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 | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 92 | 62 | 116 | 0 | 163 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.01 | 0.68 | 1.27 | 0.00 | 1.79 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.431 | 0.491 | 0.389 | 0.000 | 0.135 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 98 | 64 | 189 | 0 | 111 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.01 | 0.66 | 1.95 | 0.00 | 1.14 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.428 | 0.552 | 0.457 | 0.000 | 0.121 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 130 | 64 | 302 | 0 | 178 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.03 | 0.51 | 2.40 | 0.00 | 1.41 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.535 | 0.696 | 0.569 | 0.000 | 0.099 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 172 | 66 | 295 | 0 | 141 | 0 | 0 | 81 | 0 |
N.S. |
1 | 1.02 | 0.39 | 1.76 | 0.00 | 0.84 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.763 | 0.076 | 10.579 | 0.000 | 0.122 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 138 | 66 | 260 | 0 | 137 | 0 | 0 | 81 | 0 |
N.S. |
1 | 1.01 | 0.48 | 1.90 | 0.00 | 1.00 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.620 | 0.116 | 8.771 | 0.000 | 0.104 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 138 | 66 | 203 | 0 | 118 | 0 | 0 | 75 | 0 |
N.S. |
1 | 1.01 | 0.48 | 1.48 | 0.00 | 0.86 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.607 | 0.058 | 1.886 | 0.000 | 0.155 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 66 | 188 | 0 | 110 | 0 | 0 | 59 | 0 |
N.S. |
1 | 1.00 | 0.63 | 1.79 | 0.00 | 1.05 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.480 | 0.034 | 1.185 | 0.000 | 0.093 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 103 | 64 | 152 | 0 | 94 | 0 | 0 | 70 | 0 |
N.S. |
1 | 0.98 | 0.61 | 1.45 | 0.00 | 0.90 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.484 | 0.027 | 0.807 | 0.000 | 0.088 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 87 | 64 | 120 | 0 | 184 | 0 | 0 | 90 | 0 |
N.S. |
1 | 1.02 | 0.75 | 1.41 | 0.00 | 2.16 | 0.00 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 0.488 | 0.044 | 1.217 | 0.000 | 0.119 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 91 | 66 | 192 | 0 | 122 | 0 | 0 | 97 | 0 |
N.S. |
1 | 1.02 | 0.74 | 2.16 | 0.00 | 1.37 | 0.00 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.467 | 0.046 | 1.260 | 0.000 | 0.101 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 125 | 66 | 306 | 0 | 288 | 0 | 0 | 97 | 0 |
N.S. |
1 | 0.98 | 0.52 | 2.41 | 0.00 | 2.27 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.623 | 0.057 | 1.995 | 0.000 | 0.118 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 119 | 66 | 375 | 0 | 175 | 0 | 0 | 97 | 0 |
N.S. |
1 | 1.04 | 0.58 | 3.29 | 0.00 | 1.54 | 0.00 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.492 | 0.075 | 3.097 | 0.000 | 0.097 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 151 | 66 | 488 | 0 | 248 | 0 | 0 | 97 | 0 |
N.S. |
1 | 1.04 | 0.46 | 3.37 | 0.00 | 1.71 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.608 | 0.115 | 4.332 | 0.000 | 0.104 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 213 | 66 | 321 | 0 | 158 | 0 | 0 | 110 | 0 |
N.S. |
1 | 1.05 | 0.33 | 1.58 | 0.00 | 0.78 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.949 | 0.049 | 41.395 | 0.000 | 0.113 | 0.000 | 0.000 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 179 | 66 | 264 | 0 | 153 | 0 | 0 | 110 | 0 |
N.S. |
1 | 1.05 | 0.39 | 1.55 | 0.00 | 0.90 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.805 | 0.072 | 40.582 | 0.000 | 0.108 | 0.000 | 0.000 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 179 | 66 | 251 | 0 | 134 | 0 | 0 | 102 | 0 |
N.S. |
1 | 1.04 | 0.38 | 1.46 | 0.00 | 0.78 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.794 | 0.049 | 1.104 | 0.000 | 0.111 | 0.000 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 146 | 66 | 214 | 0 | 124 | 0 | 0 | 77 | 0 |
N.S. |
1 | 1.04 | 0.47 | 1.53 | 0.00 | 0.89 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.675 | 0.031 | 0.940 | 0.000 | 0.121 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 144 | 64 | 178 | 0 | 108 | 0 | 0 | 99 | 0 |
N.S. |
1 | 1.06 | 0.47 | 1.31 | 0.00 | 0.79 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.643 | 0.024 | 1.690 | 0.000 | 0.096 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 118 | 64 | 146 | 0 | 212 | 0 | 0 | 125 | 0 |
N.S. |
1 | 1.11 | 0.60 | 1.38 | 0.00 | 2.00 | 0.00 | 0.00 | 1.18 | 0.00 |
time (sec) |
N/A | 0.682 | 0.032 | 1.841 | 0.000 | 0.100 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 120 | 66 | 219 | 0 | 138 | 0 | 0 | 131 | 0 |
N.S. |
1 | 1.09 | 0.60 | 1.99 | 0.00 | 1.25 | 0.00 | 0.00 | 1.19 | 0.00 |
time (sec) |
N/A | 0.641 | 0.034 | 1.891 | 0.000 | 0.090 | 0.000 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 129 | 66 | 330 | 0 | 294 | 0 | 0 | 134 | 0 |
N.S. |
1 | 1.02 | 0.52 | 2.60 | 0.00 | 2.31 | 0.00 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 0.646 | 0.047 | 2.223 | 0.000 | 0.092 | 0.000 | 0.000 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 133 | 66 | 401 | 0 | 174 | 0 | 0 | 134 | 0 |
N.S. |
1 | 1.05 | 0.52 | 3.16 | 0.00 | 1.37 | 0.00 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 0.645 | 0.040 | 2.559 | 0.000 | 0.095 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 168 | 66 | 514 | 0 | 400 | 0 | 0 | 134 | 0 |
N.S. |
1 | 1.02 | 0.40 | 3.12 | 0.00 | 2.42 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.809 | 0.077 | 3.311 | 0.000 | 0.115 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 220 | 66 | 295 | 0 | 148 | 0 | 0 | 129 | 0 |
N.S. |
1 | 1.05 | 0.31 | 1.40 | 0.00 | 0.70 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 1.009 | 0.065 | 4.029 | 0.000 | 0.098 | 0.000 | 0.000 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 187 | 66 | 258 | 0 | 139 | 0 | 0 | 101 | 0 |
N.S. |
1 | 1.05 | 0.37 | 1.45 | 0.00 | 0.78 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.824 | 0.044 | 3.064 | 0.000 | 0.139 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 185 | 64 | 222 | 0 | 124 | 0 | 0 | 128 | 0 |
N.S. |
1 | 1.04 | 0.36 | 1.25 | 0.00 | 0.70 | 0.00 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.836 | 0.036 | 12.031 | 0.000 | 0.095 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 168 | 64 | 190 | 0 | 239 | 0 | 0 | 160 | 0 |
N.S. |
1 | 1.08 | 0.41 | 1.22 | 0.00 | 1.53 | 0.00 | 0.00 | 1.03 | 0.00 |
time (sec) |
N/A | 0.836 | 0.039 | 12.398 | 0.000 | 0.122 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 166 | 66 | 263 | 0 | 149 | 0 | 0 | 171 | 0 |
N.S. |
1 | 1.09 | 0.43 | 1.73 | 0.00 | 0.98 | 0.00 | 0.00 | 1.12 | 0.00 |
time (sec) |
N/A | 0.812 | 0.041 | 12.201 | 0.000 | 0.101 | 0.000 | 0.000 | 0.266 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 134 | 66 | 332 | 0 | 293 | 0 | 0 | 171 | 0 |
N.S. |
1 | 1.06 | 0.52 | 2.61 | 0.00 | 2.31 | 0.00 | 0.00 | 1.35 | 0.00 |
time (sec) |
N/A | 0.634 | 0.056 | 12.369 | 0.000 | 0.128 | 0.000 | 0.000 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 138 | 66 | 401 | 0 | 178 | 0 | 0 | 171 | 0 |
N.S. |
1 | 1.09 | 0.52 | 3.16 | 0.00 | 1.40 | 0.00 | 0.00 | 1.35 | 0.00 |
time (sec) |
N/A | 0.644 | 0.061 | 12.804 | 0.000 | 0.096 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 172 | 66 | 514 | 0 | 400 | 0 | 0 | 171 | 0 |
N.S. |
1 | 1.02 | 0.39 | 3.04 | 0.00 | 2.37 | 0.00 | 0.00 | 1.01 | 0.00 |
time (sec) |
N/A | 0.813 | 0.115 | 13.814 | 0.000 | 0.096 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 176 | 66 | 583 | 0 | 235 | 0 | 0 | 171 | 0 |
N.S. |
1 | 1.04 | 0.39 | 3.45 | 0.00 | 1.39 | 0.00 | 0.00 | 1.01 | 0.00 |
time (sec) |
N/A | 0.822 | 0.143 | 18.518 | 0.000 | 0.105 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 135 | 66 | 251 | 0 | 114 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.02 | 0.50 | 1.90 | 0.00 | 0.86 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.561 | 0.103 | 1.769 | 0.000 | 0.123 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 66 | 216 | 0 | 110 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.00 | 0.65 | 2.14 | 0.00 | 1.09 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.456 | 0.066 | 1.266 | 0.000 | 0.113 | 0.000 | 0.000 | 0.283 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 66 | 181 | 0 | 98 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.00 | 0.65 | 1.79 | 0.00 | 0.97 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.464 | 0.056 | 1.175 | 0.000 | 0.089 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 66 | 122 | 0 | 88 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.00 | 0.97 | 1.79 | 0.00 | 1.29 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.363 | 0.073 | 1.128 | 0.000 | 0.087 | 0.000 | 0.000 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 66 | 110 | 0 | 74 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.67 | 0.00 | 1.12 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.362 | 0.053 | 0.246 | 0.000 | 0.083 | 0.000 | 0.000 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 66 | 118 | 0 | 146 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 0.89 | 1.59 | 0.00 | 1.97 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.366 | 0.034 | 0.305 | 0.000 | 0.113 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 64 | 190 | 0 | 100 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.00 | 0.82 | 2.44 | 0.00 | 1.28 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.374 | 0.027 | 0.480 | 0.000 | 0.095 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 110 | 63 | 306 | 0 | 171 | 0 | 0 | 45 | 0 |
N.S. |
1 | 0.98 | 0.56 | 2.73 | 0.00 | 1.53 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.489 | 0.040 | 0.699 | 0.000 | 0.101 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 114 | 66 | 375 | 0 | 177 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.02 | 0.59 | 3.35 | 0.00 | 1.58 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.474 | 0.046 | 0.883 | 0.000 | 0.108 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 146 | 66 | 488 | 0 | 205 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.02 | 0.46 | 3.41 | 0.00 | 1.43 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.621 | 0.061 | 1.175 | 0.000 | 0.107 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 151 | 66 | 203 | 0 | 113 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.04 | 0.46 | 1.40 | 0.00 | 0.78 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.599 | 0.237 | 19.490 | 0.000 | 0.091 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 117 | 66 | 190 | 0 | 107 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.03 | 0.58 | 1.67 | 0.00 | 0.94 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.480 | 0.122 | 15.522 | 0.000 | 0.085 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 113 | 66 | 155 | 0 | 88 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.01 | 0.59 | 1.38 | 0.00 | 0.79 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.487 | 0.097 | 16.980 | 0.000 | 0.085 | 0.000 | 0.000 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 66 | 120 | 0 | 184 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.00 | 0.84 | 1.52 | 0.00 | 2.33 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.380 | 0.100 | 16.643 | 0.000 | 0.167 | 0.000 | 0.000 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 66 | 192 | 0 | 111 | 0 | 0 | 119 | 0 |
N.S. |
1 | 1.00 | 0.80 | 2.31 | 0.00 | 1.34 | 0.00 | 0.00 | 1.43 | 0.00 |
time (sec) |
N/A | 0.385 | 0.085 | 0.649 | 0.000 | 0.088 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 116 | 66 | 304 | 0 | 237 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 0.57 | 2.62 | 0.00 | 2.04 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.527 | 0.051 | 1.033 | 0.000 | 0.106 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 120 | 64 | 372 | 0 | 149 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.03 | 0.55 | 3.21 | 0.00 | 1.28 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.519 | 0.050 | 1.420 | 0.000 | 0.102 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 152 | 66 | 488 | 0 | 224 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.01 | 0.44 | 3.25 | 0.00 | 1.49 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.685 | 0.071 | 1.521 | 0.000 | 0.111 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 156 | 66 | 557 | 0 | 230 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.04 | 0.44 | 3.71 | 0.00 | 1.53 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.670 | 0.108 | 2.486 | 0.000 | 0.115 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 188 | 66 | 670 | 0 | 256 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.04 | 0.36 | 3.70 | 0.00 | 1.41 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.804 | 0.145 | 4.484 | 0.000 | 0.137 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 181 | 66 | 251 | 0 | 126 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.07 | 0.39 | 1.49 | 0.00 | 0.75 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.760 | 0.430 | 140.316 | 0.000 | 0.131 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 147 | 66 | 216 | 0 | 120 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.07 | 0.48 | 1.57 | 0.00 | 0.87 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.632 | 0.240 | 117.200 | 0.000 | 0.125 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 143 | 66 | 181 | 0 | 101 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.08 | 0.50 | 1.37 | 0.00 | 0.77 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.631 | 0.181 | 113.447 | 0.000 | 0.108 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 110 | 66 | 146 | 0 | 210 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.07 | 0.64 | 1.42 | 0.00 | 2.04 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.519 | 0.123 | 129.533 | 0.000 | 0.099 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 112 | 66 | 219 | 0 | 136 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.05 | 0.62 | 2.05 | 0.00 | 1.27 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.527 | 0.098 | 147.625 | 0.000 | 0.088 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 120 | 66 | 332 | 0 | 294 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.02 | 0.56 | 2.81 | 0.00 | 2.49 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.531 | 0.088 | 151.143 | 0.000 | 0.087 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 124 | 66 | 401 | 0 | 159 | 0 | 0 | 444 | 0 |
N.S. |
1 | 1.05 | 0.56 | 3.40 | 0.00 | 1.35 | 0.00 | 0.00 | 3.76 | 0.00 |
time (sec) |
N/A | 0.546 | 0.081 | 2.319 | 0.000 | 0.109 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 158 | 66 | 512 | 0 | 331 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.03 | 0.43 | 3.35 | 0.00 | 2.16 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.686 | 0.046 | 2.631 | 0.000 | 0.102 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 162 | 66 | 580 | 0 | 202 | 0 | 0 | 73 | 0 |
N.S. |
1 | 1.06 | 0.43 | 3.79 | 0.00 | 1.32 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.696 | 0.068 | 3.769 | 0.000 | 0.142 | 0.000 | 0.000 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 194 | 66 | 696 | 0 | 276 | 0 | 0 | 81 | 0 |
N.S. |
1 | 1.04 | 0.35 | 3.72 | 0.00 | 1.48 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.855 | 0.088 | 6.118 | 0.000 | 0.113 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 193 | 66 | 225 | 0 | 117 | 0 | 0 | 67 | 0 |
N.S. |
1 | 1.07 | 0.37 | 1.25 | 0.00 | 0.65 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.807 | 0.432 | 2.114 | 0.000 | 0.119 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 159 | 66 | 190 | 0 | 239 | 0 | 0 | 67 | 0 |
N.S. |
1 | 1.07 | 0.44 | 1.28 | 0.00 | 1.60 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.692 | 0.241 | 1.851 | 0.000 | 0.105 | 0.000 | 0.000 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 157 | 66 | 263 | 0 | 148 | 0 | 0 | 67 | 0 |
N.S. |
1 | 1.08 | 0.46 | 1.81 | 0.00 | 1.02 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.680 | 0.174 | 2.114 | 0.000 | 0.094 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 125 | 66 | 332 | 0 | 293 | 0 | 0 | 67 | 0 |
N.S. |
1 | 1.04 | 0.55 | 2.77 | 0.00 | 2.44 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.556 | 0.118 | 2.574 | 0.000 | 0.091 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 129 | 66 | 401 | 0 | 176 | 0 | 0 | 353 | 0 |
N.S. |
1 | 1.08 | 0.55 | 3.34 | 0.00 | 1.47 | 0.00 | 0.00 | 2.94 | 0.00 |
time (sec) |
N/A | 0.541 | 0.103 | 2.680 | 0.000 | 0.100 | 0.000 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 162 | 66 | 514 | 0 | 400 | 0 | 0 | 67 | 0 |
N.S. |
1 | 1.05 | 0.43 | 3.34 | 0.00 | 2.60 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.711 | 0.100 | 3.629 | 0.000 | 0.100 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 166 | 66 | 583 | 0 | 212 | 0 | 0 | 1055 | 0 |
N.S. |
1 | 1.08 | 0.43 | 3.79 | 0.00 | 1.38 | 0.00 | 0.00 | 6.85 | 0.00 |
time (sec) |
N/A | 0.724 | 0.095 | 4.599 | 0.000 | 0.098 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 200 | 66 | 694 | 0 | 419 | 0 | 0 | 56 | 0 |
N.S. |
1 | 1.05 | 0.35 | 3.63 | 0.00 | 2.19 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.913 | 0.074 | 6.234 | 0.000 | 0.107 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 204 | 66 | 762 | 0 | 250 | 0 | 0 | 89 | 0 |
N.S. |
1 | 1.07 | 0.35 | 3.99 | 0.00 | 1.31 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.889 | 0.076 | 7.206 | 0.000 | 0.125 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-1) | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 225 | 236 | 66 | 878 | 0 | 326 | 0 | 0 | 99 | 0 |
N.S. |
1 | 1.05 | 0.29 | 3.90 | 0.00 | 1.45 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 1.082 | 0.115 | 7.848 | 0.000 | 0.113 | 0.000 | 0.000 | 0.196 | 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 | 236 | 249 | 77 | 1470 | 0 | 360 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.06 | 0.33 | 6.23 | 0.00 | 1.53 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.981 | 0.368 | 9.405 | 0.000 | 0.174 | 0.000 | 0.000 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 210 | 77 | 720 | 0 | 420 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.08 | 0.40 | 3.71 | 0.00 | 2.16 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.849 | 0.256 | 3.920 | 0.000 | 0.161 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 161 | 75 | 798 | 0 | 320 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 0.47 | 4.96 | 0.00 | 1.99 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.648 | 0.215 | 3.270 | 0.000 | 0.178 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 34 | 40 | 131 | 38 | 0 | 0 | 35 | 30 |
N.S. |
1 | 1.00 | 1.00 | 1.18 | 3.85 | 1.12 | 0.00 | 0.00 | 1.03 | 0.88 |
time (sec) |
N/A | 0.245 | 0.249 | 3.633 | 0.138 | 0.102 | 0.000 | 0.000 | 0.176 | 26.576 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 46 | 57 | 206 | 48 | 0 | 0 | 35 | 61 |
N.S. |
1 | 1.00 | 0.62 | 0.77 | 2.78 | 0.65 | 0.00 | 0.00 | 0.47 | 0.82 |
time (sec) |
N/A | 0.402 | 0.332 | 5.757 | 0.152 | 0.110 | 0.000 | 0.000 | 0.202 | 26.909 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 118 | 56 | 119 | 282 | 58 | 0 | 0 | 35 | 97 |
N.S. |
1 | 1.03 | 0.49 | 1.03 | 2.45 | 0.50 | 0.00 | 0.00 | 0.30 | 0.84 |
time (sec) |
N/A | 0.553 | 0.422 | 7.627 | 0.152 | 0.122 | 0.000 | 0.000 | 0.175 | 27.663 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 160 | 74 | 163 | 357 | 70 | 0 | 0 | 35 | 129 |
N.S. |
1 | 1.04 | 0.48 | 1.06 | 2.32 | 0.45 | 0.00 | 0.00 | 0.23 | 0.84 |
time (sec) |
N/A | 0.759 | 0.568 | 11.435 | 0.155 | 0.105 | 0.000 | 0.000 | 0.183 | 28.876 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 319 | 343 | 78 | 850 | 0 | 562 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.08 | 0.24 | 2.66 | 0.00 | 1.76 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 1.438 | 0.191 | 13.372 | 0.000 | 0.183 | 0.000 | 0.000 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 278 | 292 | 78 | 796 | 0 | 379 | 0 | 0 | 64 | 0 |
N.S. |
1 | 1.05 | 0.28 | 2.86 | 0.00 | 1.36 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 1.198 | 0.143 | 10.964 | 0.000 | 0.163 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 243 | 253 | 77 | 740 | 0 | 461 | 0 | 0 | 51 | 0 |
N.S. |
1 | 1.04 | 0.32 | 3.05 | 0.00 | 1.90 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.983 | 0.122 | 7.678 | 0.000 | 0.183 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 202 | 75 | 686 | 0 | 355 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.02 | 0.38 | 3.46 | 0.00 | 1.79 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.794 | 0.111 | 4.951 | 0.000 | 0.159 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 213 | 75 | 857 | 0 | 380 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.01 | 0.36 | 4.08 | 0.00 | 1.81 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.816 | 0.122 | 4.430 | 0.000 | 0.157 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 36 | 54 | 131 | 45 | 0 | 0 | 70 | 47 |
N.S. |
1 | 1.00 | 1.00 | 1.50 | 3.64 | 1.25 | 0.00 | 0.00 | 1.94 | 1.31 |
time (sec) |
N/A | 0.243 | 0.110 | 4.046 | 0.141 | 0.090 | 0.000 | 0.000 | 0.177 | 26.932 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 72 | 61 | 207 | 69 | 0 | 0 | 70 | 71 |
N.S. |
1 | 1.00 | 0.97 | 0.82 | 2.80 | 0.93 | 0.00 | 0.00 | 0.95 | 0.96 |
time (sec) |
N/A | 0.398 | 0.141 | 4.787 | 0.152 | 0.088 | 0.000 | 0.000 | 0.180 | 27.764 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 116 | 64 | 144 | 281 | 84 | 0 | 0 | 70 | 116 |
N.S. |
1 | 1.03 | 0.57 | 1.27 | 2.49 | 0.74 | 0.00 | 0.00 | 0.62 | 1.03 |
time (sec) |
N/A | 0.569 | 0.276 | 6.974 | 0.147 | 0.086 | 0.000 | 0.000 | 0.195 | 28.147 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 158 | 74 | 190 | 357 | 98 | 0 | 0 | 70 | 261 |
N.S. |
1 | 1.04 | 0.49 | 1.25 | 2.35 | 0.64 | 0.00 | 0.00 | 0.46 | 1.72 |
time (sec) |
N/A | 0.753 | 0.281 | 10.260 | 0.148 | 0.096 | 0.000 | 0.000 | 0.178 | 33.718 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 323 | 335 | 77 | 851 | 0 | 408 | 0 | 0 | 101 | 0 |
N.S. |
1 | 1.04 | 0.24 | 2.63 | 0.00 | 1.26 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 1.402 | 0.307 | 16.034 | 0.000 | 0.153 | 0.000 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 286 | 296 | 78 | 793 | 0 | 516 | 0 | 0 | 82 | 0 |
N.S. |
1 | 1.03 | 0.27 | 2.77 | 0.00 | 1.80 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 1.216 | 0.132 | 11.044 | 0.000 | 0.163 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 247 | 245 | 76 | 708 | 0 | 377 | 0 | 0 | 109 | 0 |
N.S. |
1 | 0.99 | 0.31 | 2.87 | 0.00 | 1.53 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.992 | 0.101 | 7.882 | 0.000 | 0.171 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 254 | 75 | 888 | 0 | 402 | 0 | 0 | 109 | 0 |
N.S. |
1 | 1.06 | 0.31 | 3.72 | 0.00 | 1.68 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.996 | 0.163 | 6.545 | 0.000 | 0.152 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 207 | 77 | 1104 | 0 | 419 | 0 | 0 | 109 | 0 |
N.S. |
1 | 1.01 | 0.38 | 5.41 | 0.00 | 2.05 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.830 | 0.202 | 5.861 | 0.000 | 0.168 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 36 | 61 | 131 | 107 | 0 | 0 | 109 | 65 |
N.S. |
1 | 1.00 | 1.00 | 1.69 | 3.64 | 2.97 | 0.00 | 0.00 | 3.03 | 1.81 |
time (sec) |
N/A | 0.243 | 0.144 | 5.033 | 0.152 | 0.114 | 0.000 | 0.000 | 0.182 | 28.301 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 54 | 173 | 207 | 75 | 0 | 0 | 109 | 96 |
N.S. |
1 | 1.00 | 0.71 | 2.28 | 2.72 | 0.99 | 0.00 | 0.00 | 1.43 | 1.26 |
time (sec) |
N/A | 0.427 | 0.173 | 7.100 | 0.142 | 0.122 | 0.000 | 0.000 | 0.182 | 28.151 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 116 | 64 | 155 | 282 | 100 | 0 | 0 | 109 | 119 |
N.S. |
1 | 1.03 | 0.57 | 1.37 | 2.50 | 0.88 | 0.00 | 0.00 | 0.96 | 1.05 |
time (sec) |
N/A | 0.582 | 0.194 | 10.105 | 0.146 | 0.086 | 0.000 | 0.000 | 0.226 | 28.447 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 160 | 74 | 216 | 357 | 120 | 0 | 0 | 109 | 232 |
N.S. |
1 | 1.07 | 0.49 | 1.44 | 2.38 | 0.80 | 0.00 | 0.00 | 0.73 | 1.55 |
time (sec) |
N/A | 0.764 | 0.259 | 15.108 | 0.151 | 0.106 | 0.000 | 0.000 | 0.212 | 34.006 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 244 | 257 | 77 | 706 | 0 | 504 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.05 | 0.32 | 2.89 | 0.00 | 2.07 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 1.025 | 0.180 | 8.150 | 0.000 | 0.203 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 206 | 77 | 1522 | 0 | 354 | 0 | 0 | 66 | 0 |
N.S. |
1 | 1.03 | 0.38 | 7.61 | 0.00 | 1.77 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.843 | 0.120 | 6.813 | 0.000 | 0.146 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 169 | 77 | 827 | 0 | 320 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.00 | 0.46 | 4.89 | 0.00 | 1.89 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.666 | 0.083 | 4.012 | 0.000 | 0.152 | 0.000 | 0.000 | 0.210 | 0.000 |