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 | C | C | F | A | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 127 | 47 | 96 | 0 | 51 | 37 | 0 | 52 | 37 |
N.S. |
1 | 1.04 | 0.39 | 0.79 | 0.00 | 0.42 | 0.30 | 0.00 | 0.43 | 0.30 |
time (sec) |
N/A | 0.323 | 6.704 | 0.359 | 0.000 | 0.143 | 0.559 | 0.000 | 0.182 | 21.444 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 800 | 876 | 530 | 576 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.10 | 0.66 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.02 | 0.00 |
time (sec) |
N/A | 3.582 | 12.555 | 2.192 | 0.000 | 0.000 | 0.000 | 0.000 | 200.029 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 831 | 1816 | 549 | 604 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 2.19 | 0.66 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.02 | 0.00 |
time (sec) |
N/A | 5.370 | 12.927 | 3.478 | 0.000 | 0.000 | 0.000 | 0.000 | 200.047 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 295 | 295 | 157 | 218 | 0 | 152 | 141 | 0 | 312 | 0 |
N.S. |
1 | 1.00 | 0.53 | 0.74 | 0.00 | 0.52 | 0.48 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 0.645 | 10.180 | 1.178 | 0.000 | 0.110 | 2.071 | 0.000 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 264 | 263 | 133 | 197 | 0 | 137 | 105 | 0 | 105 | 0 |
N.S. |
1 | 1.00 | 0.50 | 0.75 | 0.00 | 0.52 | 0.40 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.587 | 10.177 | 0.735 | 0.000 | 0.112 | 1.992 | 0.000 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 79 | 96 | 0 | 72 | 61 | 0 | 72 | 0 |
N.S. |
1 | 1.00 | 0.65 | 0.79 | 0.00 | 0.60 | 0.50 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.401 | 10.049 | 0.481 | 0.000 | 0.104 | 1.287 | 0.000 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 74 | 70 | 0 | 29 | 36 | 0 | 20 | 37 |
N.S. |
1 | 1.00 | 0.84 | 0.80 | 0.00 | 0.33 | 0.41 | 0.00 | 0.23 | 0.42 |
time (sec) |
N/A | 0.272 | 0.035 | 0.321 | 0.000 | 0.075 | 0.499 | 0.000 | 0.229 | 21.249 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 401 | 431 | 200 | 169 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.07 | 0.50 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.102 | 10.377 | 0.408 | 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 | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 605 | 634 | 448 | 421 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.05 | 0.74 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 2.148 | 11.573 | 0.484 | 0.000 | 0.000 | 0.000 | 0.000 | 200.070 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 655 | 677 | 614 | 483 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.03 | 0.94 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 2.778 | 12.346 | 0.642 | 0.000 | 0.000 | 0.000 | 0.000 | 200.034 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 307 | 295 | 126 | 245 | 0 | 160 | 0 | 0 | 704 | 0 |
N.S. |
1 | 0.96 | 0.41 | 0.80 | 0.00 | 0.52 | 0.00 | 0.00 | 2.29 | 0.00 |
time (sec) |
N/A | 0.642 | 10.110 | 0.827 | 0.000 | 0.123 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 268 | 108 | 233 | 0 | 143 | 0 | 0 | 330 | 0 |
N.S. |
1 | 0.99 | 0.40 | 0.86 | 0.00 | 0.53 | 0.00 | 0.00 | 1.22 | 0.00 |
time (sec) |
N/A | 0.602 | 10.098 | 0.769 | 0.000 | 0.136 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 114 | 59 | 115 | 0 | 76 | 61 | 0 | 186 | 57 |
N.S. |
1 | 1.00 | 0.52 | 1.01 | 0.00 | 0.67 | 0.54 | 0.00 | 1.63 | 0.50 |
time (sec) |
N/A | 0.357 | 10.047 | 0.485 | 0.000 | 0.107 | 3.519 | 0.000 | 0.172 | 21.611 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 108 | 55 | 94 | 0 | 64 | 36 | 0 | 31 | 37 |
N.S. |
1 | 1.00 | 0.51 | 0.87 | 0.00 | 0.59 | 0.33 | 0.00 | 0.29 | 0.34 |
time (sec) |
N/A | 0.300 | 7.547 | 0.320 | 0.000 | 0.107 | 0.560 | 0.000 | 0.171 | 21.475 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 676 | 727 | 455 | 496 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.08 | 0.67 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 2.401 | 11.244 | 0.431 | 0.000 | 0.000 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 882 | 1336 | 578 | 642 | 0 | 0 | 0 | 0 | 98 | 0 |
N.S. |
1 | 1.51 | 0.66 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 5.060 | 13.190 | 0.524 | 0.000 | 0.000 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 177 | 152 | 0 | 0 | 0 | 155 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.573 | 0.717 | 0.000 | 0.000 | 0.000 | 24.636 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 148 | 101 | 0 | 0 | 0 | 107 | 0 | 1518 | 0 |
N.S. |
1 | 1.00 | 0.68 | 0.00 | 0.00 | 0.00 | 0.72 | 0.00 | 10.26 | 0.00 |
time (sec) |
N/A | 0.499 | 0.598 | 0.000 | 0.000 | 0.000 | 22.774 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 96 | 73 | 0 | 0 | 0 | 65 | 0 | 503 | 0 |
N.S. |
1 | 1.00 | 0.76 | 0.00 | 0.00 | 0.00 | 0.68 | 0.00 | 5.24 | 0.00 |
time (sec) |
N/A | 0.394 | 0.381 | 0.000 | 0.000 | 0.000 | 14.258 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 44 | 0 | 0 | 0 | 34 | 0 | 94 | 41 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.77 | 0.00 | 2.14 | 0.93 |
time (sec) |
N/A | 0.259 | 0.005 | 0.000 | 0.000 | 0.000 | 4.606 | 0.000 | 0.157 | 21.552 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 262 | 0 | 0 | 0 | 0 | 0 | 0 | 99 | 0 |
N.S. |
1 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.943 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 452 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1029 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.28 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.242 | 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 | 102 | 118 | 122 | 108 | 108 | 108 | 119 | 111 | 113 | 107 |
N.S. |
1 | 1.16 | 1.20 | 1.06 | 1.06 | 1.06 | 1.17 | 1.09 | 1.11 | 1.05 |
time (sec) |
N/A | 0.523 | 0.030 | 0.158 | 0.033 | 0.076 | 0.036 | 0.113 | 0.160 | 0.054 |
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 | 76 | 81 | 81 | 72 | 71 | 71 | 78 | 75 | 77 | 73 |
N.S. |
1 | 1.07 | 1.07 | 0.95 | 0.93 | 0.93 | 1.03 | 0.99 | 1.01 | 0.96 |
time (sec) |
N/A | 0.428 | 0.030 | 0.209 | 0.026 | 0.064 | 0.031 | 0.133 | 0.170 | 0.034 |
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 | 52 | 50 | 50 | 41 | 40 | 40 | 46 | 40 | 41 | 40 |
N.S. |
1 | 0.96 | 0.96 | 0.79 | 0.77 | 0.77 | 0.88 | 0.77 | 0.79 | 0.77 |
time (sec) |
N/A | 0.334 | 0.006 | 0.037 | 0.026 | 0.073 | 0.024 | 0.123 | 0.154 | 0.025 |
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 | 20 | 20 | 20 | 17 | 16 | 16 | 15 | 16 | 19 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.80 | 0.80 | 0.75 | 0.80 | 0.95 | 0.80 |
time (sec) |
N/A | 0.236 | 0.000 | 0.024 | 0.034 | 0.067 | 0.020 | 0.116 | 0.152 | 0.026 |
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 | 92 | 92 | 83 | 87 | 87 | 87 | 85 | 90 | 101 | 90 |
N.S. |
1 | 1.00 | 0.90 | 0.95 | 0.95 | 0.95 | 0.92 | 0.98 | 1.10 | 0.98 |
time (sec) |
N/A | 0.434 | 0.040 | 0.182 | 0.033 | 0.068 | 0.146 | 0.112 | 0.174 | 0.045 |
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 | 94 | 94 | 91 | 92 | 96 | 131 | 92 | 147 | 141 | 99 |
N.S. |
1 | 1.00 | 0.97 | 0.98 | 1.02 | 1.39 | 0.98 | 1.56 | 1.50 | 1.05 |
time (sec) |
N/A | 0.444 | 0.143 | 0.161 | 0.034 | 0.173 | 0.328 | 0.105 | 0.150 | 0.058 |
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 | 235 | 328 | 258 | 237 | 236 | 236 | 277 | 260 | 263 | 241 |
N.S. |
1 | 1.40 | 1.10 | 1.01 | 1.00 | 1.00 | 1.18 | 1.11 | 1.12 | 1.03 |
time (sec) |
N/A | 1.054 | 0.070 | 0.163 | 0.033 | 0.073 | 0.047 | 0.112 | 0.166 | 0.157 |
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 | 177 | 177 | 177 | 162 | 161 | 161 | 194 | 179 | 182 | 165 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.91 | 0.91 | 1.10 | 1.01 | 1.03 | 0.93 |
time (sec) |
N/A | 0.703 | 0.036 | 0.164 | 0.027 | 0.083 | 0.033 | 0.129 | 0.391 | 0.124 |
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 | 112 | 112 | 97 | 95 | 94 | 94 | 116 | 100 | 101 | 94 |
N.S. |
1 | 1.00 | 0.87 | 0.85 | 0.84 | 0.84 | 1.04 | 0.89 | 0.90 | 0.84 |
time (sec) |
N/A | 0.495 | 0.067 | 0.093 | 0.026 | 0.168 | 0.030 | 0.116 | 0.241 | 21.411 |
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 | 49 | 49 | 49 | 42 | 45 | 41 | 48 | 43 | 46 | 42 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.92 | 0.84 | 0.98 | 0.88 | 0.94 | 0.86 |
time (sec) |
N/A | 0.315 | 0.006 | 0.032 | 0.027 | 0.063 | 0.027 | 0.126 | 0.216 | 0.021 |
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 | 270 | 270 | 268 | 319 | 304 | 304 | 308 | 357 | 386 | 347 |
N.S. |
1 | 1.00 | 0.99 | 1.18 | 1.13 | 1.13 | 1.14 | 1.32 | 1.43 | 1.29 |
time (sec) |
N/A | 0.896 | 0.182 | 0.260 | 0.027 | 0.144 | 0.457 | 0.132 | 0.246 | 21.512 |
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 | 286 | 286 | 286 | 334 | 316 | 409 | 343 | 428 | 491 | 690 |
N.S. |
1 | 1.00 | 1.00 | 1.17 | 1.10 | 1.43 | 1.20 | 1.50 | 1.72 | 2.41 |
time (sec) |
N/A | 0.894 | 0.186 | 0.159 | 0.033 | 0.071 | 0.749 | 0.122 | 0.240 | 0.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F(-1) | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 273 | 302 | 65 | 0 | 0 | 0 | 3317 | 1120 | 9076 |
N.S. |
1 | 1.01 | 1.12 | 0.24 | 0.00 | 0.00 | 0.00 | 12.29 | 4.15 | 33.61 |
time (sec) |
N/A | 1.041 | 0.349 | 0.148 | 0.000 | 0.000 | 0.000 | 0.992 | 0.252 | 23.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 224 | 224 | 245 | 54 | 0 | 540080 | 0 | 1723 | 863 | 3046 |
N.S. |
1 | 1.00 | 1.09 | 0.24 | 0.00 | 2411.07 | 0.00 | 7.69 | 3.85 | 13.60 |
time (sec) |
N/A | 0.681 | 0.225 | 0.214 | 0.000 | 83.146 | 0.000 | 0.928 | 0.244 | 22.538 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 190 | 194 | 43 | 0 | 398481 | 0 | 1342 | 467 | 1308 |
N.S. |
1 | 1.01 | 1.03 | 0.23 | 0.00 | 2108.37 | 0.00 | 7.10 | 2.47 | 6.92 |
time (sec) |
N/A | 0.548 | 0.258 | 0.077 | 0.000 | 3.891 | 0.000 | 0.787 | 0.240 | 21.998 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 150 | 129 | 38 | 0 | 613 | 87 | 1026 | 351 | 763 |
N.S. |
1 | 1.00 | 0.86 | 0.25 | 0.00 | 4.09 | 0.58 | 6.84 | 2.34 | 5.09 |
time (sec) |
N/A | 0.357 | 0.082 | 0.052 | 0.000 | 0.117 | 0.694 | 0.351 | 0.252 | 0.544 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-1) | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 372 | 372 | 366 | 307 | 0 | 0 | 0 | 19589 | 1383 | 1881 |
N.S. |
1 | 1.00 | 0.98 | 0.83 | 0.00 | 0.00 | 0.00 | 52.66 | 3.72 | 5.06 |
time (sec) |
N/A | 1.582 | 0.755 | 0.292 | 0.000 | 0.000 | 0.000 | 2.970 | 0.276 | 22.129 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-1) | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 569 | 569 | 585 | 637 | 0 | 0 | 0 | 0 | 24 | 4722 |
N.S. |
1 | 1.00 | 1.03 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 8.30 |
time (sec) |
N/A | 3.125 | 1.388 | 0.293 | 0.000 | 0.000 | 0.000 | 0.000 | 200.039 | 23.989 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F(-1) | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 446 | 420 | 477 | 293 | 0 | 0 | 0 | 5647 | 5447 | 5441 |
N.S. |
1 | 0.94 | 1.07 | 0.66 | 0.00 | 0.00 | 0.00 | 12.66 | 12.21 | 12.20 |
time (sec) |
N/A | 1.370 | 1.538 | 0.253 | 0.000 | 0.000 | 0.000 | 1.166 | 0.671 | 22.479 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F(-1) | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 410 | 382 | 423 | 255 | 0 | 0 | 0 | 5199 | 4951 | 4118 |
N.S. |
1 | 0.93 | 1.03 | 0.62 | 0.00 | 0.00 | 0.00 | 12.68 | 12.08 | 10.04 |
time (sec) |
N/A | 1.131 | 1.417 | 0.221 | 0.000 | 0.000 | 0.000 | 1.368 | 0.550 | 22.377 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F(-1) | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 330 | 316 | 341 | 209 | 0 | 0 | 0 | 3429 | 2923 | 2382 |
N.S. |
1 | 0.96 | 1.03 | 0.63 | 0.00 | 0.00 | 0.00 | 10.39 | 8.86 | 7.22 |
time (sec) |
N/A | 0.978 | 0.973 | 0.194 | 0.000 | 0.000 | 0.000 | 1.017 | 0.448 | 22.963 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 236 | 243 | 151 | 0 | 2309 | 394 | 2682 | 2409 | 6404 |
N.S. |
1 | 0.94 | 0.96 | 0.60 | 0.00 | 9.16 | 1.56 | 10.64 | 9.56 | 25.41 |
time (sec) |
N/A | 0.556 | 0.503 | 0.112 | 0.000 | 0.229 | 119.815 | 0.396 | 0.310 | 23.578 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-1) | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1006 | 1006 | 1031 | 1568 | 0 | 0 | 0 | 130635 | 17358 | 27673 |
N.S. |
1 | 1.00 | 1.02 | 1.56 | 0.00 | 0.00 | 0.00 | 129.86 | 17.25 | 27.51 |
time (sec) |
N/A | 5.056 | 5.352 | 0.423 | 0.000 | 0.000 | 0.000 | 15.971 | 4.334 | 28.711 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | F(-1) | F(-1) | F(-1) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1689 | 0 | 2086 | 2539 | 0 | 0 | 0 | 0 | 24 | 45031 |
N.S. |
1 | 0.00 | 1.24 | 1.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.01 | 26.66 |
time (sec) |
N/A | 0.000 | 8.084 | 0.918 | 0.000 | 0.000 | 0.000 | 0.000 | 200.024 | 39.814 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 546 | 526 | 707 | 687 | 0 | 625 | 0 | 0 | 1216 | 0 |
N.S. |
1 | 0.96 | 1.29 | 1.26 | 0.00 | 1.14 | 0.00 | 0.00 | 2.23 | 0.00 |
time (sec) |
N/A | 1.497 | 14.291 | 4.049 | 0.000 | 0.281 | 0.000 | 0.000 | 1.581 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 491 | 474 | 640 | 561 | 0 | 551 | 0 | 0 | 836 | 0 |
N.S. |
1 | 0.97 | 1.30 | 1.14 | 0.00 | 1.12 | 0.00 | 0.00 | 1.70 | 0.00 |
time (sec) |
N/A | 1.099 | 12.801 | 3.393 | 0.000 | 0.241 | 0.000 | 0.000 | 1.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 397 | 403 | 579 | 453 | 0 | 391 | 0 | 0 | 473 | 0 |
N.S. |
1 | 1.02 | 1.46 | 1.14 | 0.00 | 0.98 | 0.00 | 0.00 | 1.19 | 0.00 |
time (sec) |
N/A | 0.932 | 11.873 | 1.625 | 0.000 | 0.195 | 0.000 | 0.000 | 0.780 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 309 | 312 | 445 | 379 | 0 | 301 | 0 | 0 | 86 | 0 |
N.S. |
1 | 1.01 | 1.44 | 1.23 | 0.00 | 0.97 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.599 | 0.849 | 1.148 | 0.000 | 0.110 | 0.000 | 0.000 | 0.264 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 794 | 846 | 5994 | 755 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.07 | 7.55 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 2.804 | 20.474 | 5.060 | 0.000 | 0.000 | 0.000 | 0.000 | 200.035 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 855 | 0 | 4221 | 749 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.00 | 4.94 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 0.000 | 19.070 | 0.867 | 0.000 | 0.000 | 0.000 | 0.000 | 200.057 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1140 | 0 | 8346 | 917 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.00 | 7.32 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.02 | 0.00 |
time (sec) |
N/A | 0.000 | 21.097 | 1.260 | 0.000 | 0.000 | 0.000 | 0.000 | 200.047 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 799 | 749 | 2681 | 1300 | 0 | 981 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.94 | 3.36 | 1.63 | 0.00 | 1.23 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 2.162 | 12.678 | 4.585 | 0.000 | 0.320 | 0.000 | 0.000 | 200.067 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 733 | 702 | 838 | 1087 | 0 | 834 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 1.14 | 1.48 | 0.00 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.605 | 15.101 | 3.780 | 0.000 | 0.241 | 0.000 | 0.000 | 112.976 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 512 | 521 | 645 | 690 | 0 | 541 | 0 | 0 | 952 | 0 |
N.S. |
1 | 1.02 | 1.26 | 1.35 | 0.00 | 1.06 | 0.00 | 0.00 | 1.86 | 0.00 |
time (sec) |
N/A | 1.281 | 12.787 | 2.122 | 0.000 | 0.177 | 0.000 | 0.000 | 84.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 381 | 383 | 533 | 471 | 0 | 396 | 0 | 0 | 231 | 0 |
N.S. |
1 | 1.01 | 1.40 | 1.24 | 0.00 | 1.04 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.781 | 1.764 | 1.649 | 0.000 | 0.089 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1150 | 1131 | 12989 | 1017 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.98 | 11.29 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.02 | 0.00 |
time (sec) |
N/A | 5.911 | 23.861 | 4.131 | 0.000 | 0.000 | 0.000 | 0.000 | 200.032 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1195 | 0 | 11129 | 1199 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.00 | 9.31 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.02 | 0.00 |
time (sec) |
N/A | 0.000 | 22.697 | 5.631 | 0.000 | 0.000 | 0.000 | 0.000 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 380 | 379 | 541 | 440 | 0 | 403 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.42 | 1.16 | 0.00 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.997 | 11.481 | 3.061 | 0.000 | 0.272 | 0.000 | 0.000 | 0.609 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 334 | 333 | 490 | 401 | 0 | 371 | 0 | 0 | 339 | 0 |
N.S. |
1 | 1.00 | 1.47 | 1.20 | 0.00 | 1.11 | 0.00 | 0.00 | 1.01 | 0.00 |
time (sec) |
N/A | 0.747 | 11.202 | 1.382 | 0.000 | 0.210 | 0.000 | 0.000 | 0.355 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 160 | 230 | 181 | 0 | 189 | 0 | 0 | 221 | 0 |
N.S. |
1 | 1.00 | 1.44 | 1.13 | 0.00 | 1.18 | 0.00 | 0.00 | 1.38 | 0.00 |
time (sec) |
N/A | 0.484 | 10.396 | 0.736 | 0.000 | 0.146 | 0.000 | 0.000 | 0.274 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 114 | 186 | 144 | 0 | 121 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 1.63 | 1.26 | 0.00 | 1.06 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.292 | 0.082 | 0.356 | 0.000 | 0.106 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 512 | 540 | 1725 | 281 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.05 | 3.37 | 0.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.467 | 17.092 | 0.595 | 0.000 | 0.000 | 0.000 | 0.000 | 200.038 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 816 | 814 | 4019 | 771 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 4.93 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 2.929 | 18.149 | 0.910 | 0.000 | 0.000 | 0.000 | 0.000 | 200.044 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 481 | 461 | 551 | 603 | 0 | 805 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 1.15 | 1.25 | 0.00 | 1.67 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.175 | 12.070 | 1.779 | 0.000 | 0.114 | 0.000 | 0.000 | 0.449 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 456 | 438 | 517 | 572 | 0 | 765 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 1.13 | 1.25 | 0.00 | 1.68 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.990 | 11.836 | 1.451 | 0.000 | 0.113 | 0.000 | 0.000 | 0.365 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 394 | 388 | 470 | 520 | 0 | 487 | 0 | 0 | 481 | 0 |
N.S. |
1 | 0.98 | 1.19 | 1.32 | 0.00 | 1.24 | 0.00 | 0.00 | 1.22 | 0.00 |
time (sec) |
N/A | 0.873 | 11.172 | 0.759 | 0.000 | 0.097 | 0.000 | 0.000 | 0.304 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 353 | 348 | 456 | 481 | 0 | 452 | 0 | 0 | 57 | 0 |
N.S. |
1 | 0.99 | 1.29 | 1.36 | 0.00 | 1.28 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.651 | 1.026 | 0.377 | 0.000 | 0.090 | 0.000 | 0.000 | 0.260 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1010 | 1036 | 4965 | 1111 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.03 | 4.92 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.02 | 0.00 |
time (sec) |
N/A | 3.569 | 18.363 | 0.645 | 0.000 | 0.000 | 0.000 | 0.000 | 200.033 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1490 | 0 | 10488 | 1545 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.00 | 7.04 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.02 | 0.00 |
time (sec) |
N/A | 0.000 | 20.723 | 0.915 | 0.000 | 0.000 | 0.000 | 0.000 | 200.032 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 128 | 105 | 364 | 0 | 221 | 0 | 203 | 100 | 0 |
N.S. |
1 | 1.15 | 0.95 | 3.28 | 0.00 | 1.99 | 0.00 | 1.83 | 0.90 | 0.00 |
time (sec) |
N/A | 0.457 | 0.136 | 0.505 | 0.000 | 0.122 | 0.000 | 0.135 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 128 | 105 | 363 | 0 | 221 | 0 | 203 | 100 | 0 |
N.S. |
1 | 1.15 | 0.95 | 3.27 | 0.00 | 1.99 | 0.00 | 1.83 | 0.90 | 0.00 |
time (sec) |
N/A | 0.462 | 0.004 | 0.309 | 0.000 | 0.098 | 0.000 | 0.143 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 128 | 105 | 364 | 0 | 221 | 0 | 203 | 100 | 0 |
N.S. |
1 | 1.15 | 0.95 | 3.28 | 0.00 | 1.99 | 0.00 | 1.83 | 0.90 | 0.00 |
time (sec) |
N/A | 0.483 | 0.004 | 0.310 | 0.000 | 0.095 | 0.000 | 0.147 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 120 | 97 | 195 | 0 | 313 | 0 | 182 | 93 | 0 |
N.S. |
1 | 1.14 | 0.92 | 1.86 | 0.00 | 2.98 | 0.00 | 1.73 | 0.89 | 0.00 |
time (sec) |
N/A | 0.449 | 0.137 | 0.524 | 0.000 | 0.139 | 0.000 | 0.149 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 120 | 97 | 195 | 0 | 313 | 0 | 182 | 93 | 0 |
N.S. |
1 | 1.14 | 0.92 | 1.86 | 0.00 | 2.98 | 0.00 | 1.73 | 0.89 | 0.00 |
time (sec) |
N/A | 0.461 | 0.003 | 0.324 | 0.000 | 0.173 | 0.000 | 0.130 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 120 | 97 | 195 | 0 | 313 | 0 | 182 | 93 | 0 |
N.S. |
1 | 1.14 | 0.92 | 1.86 | 0.00 | 2.98 | 0.00 | 1.73 | 0.89 | 0.00 |
time (sec) |
N/A | 0.457 | 0.003 | 0.318 | 0.000 | 0.167 | 0.000 | 0.145 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 120 | 97 | 195 | 0 | 313 | 0 | 182 | 93 | 0 |
N.S. |
1 | 1.14 | 0.92 | 1.86 | 0.00 | 2.98 | 0.00 | 1.73 | 0.89 | 0.00 |
time (sec) |
N/A | 0.472 | 0.003 | 0.323 | 0.000 | 0.140 | 0.000 | 0.145 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 120 | 97 | 195 | 0 | 313 | 0 | 182 | 93 | 0 |
N.S. |
1 | 1.14 | 0.92 | 1.86 | 0.00 | 2.98 | 0.00 | 1.73 | 0.89 | 0.00 |
time (sec) |
N/A | 0.464 | 0.003 | 0.331 | 0.000 | 0.153 | 0.000 | 0.135 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 120 | 97 | 195 | 0 | 313 | 0 | 182 | 93 | 0 |
N.S. |
1 | 1.14 | 0.92 | 1.86 | 0.00 | 2.98 | 0.00 | 1.73 | 0.89 | 0.00 |
time (sec) |
N/A | 0.468 | 0.003 | 0.326 | 0.000 | 0.157 | 0.000 | 0.140 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1613 | 1590 | 455 | 1153 | 0 | 0 | 0 | 0 | 45 | 0 |
N.S. |
1 | 0.99 | 0.28 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 20.675 | 11.689 | 0.766 | 0.000 | 0.000 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 191 | 139 | 105 | 0 | 603 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.32 | 0.96 | 0.72 | 0.00 | 4.16 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.592 | 0.882 | 1.093 | 0.000 | 1.383 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 239 | 151 | 351 | 0 | 669 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 0.63 | 1.47 | 0.00 | 2.80 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.611 | 0.838 | 1.836 | 0.000 | 1.431 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 82 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.321 | 0.215 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.428 | 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 | 80 | 80 | 82 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.530 | 0.006 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.405 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 437 | 449 | 86 | 68 | 0 | 0 | 65 | 0 | 115 | 338 |
N.S. |
1 | 1.03 | 0.20 | 0.16 | 0.00 | 0.00 | 0.15 | 0.00 | 0.26 | 0.77 |
time (sec) |
N/A | 2.336 | 0.034 | 0.166 | 0.000 | 0.000 | 0.133 | 0.000 | 0.182 | 22.445 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 455 | 460 | 86 | 63 | 0 | 0 | 65 | 0 | 85 | 338 |
N.S. |
1 | 1.01 | 0.19 | 0.14 | 0.00 | 0.00 | 0.14 | 0.00 | 0.19 | 0.74 |
time (sec) |
N/A | 2.099 | 0.031 | 0.139 | 0.000 | 0.000 | 0.115 | 0.000 | 0.162 | 22.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 441 | 448 | 76 | 58 | 0 | 0 | 65 | 0 | 55 | 338 |
N.S. |
1 | 1.02 | 0.17 | 0.13 | 0.00 | 0.00 | 0.15 | 0.00 | 0.12 | 0.77 |
time (sec) |
N/A | 2.142 | 0.024 | 0.042 | 0.000 | 0.000 | 0.114 | 0.000 | 0.176 | 22.326 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 383 | 370 | 62 | 53 | 0 | 0 | 65 | 0 | 24 | 306 |
N.S. |
1 | 0.97 | 0.16 | 0.14 | 0.00 | 0.00 | 0.17 | 0.00 | 0.06 | 0.80 |
time (sec) |
N/A | 1.821 | 0.012 | 0.033 | 0.000 | 0.000 | 0.108 | 0.000 | 0.181 | 22.708 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 610 | 592 | 173 | 77 | 0 | 0 | 87 | 0 | 39 | 467 |
N.S. |
1 | 0.97 | 0.28 | 0.13 | 0.00 | 0.00 | 0.14 | 0.00 | 0.06 | 0.77 |
time (sec) |
N/A | 2.968 | 0.037 | 0.142 | 0.000 | 0.000 | 0.431 | 0.000 | 0.167 | 22.151 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 610 | 474 | 139 | 77 | 0 | 0 | 87 | 0 | 39 | 467 |
N.S. |
1 | 0.78 | 0.23 | 0.13 | 0.00 | 0.00 | 0.14 | 0.00 | 0.06 | 0.77 |
time (sec) |
N/A | 2.757 | 0.027 | 0.056 | 0.000 | 0.000 | 0.422 | 0.000 | 0.177 | 22.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 651 | 647 | 185 | 84 | 0 | 0 | 94 | 0 | 44 | 480 |
N.S. |
1 | 0.99 | 0.28 | 0.13 | 0.00 | 0.00 | 0.14 | 0.00 | 0.07 | 0.74 |
time (sec) |
N/A | 3.684 | 0.049 | 0.151 | 0.000 | 0.000 | 0.774 | 0.000 | 0.176 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | C | F | F(-1) | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 651 | 485 | 185 | 84 | 0 | 0 | 94 | 0 | 44 | 480 |
N.S. |
1 | 0.75 | 0.28 | 0.13 | 0.00 | 0.00 | 0.14 | 0.00 | 0.07 | 0.74 |
time (sec) |
N/A | 2.820 | 0.028 | 0.059 | 0.000 | 0.000 | 0.772 | 0.000 | 0.172 | 21.941 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | C | A | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 0 | 95 | 67 | 0 | 5653 | 42 | 0 | 95 | 504 |
N.S. |
1 | 0.00 | 0.57 | 0.40 | 0.00 | 33.65 | 0.25 | 0.00 | 0.57 | 3.00 |
time (sec) |
N/A | 0.000 | 0.063 | 0.576 | 0.000 | 0.754 | 0.980 | 0.000 | 0.180 | 22.845 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 287 | 288 | 137 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.886 | 8.303 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.543 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 175 | 106 | 0 | 0 | 0 | 0 | 0 | 1442 | 0 |
N.S. |
1 | 1.02 | 0.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 8.43 | 0.00 |
time (sec) |
N/A | 0.551 | 5.641 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.373 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 85 | 90 | 0 | 0 | 0 | 0 | 0 | 498 | 0 |
N.S. |
1 | 0.91 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 5.35 | 0.00 |
time (sec) |
N/A | 0.354 | 0.485 | 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 | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 44 | 0 | 0 | 0 | 34 | 0 | 94 | 41 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.77 | 0.00 | 2.14 | 0.93 |
time (sec) |
N/A | 0.260 | 0.156 | 0.000 | 0.000 | 0.000 | 32.077 | 0.000 | 0.234 | 22.698 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 162 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 2.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.298 | 0.740 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 2.566 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 162 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 2.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.290 | 0.788 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 34.773 | 0.000 |