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 | Mupad | |
grade |
N/A | A | A | C | F | A | A | A | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 77 | 88 | 143 | 43 | 0 | 76 | 60 | 55 | 51 |
N.S. |
1 | 1.14 | 1.86 | 0.56 | 0.00 | 0.99 | 0.78 | 0.71 | 0.66 |
time (sec) |
N/A | 0.250 | 0.035 | 0.113 | 0.000 | 0.246 | 0.152 | 0.300 | 0.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 25 | 25 | 26 | 25 | 43 | 0 | 73 | 52 |
N.S. |
1 | 0.83 | 0.83 | 0.87 | 0.83 | 1.43 | 0.00 | 2.43 | 1.73 |
time (sec) |
N/A | 0.162 | 0.013 | 0.051 | 0.192 | 0.234 | 0.000 | 0.282 | 9.335 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 98 | 216 | 97 | 107 | 97 | 97 |
N.S. |
1 | 1.00 | 1.00 | 7.00 | 15.43 | 6.93 | 7.64 | 6.93 | 6.93 |
time (sec) |
N/A | 0.146 | 0.001 | 0.034 | 0.197 | 0.258 | 0.033 | 0.290 | 9.169 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 65 | 99 | 64 | 66 | 64 | 64 |
N.S. |
1 | 1.00 | 1.00 | 4.64 | 7.07 | 4.57 | 4.71 | 4.57 | 4.57 |
time (sec) |
N/A | 0.147 | 0.002 | 0.032 | 0.198 | 0.247 | 0.027 | 0.338 | 0.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 14 | 35 | 13 | 31 | 31 | 32 | 31 | 31 |
N.S. |
1 | 0.40 | 1.00 | 0.37 | 0.89 | 0.89 | 0.91 | 0.89 | 0.89 |
time (sec) |
N/A | 0.144 | 0.000 | 0.026 | 0.191 | 0.230 | 0.018 | 0.286 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 24 | 24 | 26 | 12 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 1.71 | 1.71 | 1.86 | 0.86 | 1.86 |
time (sec) |
N/A | 0.149 | 0.003 | 0.035 | 0.200 | 0.237 | 0.078 | 0.298 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 57 | 57 | 61 | 12 | 59 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 4.07 | 4.07 | 4.36 | 0.86 | 4.21 |
time (sec) |
N/A | 0.150 | 0.005 | 0.075 | 0.202 | 0.255 | 0.171 | 0.296 | 9.285 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 90 | 90 | 97 | 12 | 92 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 6.43 | 6.43 | 6.93 | 0.86 | 6.57 |
time (sec) |
N/A | 0.149 | 0.002 | 0.107 | 0.201 | 0.240 | 0.251 | 0.277 | 9.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 84 | 93 | 159 | 159 | 204 | 156 | 175 | 166 | 149 |
N.S. |
1 | 1.11 | 1.89 | 1.89 | 2.43 | 1.86 | 2.08 | 1.98 | 1.77 |
time (sec) |
N/A | 0.297 | 0.016 | 0.035 | 0.211 | 0.250 | 0.044 | 0.276 | 9.303 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 64 | 82 | 82 | 93 | 80 | 87 | 83 | 79 |
N.S. |
1 | 1.14 | 1.46 | 1.46 | 1.66 | 1.43 | 1.55 | 1.48 | 1.41 |
time (sec) |
N/A | 0.245 | 0.007 | 0.029 | 0.209 | 0.254 | 0.030 | 0.297 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 29 | 28 | 28 | 31 | 28 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.88 | 0.88 | 0.97 | 0.88 | 0.88 |
time (sec) |
N/A | 0.158 | 0.000 | 0.021 | 0.195 | 0.252 | 0.020 | 0.283 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 188 | 194 | 63 | 57 | 0 | 387 | 53 | 212 | 174 |
N.S. |
1 | 1.03 | 0.34 | 0.30 | 0.00 | 2.06 | 0.28 | 1.13 | 0.93 |
time (sec) |
N/A | 0.459 | 0.014 | 0.048 | 0.000 | 0.288 | 0.204 | 0.278 | 0.321 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 245 | 268 | 112 | 134 | 0 | 704 | 192 | 289 | 247 |
N.S. |
1 | 1.09 | 0.46 | 0.55 | 0.00 | 2.87 | 0.78 | 1.18 | 1.01 |
time (sec) |
N/A | 0.486 | 0.044 | 0.085 | 0.000 | 0.275 | 0.664 | 0.321 | 10.171 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 305 | 342 | 149 | 277 | 0 | 1268 | 474 | 366 | 483 |
N.S. |
1 | 1.12 | 0.49 | 0.91 | 0.00 | 4.16 | 1.55 | 1.20 | 1.58 |
time (sec) |
N/A | 0.548 | 0.058 | 0.146 | 0.000 | 0.283 | 1.390 | 0.278 | 10.188 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 361 | 361 | 653 | 842 | 461 | 727 | 1018 | 987 | 787 |
N.S. |
1 | 1.00 | 1.81 | 2.33 | 1.28 | 2.01 | 2.82 | 2.73 | 2.18 |
time (sec) |
N/A | 0.985 | 0.160 | 0.053 | 0.212 | 0.251 | 0.087 | 0.286 | 9.629 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 193 | 193 | 241 | 188 | 180 | 269 | 345 | 346 | 270 |
N.S. |
1 | 1.00 | 1.25 | 0.97 | 0.93 | 1.39 | 1.79 | 1.79 | 1.40 |
time (sec) |
N/A | 0.501 | 0.056 | 0.037 | 0.206 | 0.231 | 0.043 | 0.351 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 76 | 53 | 50 | 52 | 63 | 50 | 54 |
N.S. |
1 | 1.00 | 1.36 | 0.95 | 0.89 | 0.93 | 1.12 | 0.89 | 0.96 |
time (sec) |
N/A | 0.187 | 0.000 | 0.027 | 0.201 | 0.238 | 0.019 | 0.262 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 80 | 87 | 112 | 112 | 0 | 131 | 106 |
N.S. |
1 | 1.00 | 0.93 | 1.01 | 1.30 | 1.30 | 0.00 | 1.52 | 1.23 |
time (sec) |
N/A | 0.284 | 0.048 | 0.126 | 0.217 | 2.906 | 0.000 | 0.285 | 9.712 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | F(-1) | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 234 | 234 | 232 | 235 | 2096 | 0 | 0 | 1435 | 1940 |
N.S. |
1 | 1.00 | 0.99 | 1.00 | 8.96 | 0.00 | 0.00 | 6.13 | 8.29 |
time (sec) |
N/A | 0.633 | 0.368 | 0.716 | 0.316 | 0.000 | 0.000 | 0.282 | 13.890 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | F(-1) | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 495 | 495 | 490 | 514 | 11005 | 0 | 0 | 7111 | 82532 |
N.S. |
1 | 1.00 | 0.99 | 1.04 | 22.23 | 0.00 | 0.00 | 14.37 | 166.73 |
time (sec) |
N/A | 1.598 | 0.718 | 2.373 | 0.740 | 0.000 | 0.000 | 0.404 | 23.447 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 20 | 19 | 19 | 19 | 20 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.76 | 0.76 | 0.76 | 0.80 | 1.00 |
time (sec) |
N/A | 0.179 | 0.006 | 0.056 | 0.286 | 0.313 | 0.057 | 0.278 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 31 | 26 | 25 | 25 | 24 | 26 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.81 | 0.81 | 0.77 | 0.84 | 0.81 |
time (sec) |
N/A | 0.197 | 0.006 | 0.063 | 0.288 | 0.332 | 0.065 | 0.321 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 10 | 9 | 8 | 8 | 8 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.80 | 0.80 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.155 | 0.001 | 0.016 | 0.200 | 0.329 | 0.019 | 0.284 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 26 | 28 | 26 | 19 | 30 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 1.00 | 0.93 | 0.68 | 1.07 | 0.89 |
time (sec) |
N/A | 0.190 | 0.005 | 0.691 | 0.198 | 0.310 | 0.082 | 0.296 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 26 | 22 | 21 | 20 | 18 | 15 | 24 | 18 |
N.S. |
1 | 1.18 | 1.00 | 0.95 | 0.91 | 0.82 | 0.68 | 1.09 | 0.82 |
time (sec) |
N/A | 0.168 | 0.005 | 0.683 | 0.193 | 0.311 | 0.098 | 0.276 | 9.264 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 63 | 61 | 61 | 0 | 211 | 564 | 62 | 213 |
N.S. |
1 | 1.02 | 0.98 | 0.98 | 0.00 | 3.40 | 9.10 | 1.00 | 3.44 |
time (sec) |
N/A | 0.252 | 0.052 | 0.089 | 0.000 | 0.323 | 4.405 | 0.333 | 0.283 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 111 | 89 | 27 | 98 | 299 | 20 | 112 | 99 |
N.S. |
1 | 0.97 | 0.77 | 0.23 | 0.85 | 2.60 | 0.17 | 0.97 | 0.86 |
time (sec) |
N/A | 0.280 | 0.021 | 0.680 | 0.282 | 0.320 | 0.071 | 0.277 | 0.143 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 17 | 17 | 16 | 29 | 16 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.06 | 1.00 | 1.81 | 1.00 | 1.00 |
time (sec) |
N/A | 0.144 | 0.002 | 0.027 | 0.202 | 0.298 | 0.277 | 0.266 | 9.845 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 53 | 0 | 0 | 0 | 0 | 0 | 56 |
N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.02 |
time (sec) |
N/A | 0.192 | 0.027 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 9.640 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 53 | 59 | 61 | 0 | 0 | 0 | 0 | 0 | 56 |
N.S. |
1 | 1.11 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.06 |
time (sec) |
N/A | 0.197 | 0.030 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 10.146 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 132 | 132 | 129 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.339 | 0.138 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | B |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 35 | 44 | 203 | 0 | 0 | 0 | 34 | 0 | 41 |
N.S. |
1 | 1.26 | 5.80 | 0.00 | 0.00 | 0.00 | 0.97 | 0.00 | 1.17 |
time (sec) |
N/A | 0.171 | 0.136 | 0.000 | 0.000 | 0.000 | 5.126 | 0.000 | 10.478 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 270 | 276 | 285 | 267 | 372 | 271 | 299 | 277 | 261 |
N.S. |
1 | 1.02 | 1.06 | 0.99 | 1.38 | 1.00 | 1.11 | 1.03 | 0.97 |
time (sec) |
N/A | 0.591 | 0.032 | 0.050 | 0.196 | 0.271 | 0.048 | 0.279 | 10.568 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 189 | 171 | 163 | 205 | 163 | 180 | 166 | 160 |
N.S. |
1 | 1.11 | 1.00 | 0.95 | 1.20 | 0.95 | 1.05 | 0.97 | 0.94 |
time (sec) |
N/A | 0.422 | 0.015 | 0.047 | 0.218 | 0.263 | 0.037 | 0.281 | 10.577 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 117 | 92 | 83 | 94 | 82 | 95 | 83 | 82 |
N.S. |
1 | 1.27 | 1.00 | 0.90 | 1.02 | 0.89 | 1.03 | 0.90 | 0.89 |
time (sec) |
N/A | 0.312 | 0.010 | 0.038 | 0.190 | 0.284 | 0.028 | 0.269 | 0.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 29 | 28 | 28 | 31 | 28 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.88 | 0.88 | 0.97 | 0.88 | 0.88 |
time (sec) |
N/A | 0.167 | 0.000 | 0.029 | 0.195 | 0.279 | 0.020 | 0.266 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 529 | 555 | 71 | 64 | 0 | 905 | 88 | 603 | 1551 |
N.S. |
1 | 1.05 | 0.13 | 0.12 | 0.00 | 1.71 | 0.17 | 1.14 | 2.93 |
time (sec) |
N/A | 1.027 | 0.020 | 0.137 | 0.000 | 0.293 | 0.595 | 0.290 | 12.187 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 746 | 797 | 182 | 230 | 0 | 3222 | 0 | 1057 | 5844 |
N.S. |
1 | 1.07 | 0.24 | 0.31 | 0.00 | 4.32 | 0.00 | 1.42 | 7.83 |
time (sec) |
N/A | 1.260 | 0.071 | 0.122 | 0.000 | 0.373 | 0.000 | 0.389 | 12.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 295 | 304 | 345 | 332 | 383 | 332 | 366 | 353 | 331 |
N.S. |
1 | 1.03 | 1.17 | 1.13 | 1.30 | 1.13 | 1.24 | 1.20 | 1.12 |
time (sec) |
N/A | 0.594 | 0.045 | 0.059 | 0.195 | 0.286 | 0.051 | 0.295 | 10.542 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 203 | 215 | 207 | 200 | 214 | 198 | 218 | 205 | 201 |
N.S. |
1 | 1.06 | 1.02 | 0.99 | 1.05 | 0.98 | 1.07 | 1.01 | 0.99 |
time (sec) |
N/A | 0.427 | 0.019 | 0.048 | 0.202 | 0.274 | 0.038 | 0.295 | 0.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 107 | 135 | 109 | 99 | 101 | 98 | 112 | 99 | 98 |
N.S. |
1 | 1.26 | 1.02 | 0.93 | 0.94 | 0.92 | 1.05 | 0.93 | 0.92 |
time (sec) |
N/A | 0.314 | 0.011 | 0.038 | 0.198 | 0.272 | 0.026 | 0.293 | 10.174 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 37 | 34 | 33 | 33 | 36 | 33 | 33 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.89 | 0.89 | 0.97 | 0.89 | 0.89 |
time (sec) |
N/A | 0.169 | 0.000 | 0.030 | 0.191 | 0.258 | 0.020 | 0.275 | 0.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 153 | 165 | 71 | 67 | 0 | 1115 | 122 | 577 | 1264 |
N.S. |
1 | 1.08 | 0.46 | 0.44 | 0.00 | 7.29 | 0.80 | 3.77 | 8.26 |
time (sec) |
N/A | 0.361 | 0.018 | 0.261 | 0.000 | 0.310 | 0.991 | 0.284 | 11.302 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 342 | 377 | 234 | 288 | 0 | 4285 | 0 | 1115 | 10351 |
N.S. |
1 | 1.10 | 0.68 | 0.84 | 0.00 | 12.53 | 0.00 | 3.26 | 30.27 |
time (sec) |
N/A | 0.582 | 0.096 | 0.133 | 0.000 | 0.482 | 0.000 | 0.317 | 13.831 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 96 | 96 | 96 | 85 | 84 | 84 | 94 | 84 | 84 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.88 | 0.88 | 0.98 | 0.88 | 0.88 |
time (sec) |
N/A | 0.239 | 0.003 | 0.030 | 0.193 | 0.281 | 0.028 | 0.294 | 0.197 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 74 | 65 | 64 | 64 | 71 | 64 | 64 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.86 | 0.86 | 0.96 | 0.86 | 0.86 |
time (sec) |
N/A | 0.221 | 0.001 | 0.028 | 0.187 | 0.289 | 0.027 | 0.279 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 54 | 45 | 44 | 44 | 49 | 44 | 44 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.81 | 0.81 | 0.91 | 0.81 | 0.81 |
time (sec) |
N/A | 0.199 | 0.002 | 0.022 | 0.187 | 0.308 | 0.022 | 0.336 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 20 | 19 | 19 | 19 | 19 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 |
time (sec) |
N/A | 0.150 | 0.000 | 0.022 | 0.194 | 0.281 | 0.026 | 0.291 | 0.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 268 | 321 | 45 | 41 | 0 | 1015 | 41 | 0 | 123 |
N.S. |
1 | 1.20 | 0.17 | 0.15 | 0.00 | 3.79 | 0.15 | 0.00 | 0.46 |
time (sec) |
N/A | 0.656 | 0.008 | 0.047 | 0.000 | 1.086 | 0.540 | 0.000 | 10.581 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 357 | 432 | 113 | 83 | 0 | 1201 | 3834 | 0 | 176 |
N.S. |
1 | 1.21 | 0.32 | 0.23 | 0.00 | 3.36 | 10.74 | 0.00 | 0.49 |
time (sec) |
N/A | 0.862 | 0.014 | 0.055 | 0.000 | 1.049 | 1.777 | 0.000 | 0.136 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 97 | 78 | 77 | 77 | 94 | 77 | 77 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.79 | 0.79 | 0.97 | 0.79 | 0.79 |
time (sec) |
N/A | 0.244 | 0.002 | 0.029 | 0.199 | 0.256 | 0.029 | 0.303 | 0.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 69 | 58 | 57 | 57 | 66 | 57 | 57 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.83 | 0.83 | 0.96 | 0.83 | 0.83 |
time (sec) |
N/A | 0.220 | 0.002 | 0.026 | 0.196 | 0.270 | 0.026 | 0.277 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 45 | 38 | 37 | 37 | 42 | 37 | 37 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.82 | 0.82 | 0.93 | 0.82 | 0.82 |
time (sec) |
N/A | 0.197 | 0.002 | 0.024 | 0.199 | 0.292 | 0.025 | 0.306 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 18 | 17 | 17 | 19 | 17 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.81 | 0.81 | 0.90 | 0.81 | 0.81 |
time (sec) |
N/A | 0.152 | 0.000 | 0.021 | 0.190 | 0.242 | 0.018 | 0.304 | 0.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | B | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 234 | 270 | 47 | 41 | 0 | 499 | 3432 | 265 | 87 |
N.S. |
1 | 1.15 | 0.20 | 0.18 | 0.00 | 2.13 | 14.67 | 1.13 | 0.37 |
time (sec) |
N/A | 0.586 | 0.018 | 0.059 | 0.000 | 0.989 | 1.343 | 0.309 | 10.965 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | B | C | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 317 | 350 | 108 | 79 | 0 | 704 | 3834 | 315 | 174 |
N.S. |
1 | 1.10 | 0.34 | 0.25 | 0.00 | 2.22 | 12.09 | 0.99 | 0.55 |
time (sec) |
N/A | 0.755 | 0.019 | 0.079 | 0.000 | 0.975 | 1.936 | 0.380 | 10.660 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 104 | 104 | 85 | 84 | 84 | 100 | 84 | 84 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.81 | 0.81 | 0.96 | 0.81 | 0.81 |
time (sec) |
N/A | 0.248 | 0.002 | 0.034 | 0.208 | 0.257 | 0.031 | 0.300 | 10.543 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 76 | 65 | 64 | 64 | 73 | 64 | 64 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.84 | 0.84 | 0.96 | 0.84 | 0.84 |
time (sec) |
N/A | 0.223 | 0.002 | 0.029 | 0.196 | 0.259 | 0.027 | 0.293 | 0.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 52 | 45 | 44 | 44 | 49 | 44 | 44 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.85 | 0.85 | 0.94 | 0.85 | 0.85 |
time (sec) |
N/A | 0.197 | 0.002 | 0.025 | 0.194 | 0.242 | 0.024 | 0.285 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 25 | 24 | 24 | 27 | 24 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.80 | 0.80 | 0.90 | 0.80 | 0.80 |
time (sec) |
N/A | 0.151 | 0.000 | 0.021 | 0.200 | 0.267 | 0.018 | 0.290 | 0.012 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 263 | 313 | 55 | 49 | 0 | 1297 | 41 | 0 | 123 |
N.S. |
1 | 1.19 | 0.21 | 0.19 | 0.00 | 4.93 | 0.16 | 0.00 | 0.47 |
time (sec) |
N/A | 0.708 | 0.009 | 0.045 | 0.000 | 0.977 | 1.271 | 0.000 | 0.267 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 366 | 428 | 128 | 96 | 0 | 1540 | 3839 | 0 | 181 |
N.S. |
1 | 1.17 | 0.35 | 0.26 | 0.00 | 4.21 | 10.49 | 0.00 | 0.49 |
time (sec) |
N/A | 0.888 | 0.014 | 0.055 | 0.000 | 1.099 | 2.232 | 0.000 | 0.150 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 164 | 592 | 163 | 185 | 163 | 163 |
N.S. |
1 | 1.00 | 1.00 | 11.71 | 42.29 | 11.64 | 13.21 | 11.64 | 11.64 |
time (sec) |
N/A | 0.165 | 0.002 | 0.052 | 0.206 | 0.276 | 0.040 | 0.271 | 0.127 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 109 | 228 | 108 | 114 | 108 | 108 |
N.S. |
1 | 1.00 | 1.00 | 7.79 | 16.29 | 7.71 | 8.14 | 7.71 | 7.71 |
time (sec) |
N/A | 0.167 | 0.002 | 0.040 | 0.207 | 0.300 | 0.031 | 0.279 | 0.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 61 | 13 | 53 | 53 | 60 | 53 | 53 |
N.S. |
1 | 1.00 | 4.36 | 0.93 | 3.79 | 3.79 | 4.29 | 3.79 | 3.79 |
time (sec) |
N/A | 0.159 | 0.000 | 0.032 | 0.203 | 0.275 | 0.021 | 0.295 | 0.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 46 | 46 | 49 | 12 | 48 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 3.29 | 3.29 | 3.50 | 0.86 | 3.43 |
time (sec) |
N/A | 0.162 | 0.004 | 0.058 | 0.196 | 0.290 | 0.134 | 0.294 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 101 | 101 | 109 | 12 | 103 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 7.21 | 7.21 | 7.79 | 0.86 | 7.36 |
time (sec) |
N/A | 0.165 | 0.003 | 0.130 | 0.203 | 0.266 | 0.282 | 0.280 | 10.735 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 156 | 156 | 168 | 12 | 158 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 11.14 | 11.14 | 12.00 | 0.86 | 11.29 |
time (sec) |
N/A | 0.161 | 0.003 | 0.244 | 0.219 | 0.282 | 0.426 | 0.281 | 11.831 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 38 | 31 | 30 | 30 | 29 | 31 | 36 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.79 | 0.79 | 0.76 | 0.82 | 0.95 |
time (sec) |
N/A | 0.196 | 0.006 | 0.081 | 0.281 | 0.261 | 0.073 | 0.268 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 84 | 65 | 64 | 64 | 80 | 64 | 64 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.76 | 0.76 | 0.95 | 0.76 | 0.76 |
time (sec) |
N/A | 0.852 | 0.003 | 0.039 | 0.197 | 0.257 | 0.033 | 0.272 | 0.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 63 | 50 | 49 | 49 | 60 | 49 | 49 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.78 | 0.78 | 0.95 | 0.78 | 0.78 |
time (sec) |
N/A | 0.890 | 0.003 | 0.033 | 0.193 | 0.245 | 0.028 | 0.281 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 44 | 35 | 34 | 34 | 41 | 34 | 34 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.77 | 0.77 | 0.93 | 0.77 | 0.77 |
time (sec) |
N/A | 0.608 | 0.001 | 0.028 | 0.190 | 0.272 | 0.026 | 0.276 | 0.015 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 20 | 19 | 19 | 22 | 19 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.76 | 0.76 | 0.88 | 0.76 | 0.76 |
time (sec) |
N/A | 0.157 | 0.000 | 0.046 | 0.189 | 0.254 | 0.019 | 0.287 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 62 | 42 | 54 | 56 | 63 | 62 | 27 |
N.S. |
1 | 1.00 | 2.00 | 1.35 | 1.74 | 1.81 | 2.03 | 2.00 | 0.87 |
time (sec) |
N/A | 0.187 | 0.012 | 0.069 | 0.288 | 0.288 | 0.072 | 0.290 | 10.332 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 103 | 84 | 89 | 177 | 104 | 97 | 64 |
N.S. |
1 | 1.00 | 1.16 | 0.94 | 1.00 | 1.99 | 1.17 | 1.09 | 0.72 |
time (sec) |
N/A | 0.245 | 0.039 | 0.117 | 0.273 | 0.264 | 0.817 | 0.296 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 161 | 161 | 137 | 108 | 119 | 282 | 134 | 112 | 93 |
N.S. |
1 | 1.00 | 0.85 | 0.67 | 0.74 | 1.75 | 0.83 | 0.70 | 0.58 |
time (sec) |
N/A | 0.335 | 0.061 | 0.140 | 0.278 | 0.298 | 0.877 | 0.301 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 245 | 132 | 116 | 114 | 223 | 296 | 134 | 126 |
N.S. |
1 | 2.69 | 1.45 | 1.27 | 1.25 | 2.45 | 3.25 | 1.47 | 1.38 |
time (sec) |
N/A | 0.443 | 0.065 | 0.131 | 0.286 | 0.277 | 0.806 | 0.298 | 10.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 78 | 74 | 73 | 111 | 81 | 198 | 209 | 77 | 87 |
N.S. |
1 | 0.95 | 0.94 | 1.42 | 1.04 | 2.54 | 2.68 | 0.99 | 1.12 |
time (sec) |
N/A | 0.224 | 0.035 | 0.906 | 0.284 | 0.283 | 0.395 | 0.273 | 9.963 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 47 | 54 | 70 | 61 | 157 | 153 | 54 | 206 |
N.S. |
1 | 0.94 | 1.08 | 1.40 | 1.22 | 3.14 | 3.06 | 1.08 | 4.12 |
time (sec) |
N/A | 0.199 | 0.021 | 0.882 | 0.278 | 0.285 | 0.257 | 0.285 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 39 | 38 | 54 | 50 | 136 | 124 | 43 | 46 |
N.S. |
1 | 0.95 | 0.93 | 1.32 | 1.22 | 3.32 | 3.02 | 1.05 | 1.12 |
time (sec) |
N/A | 0.172 | 0.012 | 0.845 | 0.284 | 0.282 | 0.116 | 0.281 | 9.987 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 28 | 24 | 83 | 54 | 17 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.33 | 1.14 | 3.95 | 2.57 | 0.81 | 0.81 |
time (sec) |
N/A | 0.144 | 0.007 | 0.826 | 0.277 | 0.272 | 0.085 | 0.291 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 57 | 48 | 74 | 68 | 154 | 738 | 62 | 173 |
N.S. |
1 | 0.97 | 0.81 | 1.25 | 1.15 | 2.61 | 12.51 | 1.05 | 2.93 |
time (sec) |
N/A | 0.195 | 0.028 | 0.843 | 0.292 | 0.284 | 1.845 | 0.295 | 10.576 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 93 | 81 | 96 | 123 | 229 | 1620 | 117 | 425 |
N.S. |
1 | 1.18 | 1.03 | 1.22 | 1.56 | 2.90 | 20.51 | 1.48 | 5.38 |
time (sec) |
N/A | 0.256 | 0.031 | 0.865 | 0.288 | 0.295 | 6.884 | 0.295 | 10.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 134 | 106 | 151 | 197 | 371 | 3284 | 195 | 573 |
N.S. |
1 | 1.11 | 0.88 | 1.25 | 1.63 | 3.07 | 27.14 | 1.61 | 4.74 |
time (sec) |
N/A | 0.315 | 0.097 | 0.882 | 0.298 | 0.288 | 42.252 | 0.291 | 10.425 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 31 | 34 | 30 | 109 | 61 | 24 | 27 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 0.97 | 3.52 | 1.97 | 0.77 | 0.87 |
time (sec) |
N/A | 0.156 | 0.009 | 1.112 | 0.281 | 0.270 | 0.089 | 0.301 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 61 | 60 | 86 | 75 | 253 | 117 | 65 | 76 |
N.S. |
1 | 0.97 | 0.95 | 1.37 | 1.19 | 4.02 | 1.86 | 1.03 | 1.21 |
time (sec) |
N/A | 0.168 | 0.021 | 0.990 | 0.288 | 0.282 | 0.294 | 0.289 | 9.907 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 94 | 75 | 139 | 184 | 595 | 257 | 103 | 181 |
N.S. |
1 | 1.03 | 0.82 | 1.53 | 2.02 | 6.54 | 2.82 | 1.13 | 1.99 |
time (sec) |
N/A | 0.183 | 0.044 | 0.963 | 0.298 | 0.282 | 0.619 | 0.305 | 10.264 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 198 | 42 | 66 | 279 | 92 | 30 | 31 |
N.S. |
1 | 1.00 | 5.66 | 1.20 | 1.89 | 7.97 | 2.63 | 0.86 | 0.89 |
time (sec) |
N/A | 0.167 | 0.089 | 1.077 | 0.277 | 0.273 | 0.098 | 0.280 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 10 | 11 | 18 | 10 | 24 | 10 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 1.80 | 1.00 | 2.40 | 1.00 | 1.00 |
time (sec) |
N/A | 0.138 | 0.005 | 0.981 | 0.273 | 0.250 | 0.078 | 0.294 | 0.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 35 | 31 | 43 | 51 | 55 | 56 | 41 | 42 |
N.S. |
1 | 0.95 | 0.84 | 1.16 | 1.38 | 1.49 | 1.51 | 1.11 | 1.14 |
time (sec) |
N/A | 0.147 | 0.011 | 0.924 | 0.301 | 0.272 | 0.225 | 0.304 | 10.887 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 52 | 71 | 115 | 153 | 146 | 73 | 111 |
N.S. |
1 | 1.00 | 0.87 | 1.18 | 1.92 | 2.55 | 2.43 | 1.22 | 1.85 |
time (sec) |
N/A | 0.159 | 0.014 | 0.935 | 0.282 | 0.253 | 0.480 | 0.282 | 0.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 32 | 23 | 25 | 22 | 22 | 27 | 10 |
N.S. |
1 | 1.00 | 3.20 | 2.30 | 2.50 | 2.20 | 2.20 | 2.70 | 1.00 |
time (sec) |
N/A | 0.136 | 0.005 | 0.875 | 0.189 | 0.285 | 0.080 | 0.299 | 10.474 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 37 | 45 | 52 | 56 | 85 | 54 | 56 | 43 |
N.S. |
1 | 0.95 | 1.15 | 1.33 | 1.44 | 2.18 | 1.38 | 1.44 | 1.10 |
time (sec) |
N/A | 0.148 | 0.019 | 0.822 | 0.198 | 0.288 | 0.225 | 0.278 | 10.358 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 65 | 78 | 122 | 220 | 141 | 88 | 114 |
N.S. |
1 | 1.00 | 1.02 | 1.22 | 1.91 | 3.44 | 2.20 | 1.38 | 1.78 |
time (sec) |
N/A | 0.165 | 0.023 | 0.844 | 0.196 | 0.258 | 0.513 | 0.288 | 10.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 4 | 4 | 15 | 12 | 11 | 11 | 10 | 13 | 4 |
N.S. |
1 | 1.00 | 3.75 | 3.00 | 2.75 | 2.75 | 2.50 | 3.25 | 1.00 |
time (sec) |
N/A | 0.128 | 0.003 | 0.708 | 0.202 | 0.264 | 0.044 | 0.297 | 0.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 26 | 24 | 25 | 39 | 24 | 27 | 23 |
N.S. |
1 | 1.00 | 0.96 | 0.89 | 0.93 | 1.44 | 0.89 | 1.00 | 0.85 |
time (sec) |
N/A | 0.145 | 0.013 | 0.760 | 0.192 | 0.268 | 0.052 | 0.302 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 50 | 37 | 36 | 44 | 71 | 44 | 39 | 36 |
N.S. |
1 | 1.11 | 0.82 | 0.80 | 0.98 | 1.58 | 0.98 | 0.87 | 0.80 |
time (sec) |
N/A | 0.157 | 0.014 | 0.731 | 0.188 | 0.254 | 0.067 | 0.284 | 10.257 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 65 | 64 | 61 | 54 | 54 | 58 | 62 | 55 |
N.S. |
1 | 1.10 | 1.08 | 1.03 | 0.92 | 0.92 | 0.98 | 1.05 | 0.93 |
time (sec) |
N/A | 0.208 | 0.018 | 0.899 | 0.186 | 0.259 | 0.076 | 0.284 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 10 | 11 | 11 | 12 | 11 | 11 | 10 | 11 | 11 |
N.S. |
1 | 1.10 | 1.10 | 1.20 | 1.10 | 1.10 | 1.00 | 1.10 | 1.10 |
time (sec) |
N/A | 0.163 | 0.007 | 0.892 | 0.187 | 0.266 | 0.038 | 0.285 | 10.372 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 44 | 41 | 55 | 25 | 36 | 35 | 26 | 23 | 0 |
N.S. |
1 | 0.93 | 1.25 | 0.57 | 0.82 | 0.80 | 0.59 | 0.52 | 0.00 |
time (sec) |
N/A | 0.175 | 0.050 | 0.987 | 0.268 | 0.294 | 0.441 | 0.286 | 0.000 |