.41 | 1.38 | 0.00 | 1.33 | 0.00 | 1.74 | 0.13 | 0.00 |
time (sec) |
N/A | 0.446 | 0.077 | 0.155 | 0.000 | 0.121 | 0.000 | 0.147 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | B | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 35 | 468 | 45 | 55 | 73 | 0 | 82 | 8 | 35 |
N.S. |
1 | 0.95 | 12.65 | 1.22 | 1.49 | 1.97 | 0.00 | 2.22 | 0.22 | 0.95 |
time (sec) |
N/A | 0.228 | 1.936 | 0.041 | 0.030 | 0.128 | 0.000 | 0.140 | 0.227 | 1.007 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 263 | 284 | 374 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.32 | 1.42 | 1.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.101 | 0.222 | 0.904 | 0.000 | 0.000 | 0.000 | 0.000 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 73 | 112 | 126 | 0 | 281 | 0 | 94 | 12 | 0 |
N.S. |
1 | 1.04 | 1.60 | 1.80 | 0.00 | 4.01 | 0.00 | 1.34 | 0.17 | 0.00 |
time (sec) |
N/A | 0.412 | 0.197 | 0.348 | 0.000 | 0.130 | 0.000 | 0.148 | 0.248 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 148 | 198 | 319 | 0 | 427 | 0 | 216 | 12 | 0 |
N.S. |
1 | 1.18 | 1.58 | 2.55 | 0.00 | 3.42 | 0.00 | 1.73 | 0.10 | 0.00 |
time (sec) |
N/A | 0.742 | 0.668 | 0.334 | 0.000 | 0.132 | 0.000 | 0.164 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 222 | 241 | 528 | 0 | 548 | 0 | 451 | 12 | 0 |
N.S. |
1 | 1.23 | 1.33 | 2.92 | 0.00 | 3.03 | 0.00 | 2.49 | 0.07 | 0.00 |
time (sec) |
N/A | 1.062 | 0.287 | 0.335 | 0.000 | 0.189 | 0.000 | 0.186 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 381 | 357 | 667 | 673 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 0.94 | 1.75 | 1.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.638 | 8.171 | 0.854 | 0.000 | 0.000 | 0.000 | 0.000 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 288 | 271 | 473 | 498 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 0.94 | 1.64 | 1.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.541 | 4.011 | 0.760 | 0.000 | 0.000 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 146 | 144 | 225 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 0.95 | 0.94 | 1.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.442 | 0.094 | 0.500 | 0.000 | 0.000 | 0.000 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 89 | 111 | 162 | 0 | 0 | 0 | 0 | 10 | 0 |
N.S. |
1 | 0.95 | 1.18 | 1.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.411 | 0.078 | 0.266 | 0.000 | 0.000 | 0.000 | 0.000 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 310 | 398 | 813 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.28 | 2.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.579 | 1.515 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 244 | 248 | 686 | 336 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.02 | 2.81 | 1.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.724 | 1.459 | 0.772 | 0.000 | 0.000 | 0.000 | 0.000 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 494 | 446 | 446 | 716 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 0.90 | 0.90 | 1.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 0.728 | 0.249 | 0.739 | 0.000 | 0.000 | 0.000 | 0.000 | 0.243 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 278 | 253 | 257 | 379 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 0.91 | 0.92 | 1.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.571 | 0.095 | 0.727 | 0.000 | 0.000 | 0.000 | 0.000 | 0.249 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 149 | 160 | 0 | 0 | 0 | 0 | 0 | 10 | 0 |
N.S. |
1 | 0.97 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.576 | 0.069 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.266 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 430 | 529 | 1058 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.23 | 2.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 1.847 | 2.555 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F(-1) | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 362 | 365 | 0 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.885 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 54 | 516 | 64 | 71 | 96 | 0 | 100 | 21 | 52 |
N.S. |
1 | 0.93 | 8.90 | 1.10 | 1.22 | 1.66 | 0.00 | 1.72 | 0.36 | 0.90 |
time (sec) |
N/A | 0.252 | 2.014 | 0.221 | 0.028 | 0.113 | 0.000 | 0.240 | 0.231 | 1.208 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 54 | 516 | 64 | 71 | 96 | 0 | 100 | 23 | 52 |
N.S. |
1 | 0.93 | 8.90 | 1.10 | 1.22 | 1.66 | 0.00 | 1.72 | 0.40 | 0.90 |
time (sec) |
N/A | 0.273 | 0.274 | 0.224 | 0.040 | 0.125 | 0.000 | 0.250 | 0.234 | 0.945 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 54 | 137 | 64 | 71 | 96 | 0 | 100 | 23 | 52 |
N.S. |
1 | 0.93 | 2.36 | 1.10 | 1.22 | 1.66 | 0.00 | 1.72 | 0.40 | 0.90 |
time (sec) |
N/A | 0.277 | 0.211 | 0.242 | 0.042 | 0.112 | 0.000 | 0.261 | 0.257 | 0.909 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | A | A | F(-1) | A | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 45 | 130 | 0 | 66 | 92 | 0 | 75 | 17 | 44 |
N.S. |
1 | 0.92 | 2.65 | 0.00 | 1.35 | 1.88 | 0.00 | 1.53 | 0.35 | 0.90 |
time (sec) |
N/A | 0.323 | 0.207 | 0.000 | 0.039 | 0.130 | 0.000 | 0.196 | 0.266 | 1.317 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 100 | 280 | 111 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.18 | 3.29 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.466 | 0.806 | 0.817 | 0.000 | 0.000 | 0.000 | 0.000 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 97 | 95 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 0.98 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.341 | 0.219 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.274 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 89 | 107 | 0 | 0 | 0 | 0 | 0 | 10 | 0 |
N.S. |
1 | 0.98 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.322 | 0.137 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.300 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 89 | 54 | 0 | 0 | 0 | 0 | 0 | 8 | 0 |
N.S. |
1 | 0.98 | 0.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.304 | 0.048 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.270 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 79 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.00 | 1.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.281 | 0.038 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.252 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 43 | 34 | 0 | 0 | 23 | 0 | 43 | 12 | 0 |
N.S. |
1 | 1.10 | 0.87 | 0.00 | 0.00 | 0.59 | 0.00 | 1.10 | 0.31 | 0.00 |
time (sec) |
N/A | 0.230 | 0.030 | 0.000 | 0.000 | 0.126 | 0.000 | 0.138 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 42 | 30 | 0 | 0 | 30 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.02 | 0.73 | 0.00 | 0.00 | 0.73 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.282 | 0.031 | 0.000 | 0.000 | 0.116 | 0.000 | 0.000 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 79 | 54 | 0 | 0 | 40 | 0 | 0 | 12 | 0 |
N.S. |
1 | 0.94 | 0.64 | 0.00 | 0.00 | 0.48 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.288 | 0.107 | 0.000 | 0.000 | 0.155 | 0.000 | 0.000 | 0.254 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 68 | 59 | 99 | 0 | 0 | 0 | 115 | 21 | 0 |
N.S. |
1 | 0.99 | 0.86 | 1.43 | 0.00 | 0.00 | 0.00 | 1.67 | 0.30 | 0.00 |
time (sec) |
N/A | 0.491 | 0.050 | 0.519 | 0.000 | 0.000 | 0.000 | 0.338 | 0.237 | 0.000 |