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 | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 57 | 64 | 39 | 43 | 32 | 0 | 29 | 26 | 43 |
N.S. |
1 | 1.50 | 1.68 | 1.03 | 1.13 | 0.84 | 0.00 | 0.76 | 0.68 | 1.13 |
time (sec) |
N/A | 0.244 | 0.103 | 0.096 | 0.120 | 0.072 | 0.000 | 0.115 | 0.175 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 51 | 30 | 15 | 15 | 14 | 17 | 14 | 15 |
N.S. |
1 | 1.00 | 2.83 | 1.67 | 0.83 | 0.83 | 0.78 | 0.94 | 0.78 | 0.83 |
time (sec) |
N/A | 0.245 | 0.044 | 0.058 | 0.105 | 0.075 | 2.236 | 0.110 | 0.154 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 51 | 29 | 15 | 15 | 0 | 15 | 14 | 15 |
N.S. |
1 | 1.00 | 2.83 | 1.61 | 0.83 | 0.83 | 0.00 | 0.83 | 0.78 | 0.83 |
time (sec) |
N/A | 0.248 | 0.012 | 0.049 | 0.105 | 0.074 | 0.000 | 0.119 | 0.167 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 209 | 80 | 92 | 0 | 76 | 0 | 0 | 18 | 83 |
N.S. |
1 | 4.10 | 1.57 | 1.80 | 0.00 | 1.49 | 0.00 | 0.00 | 0.35 | 1.63 |
time (sec) |
N/A | 0.802 | 0.332 | 1.181 | 0.000 | 0.097 | 0.000 | 0.000 | 0.158 | 0.087 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 209 | 80 | 92 | 0 | 76 | 0 | 0 | 18 | 83 |
N.S. |
1 | 4.10 | 1.57 | 1.80 | 0.00 | 1.49 | 0.00 | 0.00 | 0.35 | 1.63 |
time (sec) |
N/A | 0.814 | 0.296 | 0.421 | 0.000 | 0.095 | 0.000 | 0.000 | 0.158 | 22.531 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 15 | 23 | 23 | 0 | 14 | 22 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 1.44 | 1.44 | 0.00 | 0.88 | 1.38 | 0.88 |
time (sec) |
N/A | 0.244 | 1.873 | 0.546 | 0.062 | 0.074 | 0.000 | 0.125 | 0.167 | 22.401 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 35 | 28 | 0 | 201 | 0 | 0 | 103 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.00 | 5.74 | 0.00 | 0.00 | 2.94 | 0.00 |
time (sec) |
N/A | 0.494 | 1.901 | 0.753 | 0.000 | 1.519 | 0.000 | 0.000 | 0.365 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 30 | 0 | 156 | 0 | 0 | 109 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.00 | 4.73 | 0.00 | 0.00 | 3.30 | 0.00 |
time (sec) |
N/A | 0.500 | 1.856 | 1.077 | 0.000 | 0.248 | 0.000 | 0.000 | 0.273 | 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 | 52 | 52 | 403 | 44 | 0 | 281 | 0 | 0 | 153 | 0 |
N.S. |
1 | 1.00 | 7.75 | 0.85 | 0.00 | 5.40 | 0.00 | 0.00 | 2.94 | 0.00 |
time (sec) |
N/A | 0.563 | 12.967 | 1.592 | 0.000 | 7.301 | 0.000 | 0.000 | 0.499 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 0 | 485 | 161 | 0 | 1496 | 0 | 0 | 54 | 0 |
N.S. |
1 | 0.00 | 2.47 | 0.82 | 0.00 | 7.63 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.000 | 13.370 | 11.549 | 0.000 | 27.399 | 0.000 | 0.000 | 200.023 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 182 | 1265 | 121 | 0 | 827 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.30 | 9.04 | 0.86 | 0.00 | 5.91 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.575 | 13.848 | 4.054 | 0.000 | 26.849 | 0.000 | 0.000 | 30.834 | 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 | 80 | 80 | 383 | 66 | 0 | 472 | 0 | 0 | 239 | 0 |
N.S. |
1 | 1.00 | 4.79 | 0.82 | 0.00 | 5.90 | 0.00 | 0.00 | 2.99 | 0.00 |
time (sec) |
N/A | 0.676 | 10.899 | 1.365 | 0.000 | 27.017 | 0.000 | 0.000 | 0.521 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 17 | 16 | 16 | 0 | 16 | 29 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.89 | 0.89 | 0.00 | 0.89 | 1.61 | 0.89 |
time (sec) |
N/A | 0.269 | 0.023 | 0.685 | 0.068 | 0.077 | 0.000 | 0.426 | 0.154 | 22.611 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 54 | 50 | 90 | 90 | 0 | 489 | 98 | 75 |
N.S. |
1 | 1.00 | 0.90 | 0.83 | 1.50 | 1.50 | 0.00 | 8.15 | 1.63 | 1.25 |
time (sec) |
N/A | 0.581 | 10.309 | 3.138 | 0.099 | 0.085 | 0.000 | 0.408 | 0.189 | 23.359 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 205 | 149 | 133 | 241 | 236 | 0 | 1828 | 270 | 13164 |
N.S. |
1 | 1.22 | 0.89 | 0.79 | 1.43 | 1.40 | 0.00 | 10.88 | 1.61 | 78.36 |
time (sec) |
N/A | 2.031 | 10.661 | 8.860 | 0.229 | 0.139 | 0.000 | 1.210 | 0.260 | 33.239 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 0 | 485 | 161 | 0 | 1496 | 0 | 0 | 46 | 0 |
N.S. |
1 | 0.00 | 2.47 | 0.82 | 0.00 | 7.63 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.000 | 1.681 | 2.562 | 0.000 | 27.362 | 0.000 | 0.000 | 200.025 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 182 | 1265 | 121 | 0 | 827 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.30 | 9.04 | 0.86 | 0.00 | 5.91 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 4.020 | 2.796 | 0.752 | 0.000 | 26.837 | 0.000 | 0.000 | 30.889 | 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 | 80 | 80 | 383 | 66 | 0 | 472 | 0 | 0 | 239 | 0 |
N.S. |
1 | 1.00 | 4.79 | 0.82 | 0.00 | 5.90 | 0.00 | 0.00 | 2.99 | 0.00 |
time (sec) |
N/A | 0.852 | 0.195 | 0.296 | 0.000 | 27.612 | 0.000 | 0.000 | 0.548 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 17 | 16 | 16 | 0 | 16 | 29 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.89 | 0.89 | 0.00 | 0.89 | 1.61 | 0.89 |
time (sec) |
N/A | 0.264 | 0.021 | 0.000 | 0.067 | 0.073 | 0.000 | 0.438 | 0.171 | 0.004 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 54 | 50 | 90 | 90 | 0 | 489 | 98 | 75 |
N.S. |
1 | 1.00 | 0.90 | 0.83 | 1.50 | 1.50 | 0.00 | 8.15 | 1.63 | 1.25 |
time (sec) |
N/A | 0.624 | 0.086 | 0.646 | 0.106 | 0.082 | 0.000 | 0.417 | 0.181 | 23.186 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 205 | 149 | 133 | 241 | 236 | 0 | 1828 | 270 | 13164 |
N.S. |
1 | 1.22 | 0.89 | 0.79 | 1.43 | 1.40 | 0.00 | 10.88 | 1.61 | 78.36 |
time (sec) |
N/A | 2.120 | 0.244 | 2.517 | 0.217 | 0.120 | 0.000 | 1.225 | 0.275 | 33.283 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | F | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 81 | 191 | 74 | 0 | 141 | 70 | 397 | 307 | 50 |
N.S. |
1 | 2.13 | 5.03 | 1.95 | 0.00 | 3.71 | 1.84 | 10.45 | 8.08 | 1.32 |
time (sec) |
N/A | 0.415 | 0.132 | 0.092 | 0.000 | 0.073 | 0.346 | 0.269 | 0.163 | 0.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 73 | 233 | 66 | 0 | 146 | 63 | 415 | 297 | 28 |
N.S. |
1 | 1.92 | 6.13 | 1.74 | 0.00 | 3.84 | 1.66 | 10.92 | 7.82 | 0.74 |
time (sec) |
N/A | 0.362 | 0.159 | 0.083 | 0.000 | 0.073 | 0.351 | 0.272 | 0.144 | 23.246 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 87 | 70 | 0 | 152 | 70 | 67 | 70 | 54 |
N.S. |
1 | 1.00 | 2.29 | 1.84 | 0.00 | 4.00 | 1.84 | 1.76 | 1.84 | 1.42 |
time (sec) |
N/A | 0.374 | 0.063 | 0.039 | 0.000 | 0.076 | 0.409 | 0.132 | 0.160 | 23.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 87 | 72 | 0 | 155 | 63 | 63 | 75 | 67 |
N.S. |
1 | 1.00 | 2.29 | 1.89 | 0.00 | 4.08 | 1.66 | 1.66 | 1.97 | 1.76 |
time (sec) |
N/A | 0.367 | 0.063 | 0.054 | 0.000 | 0.075 | 0.422 | 0.132 | 0.161 | 22.760 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 54 | 38 | 78 | 0 | 144 | 109 | 0 | 114 | 196 |
N.S. |
1 | 1.42 | 1.00 | 2.05 | 0.00 | 3.79 | 2.87 | 0.00 | 3.00 | 5.16 |
time (sec) |
N/A | 0.435 | 0.439 | 0.207 | 0.000 | 0.079 | 17.549 | 0.000 | 0.144 | 22.838 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 54 | 38 | 72 | 0 | 144 | 99 | 0 | 47 | 139 |
N.S. |
1 | 1.42 | 1.00 | 1.89 | 0.00 | 3.79 | 2.61 | 0.00 | 1.24 | 3.66 |
time (sec) |
N/A | 0.424 | 0.400 | 0.190 | 0.000 | 0.094 | 17.848 | 0.000 | 0.166 | 25.324 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 49 | 42 | 42 | 36 | 155 | 78 | 39 | 120 | 42 |
N.S. |
1 | 1.17 | 1.00 | 1.00 | 0.86 | 3.69 | 1.86 | 0.93 | 2.86 | 1.00 |
time (sec) |
N/A | 0.316 | 0.024 | 0.039 | 0.111 | 0.082 | 0.372 | 0.129 | 0.155 | 0.112 |
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 | 44 | 51 | 46 | 42 | 67 | 168 | 75 | 42 | 98 | 199 |
N.S. |
1 | 1.16 | 1.05 | 0.95 | 1.52 | 3.82 | 1.70 | 0.95 | 2.23 | 4.52 |
time (sec) |
N/A | 0.313 | 0.027 | 0.034 | 0.107 | 0.086 | 0.411 | 0.128 | 0.155 | 23.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 85 | 74 | 0 | 208 | 90 | 0 | 75 | 278 |
N.S. |
1 | 1.00 | 2.12 | 1.85 | 0.00 | 5.20 | 2.25 | 0.00 | 1.88 | 6.95 |
time (sec) |
N/A | 0.462 | 0.052 | 0.128 | 0.000 | 0.076 | 0.716 | 0.000 | 0.162 | 22.851 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 85 | 77 | 0 | 213 | 80 | 0 | 79 | 30 |
N.S. |
1 | 1.00 | 2.12 | 1.92 | 0.00 | 5.32 | 2.00 | 0.00 | 1.98 | 0.75 |
time (sec) |
N/A | 0.462 | 0.054 | 0.118 | 0.000 | 0.080 | 0.685 | 0.000 | 0.152 | 22.688 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 78 | 42 | 78 | 0 | 138 | 122 | 0 | 175 | 0 |
N.S. |
1 | 1.86 | 1.00 | 1.86 | 0.00 | 3.29 | 2.90 | 0.00 | 4.17 | 0.00 |
time (sec) |
N/A | 0.596 | 1.300 | 0.590 | 0.000 | 0.079 | 114.813 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 78 | 42 | 74 | 0 | 138 | 112 | 0 | 185 | 0 |
N.S. |
1 | 1.86 | 1.00 | 1.76 | 0.00 | 3.29 | 2.67 | 0.00 | 4.40 | 0.00 |
time (sec) |
N/A | 0.599 | 0.407 | 0.585 | 0.000 | 0.117 | 112.115 | 0.000 | 0.316 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 86 | 74 | 0 | 153 | 73 | 71 | 73 | 233 |
N.S. |
1 | 1.00 | 2.15 | 1.85 | 0.00 | 3.82 | 1.82 | 1.78 | 1.82 | 5.82 |
time (sec) |
N/A | 0.408 | 0.054 | 0.051 | 0.000 | 0.081 | 0.751 | 0.129 | 0.148 | 0.243 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 86 | 74 | 0 | 155 | 66 | 67 | 77 | 67 |
N.S. |
1 | 1.00 | 2.15 | 1.85 | 0.00 | 3.88 | 1.65 | 1.68 | 1.92 | 1.68 |
time (sec) |
N/A | 0.409 | 0.051 | 0.051 | 0.000 | 0.080 | 0.728 | 0.125 | 0.157 | 22.730 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 49 | 42 | 42 | 36 | 155 | 78 | 39 | 34 | 42 |
N.S. |
1 | 1.17 | 1.00 | 1.00 | 0.86 | 3.69 | 1.86 | 0.93 | 0.81 | 1.00 |
time (sec) |
N/A | 0.318 | 0.023 | 0.036 | 0.110 | 0.095 | 0.571 | 0.136 | 0.139 | 23.419 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 51 | 46 | 42 | 67 | 168 | 75 | 42 | 38 | 923 |
N.S. |
1 | 1.16 | 1.05 | 0.95 | 1.52 | 3.82 | 1.70 | 0.95 | 0.86 | 20.98 |
time (sec) |
N/A | 0.317 | 0.026 | 0.036 | 0.109 | 0.091 | 0.536 | 0.132 | 0.148 | 23.517 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 42 | 78 | 0 | 138 | 0 | 0 | 175 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.86 | 0.00 | 3.29 | 0.00 | 0.00 | 4.17 | 0.00 |
time (sec) |
N/A | 0.614 | 2.633 | 1.413 | 0.000 | 0.093 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 42 | 74 | 0 | 138 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.76 | 0.00 | 3.29 | 0.00 | 0.00 | 1.62 | 0.00 |
time (sec) |
N/A | 0.592 | 0.595 | 1.427 | 0.000 | 0.101 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 70 | 42 | 84 | 0 | 165 | 0 | 0 | 228 | 0 |
N.S. |
1 | 1.67 | 1.00 | 2.00 | 0.00 | 3.93 | 0.00 | 0.00 | 5.43 | 0.00 |
time (sec) |
N/A | 0.657 | 0.739 | 2.018 | 0.000 | 0.084 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 70 | 42 | 78 | 0 | 165 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.67 | 1.00 | 1.86 | 0.00 | 3.93 | 0.00 | 0.00 | 1.62 | 0.00 |
time (sec) |
N/A | 0.632 | 0.899 | 1.912 | 0.000 | 0.087 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 53 | 53 | 53 | 0 | 44 | 0 | 29 | 34 | 30 |
N.S. |
1 | 1.10 | 1.10 | 1.10 | 0.00 | 0.92 | 0.00 | 0.60 | 0.71 | 0.62 |
time (sec) |
N/A | 0.344 | 0.240 | 0.085 | 0.000 | 0.070 | 0.000 | 0.119 | 0.148 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 42 | 46 | 0 | 36 | 0 | 22 | 21 | 22 |
N.S. |
1 | 1.00 | 1.40 | 1.53 | 0.00 | 1.20 | 0.00 | 0.73 | 0.70 | 0.73 |
time (sec) |
N/A | 0.332 | 0.202 | 0.054 | 0.000 | 0.069 | 0.000 | 0.125 | 0.144 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 4 | 4 | 22 | 29 | 0 | 20 | 0 | 4 | 4 | 4 |
N.S. |
1 | 1.00 | 5.50 | 7.25 | 0.00 | 5.00 | 0.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.287 | 0.171 | 0.052 | 0.000 | 0.069 | 0.000 | 0.120 | 0.164 | 0.014 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 18 | 24 | 0 | 16 | 0 | 38 | 9 | 16 |
N.S. |
1 | 1.00 | 0.82 | 1.09 | 0.00 | 0.73 | 0.00 | 1.73 | 0.41 | 0.73 |
time (sec) |
N/A | 0.266 | 0.150 | 0.021 | 0.000 | 0.068 | 0.000 | 0.117 | 0.152 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 28 | 39 | 0 | 24 | 0 | 78 | 29 | 28 |
N.S. |
1 | 1.00 | 0.64 | 0.89 | 0.00 | 0.55 | 0.00 | 1.77 | 0.66 | 0.64 |
time (sec) |
N/A | 0.321 | 0.172 | 0.030 | 0.000 | 0.070 | 0.000 | 0.117 | 0.143 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 67 | 33 | 54 | 0 | 29 | 0 | 114 | 52 | 33 |
N.S. |
1 | 1.08 | 0.53 | 0.87 | 0.00 | 0.47 | 0.00 | 1.84 | 0.84 | 0.53 |
time (sec) |
N/A | 0.349 | 0.186 | 0.035 | 0.000 | 0.069 | 0.000 | 0.117 | 0.159 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | A | A | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 109 | 108 | 1806 | 125 | 233 | 138 | 160 | 326 | 167 |
N.S. |
1 | 0.81 | 0.81 | 13.48 | 0.93 | 1.74 | 1.03 | 1.19 | 2.43 | 1.25 |
time (sec) |
N/A | 0.855 | 0.267 | 0.080 | 0.034 | 0.097 | 2.483 | 0.118 | 0.148 | 23.689 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | A | A | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 64 | 66 | 1699 | 62 | 161 | 85 | 72 | 177 | 123 |
N.S. |
1 | 0.93 | 0.96 | 24.62 | 0.90 | 2.33 | 1.23 | 1.04 | 2.57 | 1.78 |
time (sec) |
N/A | 0.681 | 0.086 | 0.032 | 0.032 | 0.103 | 1.917 | 0.117 | 0.157 | 23.117 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 26 | 1628 | 21 | 105 | 46 | 22 | 73 | 45 |
N.S. |
1 | 1.00 | 1.13 | 70.78 | 0.91 | 4.57 | 2.00 | 0.96 | 3.17 | 1.96 |
time (sec) |
N/A | 0.466 | 0.038 | 0.026 | 0.026 | 0.084 | 1.656 | 0.112 | 0.153 | 23.815 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | A | A | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 86 | 69 | 1697 | 0 | 319 | 139 | 94 | 364 | 1270 |
N.S. |
1 | 0.98 | 0.78 | 19.28 | 0.00 | 3.62 | 1.58 | 1.07 | 4.14 | 14.43 |
time (sec) |
N/A | 0.719 | 0.122 | 0.042 | 0.000 | 0.133 | 3.713 | 0.116 | 0.160 | 23.985 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 184 | 139 | 1910 | 0 | 533 | 0 | 210 | 364 | 4602 |
N.S. |
1 | 1.22 | 0.92 | 12.65 | 0.00 | 3.53 | 0.00 | 1.39 | 2.41 | 30.48 |
time (sec) |
N/A | 0.943 | 0.337 | 0.048 | 0.000 | 0.442 | 0.000 | 0.120 | 0.182 | 25.108 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 222 | 150 | 1905 | 0 | 1475 | 0 | 0 | 211 | 0 |
N.S. |
1 | 1.13 | 0.77 | 9.72 | 0.00 | 7.53 | 0.00 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 0.960 | 0.706 | 0.044 | 0.000 | 0.388 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 156 | 99 | 1780 | 0 | 1168 | 0 | 0 | 85 | 0 |
N.S. |
1 | 1.47 | 0.93 | 16.79 | 0.00 | 11.02 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.674 | 0.389 | 0.032 | 0.000 | 0.169 | 0.000 | 0.000 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 103 | 63 | 1722 | 0 | 510 | 0 | 107 | 65 | 0 |
N.S. |
1 | 1.63 | 1.00 | 27.33 | 0.00 | 8.10 | 0.00 | 1.70 | 1.03 | 0.00 |
time (sec) |
N/A | 0.418 | 0.328 | 0.023 | 0.000 | 0.097 | 0.000 | 0.125 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 168 | 105 | 1811 | 0 | 581 | 0 | 211 | 142 | 0 |
N.S. |
1 | 1.41 | 0.88 | 15.22 | 0.00 | 4.88 | 0.00 | 1.77 | 1.19 | 0.00 |
time (sec) |
N/A | 0.669 | 0.564 | 0.042 | 0.000 | 0.140 | 0.000 | 0.134 | 0.157 | 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 | 192 | 277 | 178 | 1983 | 0 | 744 | 0 | 361 | 306 | 0 |
N.S. |
1 | 1.44 | 0.93 | 10.33 | 0.00 | 3.88 | 0.00 | 1.88 | 1.59 | 0.00 |
time (sec) |
N/A | 0.923 | 1.064 | 0.048 | 0.000 | 0.203 | 0.000 | 0.139 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F(-1) | A | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 112 | 108 | 332 | 125 | 191 | 0 | 160 | 29 | 200 |
N.S. |
1 | 0.80 | 0.77 | 2.37 | 0.89 | 1.36 | 0.00 | 1.14 | 0.21 | 1.43 |
time (sec) |
N/A | 0.841 | 0.267 | 0.661 | 0.034 | 0.088 | 0.000 | 0.116 | 200.035 | 23.692 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F(-1) | A | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 67 | 66 | 246 | 62 | 118 | 0 | 72 | 29 | 119 |
N.S. |
1 | 0.92 | 0.90 | 3.37 | 0.85 | 1.62 | 0.00 | 0.99 | 0.40 | 1.63 |
time (sec) |
N/A | 0.695 | 0.089 | 0.048 | 0.031 | 0.074 | 0.000 | 0.114 | 200.033 | 23.949 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 29 | 160 | 22 | 61 | 49 | 23 | 29 | 60 |
N.S. |
1 | 1.00 | 1.12 | 6.15 | 0.85 | 2.35 | 1.88 | 0.88 | 1.12 | 2.31 |
time (sec) |
N/A | 0.491 | 0.048 | 0.043 | 0.030 | 0.092 | 156.938 | 0.118 | 200.035 | 22.857 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | A | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 90 | 69 | 223 | 0 | 228 | 0 | 94 | 225 | 156 |
N.S. |
1 | 0.97 | 0.74 | 2.40 | 0.00 | 2.45 | 0.00 | 1.01 | 2.42 | 1.68 |
time (sec) |
N/A | 0.715 | 0.130 | 0.127 | 0.000 | 0.090 | 0.000 | 0.121 | 0.469 | 23.946 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | A | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 187 | 139 | 405 | 0 | 442 | 0 | 211 | 956 | 248 |
N.S. |
1 | 1.21 | 0.90 | 2.63 | 0.00 | 2.87 | 0.00 | 1.37 | 6.21 | 1.61 |
time (sec) |
N/A | 0.939 | 0.337 | 0.077 | 0.000 | 0.142 | 0.000 | 0.118 | 1.490 | 25.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 311 | 325 | 296 | 994 | 0 | 0 | 0 | 0 | 256 | 0 |
N.S. |
1 | 1.05 | 0.95 | 3.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.82 | 0.00 |
time (sec) |
N/A | 1.316 | 10.704 | 0.587 | 0.000 | 0.000 | 0.000 | 0.000 | 0.726 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 304 | 307 | 252 | 665 | 0 | 0 | 0 | 0 | 219 | 0 |
N.S. |
1 | 1.01 | 0.83 | 2.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 1.040 | 10.344 | 0.516 | 0.000 | 0.000 | 0.000 | 0.000 | 0.393 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 300 | 312 | 425 | 665 | 0 | 0 | 0 | 0 | 317 | 0 |
N.S. |
1 | 1.04 | 1.42 | 2.22 | 0.00 | 0.00 | 0.00 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 1.109 | 10.740 | 0.397 | 0.000 | 0.000 | 0.000 | 0.000 | 0.378 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 319 | 342 | 496 | 1200 | 0 | 0 | 0 | 0 | 354 | 0 |
N.S. |
1 | 1.07 | 1.55 | 3.76 | 0.00 | 0.00 | 0.00 | 0.00 | 1.11 | 0.00 |
time (sec) |
N/A | 1.273 | 10.940 | 0.452 | 0.000 | 0.000 | 0.000 | 0.000 | 0.450 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 324 | 337 | 604 | 1049 | 0 | 0 | 0 | 0 | 463 | 0 |
N.S. |
1 | 1.04 | 1.86 | 3.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.43 | 0.00 |
time (sec) |
N/A | 1.213 | 15.257 | 0.511 | 0.000 | 0.000 | 0.000 | 0.000 | 0.494 | 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 | 135 | 135 | 320 | 0 | 0 | 0 | 0 | 0 | 170 | 0 |
N.S. |
1 | 1.00 | 2.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.26 | 0.00 |
time (sec) |
N/A | 0.550 | 1.052 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 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 | 167 | 167 | 156 | 0 | 0 | 0 | 0 | 0 | 179 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.07 | 0.00 |
time (sec) |
N/A | 0.735 | 0.698 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | A | B | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 32 | 0 | 61 | 25 | 49 | 26 | 103 | 25 |
N.S. |
1 | 1.00 | 1.19 | 0.00 | 2.26 | 0.93 | 1.81 | 0.96 | 3.81 | 0.93 |
time (sec) |
N/A | 0.500 | 0.086 | 0.000 | 0.043 | 0.070 | 4.109 | 0.116 | 0.192 | 23.650 |
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 | 8 | 8 | 8 | 7 | 6 | 6 | 7 | 6 | 5 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.75 | 0.75 | 0.88 | 0.75 | 0.62 | 0.75 |
time (sec) |
N/A | 0.237 | 0.019 | 0.081 | 0.105 | 0.065 | 0.085 | 0.110 | 0.165 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 23 | 13 | 10 | 21 | 21 | 26 | 22 | 18 | 9 |
N.S. |
1 | 1.77 | 1.00 | 0.77 | 1.62 | 1.62 | 2.00 | 1.69 | 1.38 | 0.69 |
time (sec) |
N/A | 0.258 | 0.034 | 0.110 | 0.103 | 0.071 | 0.120 | 0.112 | 0.183 | 23.601 |
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 | 27 | 27 | 25 | 20 | 19 | 19 | 22 | 20 | 18 | 19 |
N.S. |
1 | 1.00 | 0.93 | 0.74 | 0.70 | 0.70 | 0.81 | 0.74 | 0.67 | 0.70 |
time (sec) |
N/A | 0.282 | 0.032 | 0.029 | 0.025 | 0.064 | 0.090 | 0.116 | 0.166 | 22.645 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 36 | 33 | 25 | 24 | 24 | 0 | 24 | 23 | 24 |
N.S. |
1 | 1.12 | 1.03 | 0.78 | 0.75 | 0.75 | 0.00 | 0.75 | 0.72 | 0.75 |
time (sec) |
N/A | 0.286 | 0.038 | 0.036 | 0.031 | 0.060 | 0.000 | 0.116 | 0.193 | 0.032 |
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 | 25 | 27 | 25 | 20 | 19 | 19 | 22 | 19 | 18 | 19 |
N.S. |
1 | 1.08 | 1.00 | 0.80 | 0.76 | 0.76 | 0.88 | 0.76 | 0.72 | 0.76 |
time (sec) |
N/A | 0.275 | 0.029 | 0.017 | 0.024 | 0.065 | 0.129 | 0.109 | 0.194 | 0.031 |
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 | 18 | 18 | 15 | 14 | 14 | 15 | 15 | 14 | 14 |
N.S. |
1 | 0.90 | 0.90 | 0.75 | 0.70 | 0.70 | 0.75 | 0.75 | 0.70 | 0.70 |
time (sec) |
N/A | 0.272 | 0.019 | 0.078 | 0.027 | 0.061 | 0.069 | 0.112 | 0.197 | 0.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 81 | 72 | 50 | 49 | 49 | 0 | 49 | 48 | 49 |
N.S. |
1 | 1.11 | 0.99 | 0.68 | 0.67 | 0.67 | 0.00 | 0.67 | 0.66 | 0.67 |
time (sec) |
N/A | 0.328 | 0.055 | 0.093 | 0.029 | 0.080 | 0.000 | 0.113 | 0.193 | 0.038 |
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 | 130 | 140 | 117 | 83 | 82 | 76 | 121 | 82 | 81 | 82 |
N.S. |
1 | 1.08 | 0.90 | 0.64 | 0.63 | 0.58 | 0.93 | 0.63 | 0.62 | 0.63 |
time (sec) |
N/A | 0.391 | 0.073 | 0.029 | 0.025 | 0.065 | 1.152 | 0.115 | 0.194 | 0.202 |
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 | 8 | 8 | 8 | 7 | 6 | 6 | 7 | 6 | 5 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.75 | 0.75 | 0.88 | 0.75 | 0.62 | 0.75 |
time (sec) |
N/A | 0.218 | 0.017 | 0.089 | 0.104 | 0.067 | 0.105 | 0.108 | 0.185 | 22.598 |
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 | 19 | 25 | 19 | 16 | 15 | 15 | 17 | 15 | 13 | 15 |
N.S. |
1 | 1.32 | 1.00 | 0.84 | 0.79 | 0.79 | 0.89 | 0.79 | 0.68 | 0.79 |
time (sec) |
N/A | 0.264 | 0.021 | 0.046 | 0.024 | 0.064 | 0.057 | 0.110 | 0.169 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 124 | 62 | 66 | 83 | 73 | 0 | 83 | 76 | 42 |
N.S. |
1 | 1.57 | 0.78 | 0.84 | 1.05 | 0.92 | 0.00 | 1.05 | 0.96 | 0.53 |
time (sec) |
N/A | 0.509 | 0.127 | 0.028 | 0.109 | 0.069 | 0.000 | 0.119 | 0.200 | 0.084 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 83 | 83 | 61 | 60 | 62 | 0 | 60 | 59 | 78 |
N.S. |
1 | 1.09 | 1.09 | 0.80 | 0.79 | 0.82 | 0.00 | 0.79 | 0.78 | 1.03 |
time (sec) |
N/A | 0.339 | 0.079 | 0.028 | 0.107 | 0.069 | 0.000 | 0.116 | 0.167 | 22.398 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 131 | 110 | 76 | 75 | 71 | 0 | 75 | 74 | 75 |
N.S. |
1 | 1.10 | 0.92 | 0.64 | 0.63 | 0.60 | 0.00 | 0.63 | 0.62 | 0.63 |
time (sec) |
N/A | 0.367 | 0.047 | 0.020 | 0.025 | 0.064 | 0.000 | 0.116 | 0.162 | 0.171 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 208 | 127 | 132 | 293 | 156 | 0 | 140 | 43 | 208 |
N.S. |
1 | 1.03 | 0.63 | 0.66 | 1.46 | 0.78 | 0.00 | 0.70 | 0.21 | 1.03 |
time (sec) |
N/A | 0.736 | 0.089 | 0.059 | 0.114 | 0.076 | 0.000 | 0.188 | 0.201 | 0.117 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 12 | 11 | 11 | 12 | 11 | 29 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.73 | 0.73 | 0.80 | 0.73 | 1.93 | 0.73 |
time (sec) |
N/A | 0.243 | 10.038 | 0.080 | 0.028 | 0.064 | 0.082 | 0.111 | 0.182 | 22.763 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 72 | 14 | 13 | 20 | 31 | 13 | 14 | 19 |
N.S. |
1 | 1.00 | 4.24 | 0.82 | 0.76 | 1.18 | 1.82 | 0.76 | 0.82 | 1.12 |
time (sec) |
N/A | 0.246 | 10.069 | 0.085 | 0.031 | 0.067 | 0.090 | 0.105 | 0.217 | 22.264 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 12 | 11 | 11 | 31 | 11 | 16 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.73 | 0.73 | 2.07 | 0.73 | 1.07 | 0.73 |
time (sec) |
N/A | 0.244 | 10.038 | 0.079 | 0.025 | 0.079 | 0.088 | 0.110 | 0.171 | 22.230 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 12 | 11 | 11 | 31 | 11 | 16 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.73 | 0.73 | 2.07 | 0.73 | 1.07 | 0.73 |
time (sec) |
N/A | 0.244 | 10.051 | 0.082 | 0.031 | 0.064 | 0.085 | 0.113 | 0.175 | 22.280 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 11 | 11 | 10 | 23 | 8 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 0.85 | 0.77 | 1.77 | 0.62 | 0.77 |
time (sec) |
N/A | 0.240 | 0.023 | 0.063 | 0.029 | 0.063 | 0.062 | 0.113 | 0.180 | 22.370 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 46 | 45 | 34 | 33 | 32 | 39 | 33 | 33 | 32 |
N.S. |
1 | 1.05 | 1.02 | 0.77 | 0.75 | 0.73 | 0.89 | 0.75 | 0.75 | 0.73 |
time (sec) |
N/A | 0.297 | 0.039 | 0.084 | 0.025 | 0.065 | 0.071 | 0.148 | 0.182 | 0.112 |
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 | 21 | 27 | 19 | 16 | 15 | 15 | 17 | 16 | 13 | 15 |
N.S. |
1 | 1.29 | 0.90 | 0.76 | 0.71 | 0.71 | 0.81 | 0.76 | 0.62 | 0.71 |
time (sec) |
N/A | 0.273 | 0.021 | 0.054 | 0.039 | 0.063 | 0.057 | 0.114 | 0.187 | 22.128 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 34 | 27 | 26 | 25 | 27 | 26 | 24 | 25 |
N.S. |
1 | 1.00 | 1.03 | 0.82 | 0.79 | 0.76 | 0.82 | 0.79 | 0.73 | 0.76 |
time (sec) |
N/A | 0.296 | 0.033 | 0.053 | 0.027 | 0.064 | 0.090 | 0.114 | 0.172 | 0.148 |
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 | 33 | 43 | 36 | 35 | 30 | 29 | 42 | 38 | 28 | 29 |
N.S. |
1 | 1.30 | 1.09 | 1.06 | 0.91 | 0.88 | 1.27 | 1.15 | 0.85 | 0.88 |
time (sec) |
N/A | 0.310 | 0.051 | 0.042 | 0.029 | 0.068 | 0.112 | 0.108 | 0.165 | 22.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 37 | 10 | 12 | 10 | 10 | 14 | 0 | 10 | 10 |
N.S. |
1 | 3.70 | 1.00 | 1.20 | 1.00 | 1.00 | 1.40 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.385 | 0.039 | 0.114 | 0.024 | 0.070 | 0.871 | 0.000 | 0.185 | 22.401 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 37 | 10 | 12 | 86 | 10 | 24 | 0 | 10 | 39 |
N.S. |
1 | 2.18 | 0.59 | 0.71 | 5.06 | 0.59 | 1.41 | 0.00 | 0.59 | 2.29 |
time (sec) |
N/A | 0.342 | 0.009 | 0.129 | 0.042 | 0.067 | 12.761 | 0.000 | 0.162 | 22.532 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F(-1) | F(-1) | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 34 | 38 | 97 | 0 | 0 | 0 | 99 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.03 | 2.62 | 0.00 | 0.00 | 0.00 | 2.68 | 0.00 |
time (sec) |
N/A | 0.454 | 4.618 | 32.494 | 0.127 | 0.000 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F(-1) | F(-1) | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 32 | 36 | 95 | 0 | 0 | 0 | 97 | 0 |
N.S. |
1 | 1.00 | 0.91 | 1.03 | 2.71 | 0.00 | 0.00 | 0.00 | 2.77 | 0.00 |
time (sec) |
N/A | 0.431 | 10.499 | 25.066 | 0.125 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F(-1) | F(-1) | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 31 | 35 | 92 | 0 | 0 | 0 | 96 | 148 |
N.S. |
1 | 1.00 | 0.91 | 1.03 | 2.71 | 0.00 | 0.00 | 0.00 | 2.82 | 4.35 |
time (sec) |
N/A | 0.463 | 8.570 | 18.982 | 0.119 | 0.000 | 0.000 | 0.000 | 0.183 | 33.285 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | F(-1) | F(-1) | F(-1) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 34 | 38 | 95 | 0 | 0 | 0 | 99 | 37 |
N.S. |
1 | 0.00 | 0.92 | 1.03 | 2.57 | 0.00 | 0.00 | 0.00 | 2.68 | 1.00 |
time (sec) |
N/A | 0.000 | 10.798 | 50.033 | 0.129 | 0.000 | 0.000 | 0.000 | 0.204 | 31.777 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | F(-1) | F(-1) | F(-1) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 34 | 38 | 95 | 0 | 0 | 0 | 99 | 146 |
N.S. |
1 | 0.00 | 0.92 | 1.03 | 2.57 | 0.00 | 0.00 | 0.00 | 2.68 | 3.95 |
time (sec) |
N/A | 0.000 | 11.073 | 49.302 | 0.116 | 0.000 | 0.000 | 0.000 | 0.187 | 31.204 |