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 | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 57 | 35 | 37 | 80 | 80 | 83 | 33 | 79 | 81 |
N.S. |
1 | 1.08 | 0.66 | 0.70 | 1.51 | 1.51 | 1.57 | 0.62 | 1.49 | 1.53 |
time (sec) |
N/A | 0.364 | 0.011 | 0.125 | 0.029 | 0.061 | 0.262 | 0.113 | 0.162 | 18.391 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 38 | 24 | 26 | 69 | 69 | 71 | 22 | 68 | 70 |
N.S. |
1 | 1.12 | 0.71 | 0.76 | 2.03 | 2.03 | 2.09 | 0.65 | 2.00 | 2.06 |
time (sec) |
N/A | 0.326 | 0.007 | 0.125 | 0.032 | 0.065 | 0.238 | 0.110 | 0.159 | 0.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 15 | 59 | 59 | 63 | 14 | 58 | 61 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 3.69 | 3.69 | 3.94 | 0.88 | 3.62 | 3.81 |
time (sec) |
N/A | 0.263 | 0.002 | 0.120 | 0.034 | 0.068 | 0.218 | 0.120 | 0.165 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 103 | 76 | 85 | 126 | 222 | 128 | 92 | 269 | 122 |
N.S. |
1 | 1.01 | 0.75 | 0.83 | 1.24 | 2.18 | 1.25 | 0.90 | 2.64 | 1.20 |
time (sec) |
N/A | 0.438 | 0.033 | 0.164 | 0.036 | 0.067 | 0.346 | 0.137 | 0.168 | 18.654 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 116 | 92 | 98 | 143 | 251 | 150 | 115 | 295 | 141 |
N.S. |
1 | 1.00 | 0.79 | 0.84 | 1.23 | 2.16 | 1.29 | 0.99 | 2.54 | 1.22 |
time (sec) |
N/A | 0.483 | 0.055 | 0.187 | 0.035 | 0.070 | 0.403 | 0.107 | 0.160 | 0.181 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 141 | 107 | 111 | 158 | 266 | 165 | 130 | 310 | 155 |
N.S. |
1 | 1.01 | 0.76 | 0.79 | 1.13 | 1.90 | 1.18 | 0.93 | 2.21 | 1.11 |
time (sec) |
N/A | 0.520 | 0.040 | 0.198 | 0.043 | 0.077 | 0.438 | 0.106 | 0.166 | 18.167 |
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 | 156 | 190 | 122 | 107 | 159 | 454 | 218 | 117 | 292 | 153 |
N.S. |
1 | 1.22 | 0.78 | 0.69 | 1.02 | 2.91 | 1.40 | 0.75 | 1.87 | 0.98 |
time (sec) |
N/A | 0.553 | 0.043 | 0.163 | 0.116 | 0.078 | 0.468 | 0.111 | 0.161 | 17.530 |
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 | 145 | 177 | 111 | 96 | 148 | 428 | 204 | 106 | 279 | 143 |
N.S. |
1 | 1.22 | 0.77 | 0.66 | 1.02 | 2.95 | 1.41 | 0.73 | 1.92 | 0.99 |
time (sec) |
N/A | 0.530 | 0.040 | 0.145 | 0.108 | 0.074 | 0.447 | 0.137 | 0.165 | 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 | 131 | 166 | 100 | 84 | 134 | 400 | 178 | 87 | 265 | 130 |
N.S. |
1 | 1.27 | 0.76 | 0.64 | 1.02 | 3.05 | 1.36 | 0.66 | 2.02 | 0.99 |
time (sec) |
N/A | 0.446 | 0.035 | 0.136 | 0.109 | 0.074 | 0.420 | 0.121 | 0.176 | 17.908 |
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 | 121 | 153 | 88 | 80 | 125 | 386 | 182 | 78 | 260 | 122 |
N.S. |
1 | 1.26 | 0.73 | 0.66 | 1.03 | 3.19 | 1.50 | 0.64 | 2.15 | 1.01 |
time (sec) |
N/A | 0.415 | 0.037 | 0.148 | 0.118 | 0.086 | 0.363 | 0.106 | 0.162 | 18.357 |
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 | 122 | 151 | 91 | 80 | 131 | 390 | 194 | 84 | 260 | 119 |
N.S. |
1 | 1.24 | 0.75 | 0.66 | 1.07 | 3.20 | 1.59 | 0.69 | 2.13 | 0.98 |
time (sec) |
N/A | 0.407 | 0.040 | 0.144 | 0.116 | 0.080 | 0.324 | 0.114 | 0.161 | 18.812 |
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 | 123 | 149 | 91 | 78 | 133 | 390 | 196 | 84 | 260 | 117 |
N.S. |
1 | 1.21 | 0.74 | 0.63 | 1.08 | 3.17 | 1.59 | 0.68 | 2.11 | 0.95 |
time (sec) |
N/A | 0.407 | 0.039 | 0.144 | 0.112 | 0.082 | 0.299 | 0.135 | 0.173 | 0.122 |
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 | 124 | 147 | 91 | 78 | 133 | 390 | 196 | 84 | 260 | 116 |
N.S. |
1 | 1.19 | 0.73 | 0.63 | 1.07 | 3.15 | 1.58 | 0.68 | 2.10 | 0.94 |
time (sec) |
N/A | 0.395 | 0.034 | 0.142 | 0.113 | 0.085 | 0.277 | 0.110 | 0.168 | 18.428 |
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 | 125 | 145 | 91 | 80 | 131 | 390 | 190 | 84 | 260 | 118 |
N.S. |
1 | 1.16 | 0.73 | 0.64 | 1.05 | 3.12 | 1.52 | 0.67 | 2.08 | 0.94 |
time (sec) |
N/A | 0.390 | 0.038 | 0.148 | 0.118 | 0.093 | 0.270 | 0.107 | 0.164 | 18.171 |
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 | 113 | 176 | 89 | 120 | 124 | 386 | 177 | 78 | 260 | 121 |
N.S. |
1 | 1.56 | 0.79 | 1.06 | 1.10 | 3.42 | 1.57 | 0.69 | 2.30 | 1.07 |
time (sec) |
N/A | 0.424 | 0.030 | 0.130 | 0.112 | 0.101 | 0.280 | 0.108 | 0.168 | 17.971 |
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 | 126 | 169 | 101 | 87 | 137 | 400 | 187 | 90 | 268 | 132 |
N.S. |
1 | 1.34 | 0.80 | 0.69 | 1.09 | 3.17 | 1.48 | 0.71 | 2.13 | 1.05 |
time (sec) |
N/A | 0.446 | 0.037 | 0.170 | 0.114 | 0.087 | 0.367 | 0.137 | 0.163 | 0.170 |
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 | 147 | 186 | 113 | 97 | 152 | 436 | 209 | 104 | 284 | 146 |
N.S. |
1 | 1.27 | 0.77 | 0.66 | 1.03 | 2.97 | 1.42 | 0.71 | 1.93 | 0.99 |
time (sec) |
N/A | 0.464 | 0.043 | 0.194 | 0.132 | 0.096 | 0.393 | 0.133 | 0.170 | 18.642 |
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 | 158 | 203 | 123 | 109 | 163 | 462 | 221 | 115 | 297 | 158 |
N.S. |
1 | 1.28 | 0.78 | 0.69 | 1.03 | 2.92 | 1.40 | 0.73 | 1.88 | 1.00 |
time (sec) |
N/A | 0.515 | 0.042 | 0.220 | 0.118 | 0.082 | 0.423 | 0.110 | 0.166 | 18.318 |
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 | 19 | 16 | 16 | 15 | 19 | 12 | 15 | 20 | 16 |
N.S. |
1 | 1.00 | 0.84 | 0.84 | 0.79 | 1.00 | 0.63 | 0.79 | 1.05 | 0.84 |
time (sec) |
N/A | 0.242 | 0.005 | 0.056 | 0.104 | 0.066 | 0.043 | 0.129 | 0.167 | 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 | 11 | 11 | 11 | 10 | 9 | 9 | 8 | 9 | 13 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.82 | 0.82 | 0.73 | 0.82 | 1.18 | 1.00 |
time (sec) |
N/A | 0.239 | 0.001 | 0.036 | 0.029 | 0.068 | 0.028 | 0.110 | 0.174 | 0.018 |
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 | 19 | 19 | 16 | 15 | 21 | 12 | 15 | 22 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.79 | 1.11 | 0.63 | 0.79 | 1.16 | 0.89 |
time (sec) |
N/A | 0.251 | 0.006 | 0.062 | 0.107 | 0.073 | 0.037 | 0.107 | 0.163 | 0.028 |
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 | 22 | 18 | 18 | 19 | 18 | 23 | 15 | 18 | 32 | 18 |
N.S. |
1 | 0.82 | 0.82 | 0.86 | 0.82 | 1.05 | 0.68 | 0.82 | 1.45 | 0.82 |
time (sec) |
N/A | 0.279 | 0.005 | 0.042 | 0.028 | 0.065 | 0.032 | 0.102 | 0.165 | 17.606 |
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 | 13 | 13 | 11 | 10 | 9 | 9 | 8 | 9 | 14 | 11 |
N.S. |
1 | 1.00 | 0.85 | 0.77 | 0.69 | 0.69 | 0.62 | 0.69 | 1.08 | 0.85 |
time (sec) |
N/A | 0.239 | 0.001 | 0.043 | 0.029 | 0.061 | 0.028 | 0.149 | 0.166 | 0.044 |
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 | 24 | 24 | 20 | 19 | 18 | 23 | 14 | 19 | 44 | 18 |
N.S. |
1 | 1.00 | 0.83 | 0.79 | 0.75 | 0.96 | 0.58 | 0.79 | 1.83 | 0.75 |
time (sec) |
N/A | 0.293 | 0.006 | 0.049 | 0.030 | 0.066 | 0.031 | 0.108 | 0.166 | 0.062 |
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 | 51 | 51 | 33 | 30 | 41 | 40 | 48 | 48 | 33 | 40 |
N.S. |
1 | 1.00 | 0.65 | 0.59 | 0.80 | 0.78 | 0.94 | 0.94 | 0.65 | 0.78 |
time (sec) |
N/A | 0.323 | 0.022 | 0.127 | 0.032 | 0.101 | 0.320 | 0.106 | 0.168 | 0.072 |
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 | 51 | 51 | 33 | 30 | 41 | 34 | 48 | 42 | 31 | 41 |
N.S. |
1 | 1.00 | 0.65 | 0.59 | 0.80 | 0.67 | 0.94 | 0.82 | 0.61 | 0.80 |
time (sec) |
N/A | 0.329 | 0.018 | 0.100 | 0.034 | 0.077 | 0.197 | 0.106 | 0.164 | 17.625 |
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 | 51 | 51 | 33 | 30 | 41 | 29 | 48 | 37 | 28 | 41 |
N.S. |
1 | 1.00 | 0.65 | 0.59 | 0.80 | 0.57 | 0.94 | 0.73 | 0.55 | 0.80 |
time (sec) |
N/A | 0.329 | 0.015 | 0.103 | 0.029 | 0.096 | 0.118 | 0.123 | 0.164 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 33 | 30 | 41 | 31 | 46 | 41 | 30 | 41 |
N.S. |
1 | 1.00 | 0.67 | 0.61 | 0.84 | 0.63 | 0.94 | 0.84 | 0.61 | 0.84 |
time (sec) |
N/A | 0.320 | 0.017 | 0.108 | 0.028 | 0.073 | 0.211 | 0.136 | 0.171 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 33 | 30 | 44 | 34 | 46 | 51 | 32 | 31 |
N.S. |
1 | 1.00 | 0.67 | 0.61 | 0.90 | 0.69 | 0.94 | 1.04 | 0.65 | 0.63 |
time (sec) |
N/A | 0.319 | 0.021 | 0.117 | 0.027 | 0.111 | 0.216 | 0.101 | 0.163 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 33 | 30 | 43 | 34 | 46 | 55 | 35 | 34 |
N.S. |
1 | 1.00 | 0.67 | 0.61 | 0.88 | 0.69 | 0.94 | 1.12 | 0.71 | 0.69 |
time (sec) |
N/A | 0.318 | 0.020 | 0.120 | 0.031 | 0.155 | 0.250 | 0.110 | 0.166 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 38 | 30 | 47 | 34 | 46 | 48 | 35 | 34 |
N.S. |
1 | 1.00 | 0.78 | 0.61 | 0.96 | 0.69 | 0.94 | 0.98 | 0.71 | 0.69 |
time (sec) |
N/A | 0.312 | 0.023 | 0.126 | 0.031 | 0.159 | 0.341 | 0.140 | 0.172 | 17.757 |
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 | 91 | 91 | 55 | 52 | 73 | 68 | 88 | 86 | 55 | 71 |
N.S. |
1 | 1.00 | 0.60 | 0.57 | 0.80 | 0.75 | 0.97 | 0.95 | 0.60 | 0.78 |
time (sec) |
N/A | 0.383 | 0.028 | 0.336 | 0.026 | 0.087 | 0.515 | 0.127 | 0.163 | 0.040 |
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 | 91 | 91 | 55 | 52 | 73 | 58 | 88 | 74 | 53 | 71 |
N.S. |
1 | 1.00 | 0.60 | 0.57 | 0.80 | 0.64 | 0.97 | 0.81 | 0.58 | 0.78 |
time (sec) |
N/A | 0.380 | 0.028 | 0.221 | 0.027 | 0.093 | 0.334 | 0.123 | 0.166 | 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 | 91 | 91 | 55 | 50 | 73 | 51 | 88 | 69 | 50 | 71 |
N.S. |
1 | 1.00 | 0.60 | 0.55 | 0.80 | 0.56 | 0.97 | 0.76 | 0.55 | 0.78 |
time (sec) |
N/A | 0.384 | 0.027 | 0.245 | 0.030 | 0.076 | 0.206 | 0.127 | 0.167 | 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 | 89 | 89 | 55 | 52 | 90 | 53 | 87 | 73 | 52 | 71 |
N.S. |
1 | 1.00 | 0.62 | 0.58 | 1.01 | 0.60 | 0.98 | 0.82 | 0.58 | 0.80 |
time (sec) |
N/A | 0.366 | 0.027 | 0.153 | 0.032 | 0.126 | 0.289 | 0.110 | 0.164 | 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 | 89 | 89 | 55 | 52 | 76 | 56 | 87 | 89 | 54 | 71 |
N.S. |
1 | 1.00 | 0.62 | 0.58 | 0.85 | 0.63 | 0.98 | 1.00 | 0.61 | 0.80 |
time (sec) |
N/A | 0.374 | 0.026 | 0.164 | 0.027 | 0.115 | 0.291 | 0.170 | 0.168 | 0.033 |
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 | 89 | 89 | 55 | 52 | 76 | 56 | 87 | 94 | 57 | 71 |
N.S. |
1 | 1.00 | 0.62 | 0.58 | 0.85 | 0.63 | 0.98 | 1.06 | 0.64 | 0.80 |
time (sec) |
N/A | 0.369 | 0.024 | 0.167 | 0.027 | 0.148 | 0.319 | 0.146 | 0.163 | 0.033 |
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 | 87 | 87 | 60 | 52 | 82 | 56 | 85 | 95 | 57 | 75 |
N.S. |
1 | 1.00 | 0.69 | 0.60 | 0.94 | 0.64 | 0.98 | 1.09 | 0.66 | 0.86 |
time (sec) |
N/A | 0.366 | 0.027 | 0.179 | 0.033 | 0.094 | 0.372 | 0.148 | 0.162 | 0.060 |
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 | 129 | 129 | 77 | 74 | 105 | 96 | 128 | 124 | 77 | 103 |
N.S. |
1 | 1.00 | 0.60 | 0.57 | 0.81 | 0.74 | 0.99 | 0.96 | 0.60 | 0.80 |
time (sec) |
N/A | 0.435 | 0.030 | 0.819 | 0.027 | 0.098 | 0.792 | 0.167 | 0.229 | 0.041 |
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 | 131 | 131 | 77 | 74 | 105 | 82 | 129 | 106 | 75 | 103 |
N.S. |
1 | 1.00 | 0.59 | 0.56 | 0.80 | 0.63 | 0.98 | 0.81 | 0.57 | 0.79 |
time (sec) |
N/A | 0.432 | 0.027 | 0.316 | 0.035 | 0.140 | 0.524 | 0.149 | 0.217 | 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 | 131 | 131 | 77 | 72 | 105 | 73 | 129 | 101 | 72 | 103 |
N.S. |
1 | 1.00 | 0.59 | 0.55 | 0.80 | 0.56 | 0.98 | 0.77 | 0.55 | 0.79 |
time (sec) |
N/A | 0.452 | 0.023 | 0.342 | 0.026 | 0.070 | 0.341 | 0.152 | 0.232 | 0.039 |
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 | 129 | 129 | 77 | 74 | 155 | 75 | 128 | 105 | 74 | 103 |
N.S. |
1 | 1.00 | 0.60 | 0.57 | 1.20 | 0.58 | 0.99 | 0.81 | 0.57 | 0.80 |
time (sec) |
N/A | 0.420 | 0.023 | 0.256 | 0.032 | 0.130 | 0.402 | 0.136 | 0.220 | 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 | 125 | 125 | 77 | 74 | 108 | 78 | 124 | 127 | 76 | 103 |
N.S. |
1 | 1.00 | 0.62 | 0.59 | 0.86 | 0.62 | 0.99 | 1.02 | 0.61 | 0.82 |
time (sec) |
N/A | 0.410 | 0.028 | 0.273 | 0.028 | 0.086 | 0.422 | 0.155 | 0.227 | 0.041 |
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 | 127 | 127 | 77 | 74 | 108 | 78 | 126 | 132 | 79 | 103 |
N.S. |
1 | 1.00 | 0.61 | 0.58 | 0.85 | 0.61 | 0.99 | 1.04 | 0.62 | 0.81 |
time (sec) |
N/A | 0.414 | 0.028 | 0.274 | 0.028 | 0.079 | 0.453 | 0.117 | 0.222 | 0.041 |
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 | 127 | 127 | 82 | 74 | 114 | 78 | 126 | 133 | 79 | 107 |
N.S. |
1 | 1.00 | 0.65 | 0.58 | 0.90 | 0.61 | 0.99 | 1.05 | 0.62 | 0.84 |
time (sec) |
N/A | 0.422 | 0.029 | 0.285 | 0.031 | 0.121 | 0.535 | 0.131 | 0.224 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 349 | 178 | 202 | 300 | 295 | 0 | 306 | 331 | 129 |
N.S. |
1 | 1.46 | 0.74 | 0.85 | 1.26 | 1.23 | 0.00 | 1.28 | 1.38 | 0.54 |
time (sec) |
N/A | 1.013 | 0.308 | 1.925 | 0.118 | 0.128 | 0.000 | 0.126 | 0.233 | 17.922 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 326 | 167 | 188 | 273 | 290 | 0 | 277 | 319 | 112 |
N.S. |
1 | 1.48 | 0.76 | 0.85 | 1.24 | 1.31 | 0.00 | 1.25 | 1.44 | 0.51 |
time (sec) |
N/A | 0.919 | 0.297 | 0.963 | 0.120 | 0.120 | 0.000 | 0.129 | 0.313 | 0.129 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 324 | 167 | 190 | 282 | 261 | 0 | 278 | 318 | 112 |
N.S. |
1 | 1.47 | 0.76 | 0.86 | 1.28 | 1.18 | 0.00 | 1.26 | 1.44 | 0.51 |
time (sec) |
N/A | 0.897 | 0.278 | 0.487 | 0.114 | 0.169 | 0.000 | 0.116 | 0.178 | 0.126 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 301 | 154 | 171 | 256 | 259 | 0 | 277 | 312 | 92 |
N.S. |
1 | 1.48 | 0.75 | 0.84 | 1.25 | 1.27 | 0.00 | 1.36 | 1.53 | 0.45 |
time (sec) |
N/A | 0.860 | 0.276 | 0.433 | 0.114 | 0.107 | 0.000 | 0.116 | 0.177 | 18.236 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 301 | 153 | 177 | 265 | 234 | 0 | 275 | 307 | 92 |
N.S. |
1 | 1.48 | 0.75 | 0.87 | 1.30 | 1.15 | 0.00 | 1.35 | 1.50 | 0.45 |
time (sec) |
N/A | 0.843 | 0.268 | 0.351 | 0.113 | 0.150 | 0.000 | 0.121 | 0.172 | 17.797 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 301 | 152 | 180 | 255 | 247 | 0 | 264 | 307 | 90 |
N.S. |
1 | 1.46 | 0.74 | 0.87 | 1.24 | 1.20 | 0.00 | 1.28 | 1.49 | 0.44 |
time (sec) |
N/A | 0.848 | 0.264 | 0.355 | 0.116 | 0.185 | 0.000 | 0.120 | 0.174 | 0.112 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 305 | 154 | 177 | 261 | 244 | 0 | 269 | 311 | 90 |
N.S. |
1 | 1.48 | 0.75 | 0.86 | 1.27 | 1.18 | 0.00 | 1.31 | 1.51 | 0.44 |
time (sec) |
N/A | 0.840 | 0.255 | 0.342 | 0.112 | 0.107 | 0.000 | 0.162 | 0.168 | 17.906 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 325 | 165 | 186 | 268 | 294 | 0 | 294 | 334 | 102 |
N.S. |
1 | 1.46 | 0.74 | 0.83 | 1.20 | 1.32 | 0.00 | 1.32 | 1.50 | 0.46 |
time (sec) |
N/A | 0.901 | 0.287 | 0.426 | 0.113 | 0.123 | 0.000 | 0.141 | 0.170 | 0.130 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 329 | 165 | 192 | 275 | 320 | 0 | 276 | 341 | 102 |
N.S. |
1 | 1.48 | 0.74 | 0.86 | 1.23 | 1.43 | 0.00 | 1.24 | 1.53 | 0.46 |
time (sec) |
N/A | 0.900 | 0.290 | 0.455 | 0.114 | 0.130 | 0.000 | 0.109 | 0.178 | 17.755 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 241 | 352 | 181 | 198 | 290 | 339 | 0 | 307 | 360 | 113 |
N.S. |
1 | 1.46 | 0.75 | 0.82 | 1.20 | 1.41 | 0.00 | 1.27 | 1.49 | 0.47 |
time (sec) |
N/A | 0.936 | 0.305 | 0.445 | 0.113 | 0.115 | 0.000 | 0.163 | 0.178 | 17.844 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 291 | 419 | 205 | 232 | 361 | 433 | 0 | 345 | 673 | 188 |
N.S. |
1 | 1.44 | 0.70 | 0.80 | 1.24 | 1.49 | 0.00 | 1.19 | 2.31 | 0.65 |
time (sec) |
N/A | 1.070 | 0.610 | 2.516 | 0.118 | 0.168 | 0.000 | 0.161 | 0.184 | 0.136 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 273 | 396 | 194 | 218 | 334 | 428 | 0 | 316 | 661 | 171 |
N.S. |
1 | 1.45 | 0.71 | 0.80 | 1.22 | 1.57 | 0.00 | 1.16 | 2.42 | 0.63 |
time (sec) |
N/A | 1.002 | 0.589 | 2.501 | 0.115 | 0.140 | 0.000 | 0.154 | 0.178 | 18.368 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 273 | 394 | 175 | 220 | 343 | 399 | 0 | 317 | 660 | 171 |
N.S. |
1 | 1.44 | 0.64 | 0.81 | 1.26 | 1.46 | 0.00 | 1.16 | 2.42 | 0.63 |
time (sec) |
N/A | 1.008 | 0.507 | 2.382 | 0.115 | 0.172 | 0.000 | 0.130 | 0.178 | 17.806 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 256 | 371 | 164 | 203 | 317 | 406 | 0 | 314 | 654 | 153 |
N.S. |
1 | 1.45 | 0.64 | 0.79 | 1.24 | 1.59 | 0.00 | 1.23 | 2.55 | 0.60 |
time (sec) |
N/A | 0.948 | 0.521 | 2.353 | 0.121 | 0.139 | 0.000 | 0.122 | 0.183 | 0.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 256 | 371 | 164 | 209 | 326 | 405 | 0 | 313 | 653 | 153 |
N.S. |
1 | 1.45 | 0.64 | 0.82 | 1.27 | 1.58 | 0.00 | 1.22 | 2.55 | 0.60 |
time (sec) |
N/A | 0.981 | 0.496 | 2.388 | 0.114 | 0.126 | 0.000 | 0.148 | 0.182 | 18.417 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 259 | 371 | 164 | 206 | 323 | 429 | 0 | 317 | 654 | 150 |
N.S. |
1 | 1.43 | 0.63 | 0.80 | 1.25 | 1.66 | 0.00 | 1.22 | 2.53 | 0.58 |
time (sec) |
N/A | 1.010 | 0.477 | 2.398 | 0.120 | 0.162 | 0.000 | 0.188 | 0.185 | 18.407 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 259 | 375 | 164 | 206 | 332 | 428 | 0 | 316 | 653 | 150 |
N.S. |
1 | 1.45 | 0.63 | 0.80 | 1.28 | 1.65 | 0.00 | 1.22 | 2.52 | 0.58 |
time (sec) |
N/A | 0.986 | 0.464 | 2.352 | 0.120 | 0.149 | 0.000 | 0.118 | 0.174 | 18.132 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 370 | 161 | 206 | 323 | 429 | 0 | 317 | 654 | 149 |
N.S. |
1 | 1.43 | 0.62 | 0.80 | 1.25 | 1.66 | 0.00 | 1.23 | 2.53 | 0.58 |
time (sec) |
N/A | 0.962 | 0.424 | 2.300 | 0.114 | 0.190 | 0.000 | 0.144 | 0.178 | 18.732 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 374 | 161 | 206 | 332 | 406 | 0 | 316 | 651 | 149 |
N.S. |
1 | 1.45 | 0.62 | 0.80 | 1.29 | 1.57 | 0.00 | 1.22 | 2.52 | 0.58 |
time (sec) |
N/A | 0.969 | 0.411 | 0.477 | 0.115 | 0.183 | 0.000 | 0.122 | 0.182 | 0.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 369 | 161 | 212 | 317 | 394 | 0 | 302 | 651 | 150 |
N.S. |
1 | 1.43 | 0.62 | 0.82 | 1.23 | 1.53 | 0.00 | 1.17 | 2.52 | 0.58 |
time (sec) |
N/A | 0.994 | 0.305 | 0.510 | 0.119 | 0.135 | 0.000 | 0.133 | 0.178 | 0.108 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 373 | 161 | 209 | 322 | 395 | 0 | 308 | 653 | 150 |
N.S. |
1 | 1.45 | 0.62 | 0.81 | 1.25 | 1.53 | 0.00 | 1.19 | 2.53 | 0.58 |
time (sec) |
N/A | 0.961 | 0.287 | 0.440 | 0.114 | 0.148 | 0.000 | 0.176 | 0.185 | 18.607 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 275 | 393 | 173 | 217 | 328 | 456 | 0 | 327 | 688 | 166 |
N.S. |
1 | 1.43 | 0.63 | 0.79 | 1.19 | 1.66 | 0.00 | 1.19 | 2.50 | 0.60 |
time (sec) |
N/A | 0.997 | 0.517 | 0.599 | 0.121 | 0.157 | 0.000 | 0.155 | 0.176 | 0.144 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 275 | 397 | 173 | 222 | 335 | 482 | 0 | 308 | 695 | 166 |
N.S. |
1 | 1.44 | 0.63 | 0.81 | 1.22 | 1.75 | 0.00 | 1.12 | 2.53 | 0.60 |
time (sec) |
N/A | 1.041 | 0.513 | 0.565 | 0.119 | 0.187 | 0.000 | 0.158 | 0.181 | 0.180 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 293 | 420 | 189 | 229 | 350 | 501 | 0 | 349 | 714 | 179 |
N.S. |
1 | 1.43 | 0.65 | 0.78 | 1.19 | 1.71 | 0.00 | 1.19 | 2.44 | 0.61 |
time (sec) |
N/A | 1.060 | 0.563 | 0.652 | 0.141 | 0.188 | 0.000 | 0.186 | 0.184 | 18.672 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 343 | 489 | 227 | 256 | 421 | 571 | 0 | 383 | 1015 | 248 |
N.S. |
1 | 1.43 | 0.66 | 0.75 | 1.23 | 1.66 | 0.00 | 1.12 | 2.96 | 0.72 |
time (sec) |
N/A | 1.199 | 1.034 | 14.829 | 0.126 | 0.167 | 0.000 | 0.151 | 0.187 | 18.674 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 325 | 466 | 216 | 250 | 394 | 566 | 0 | 354 | 1003 | 231 |
N.S. |
1 | 1.43 | 0.66 | 0.77 | 1.21 | 1.74 | 0.00 | 1.09 | 3.09 | 0.71 |
time (sec) |
N/A | 1.162 | 1.040 | 14.726 | 0.120 | 0.124 | 0.000 | 0.146 | 0.190 | 18.628 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 325 | 464 | 216 | 245 | 403 | 537 | 0 | 355 | 1002 | 231 |
N.S. |
1 | 1.43 | 0.66 | 0.75 | 1.24 | 1.65 | 0.00 | 1.09 | 3.08 | 0.71 |
time (sec) |
N/A | 1.150 | 0.961 | 14.768 | 0.127 | 0.207 | 0.000 | 0.136 | 0.188 | 18.491 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 308 | 441 | 205 | 235 | 377 | 544 | 0 | 352 | 996 | 213 |
N.S. |
1 | 1.43 | 0.67 | 0.76 | 1.22 | 1.77 | 0.00 | 1.14 | 3.23 | 0.69 |
time (sec) |
N/A | 1.120 | 1.012 | 14.742 | 0.116 | 0.157 | 0.000 | 0.165 | 0.190 | 0.231 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 308 | 441 | 205 | 240 | 386 | 543 | 0 | 351 | 995 | 213 |
N.S. |
1 | 1.43 | 0.67 | 0.78 | 1.25 | 1.76 | 0.00 | 1.14 | 3.23 | 0.69 |
time (sec) |
N/A | 1.105 | 0.957 | 14.626 | 0.125 | 0.136 | 0.000 | 0.150 | 0.183 | 0.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 311 | 441 | 205 | 238 | 383 | 567 | 0 | 355 | 996 | 210 |
N.S. |
1 | 1.42 | 0.66 | 0.77 | 1.23 | 1.82 | 0.00 | 1.14 | 3.20 | 0.68 |
time (sec) |
N/A | 1.082 | 0.978 | 14.700 | 0.120 | 0.181 | 0.000 | 0.141 | 0.186 | 17.733 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 311 | 445 | 186 | 238 | 392 | 566 | 0 | 354 | 995 | 210 |
N.S. |
1 | 1.43 | 0.60 | 0.77 | 1.26 | 1.82 | 0.00 | 1.14 | 3.20 | 0.68 |
time (sec) |
N/A | 1.122 | 0.806 | 14.635 | 0.131 | 0.170 | 0.000 | 0.118 | 0.190 | 0.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 314 | 440 | 186 | 236 | 385 | 577 | 0 | 355 | 996 | 208 |
N.S. |
1 | 1.40 | 0.59 | 0.75 | 1.23 | 1.84 | 0.00 | 1.13 | 3.17 | 0.66 |
time (sec) |
N/A | 1.092 | 0.782 | 14.659 | 0.117 | 0.130 | 0.000 | 0.154 | 0.183 | 17.808 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 314 | 444 | 186 | 236 | 394 | 576 | 0 | 354 | 995 | 208 |
N.S. |
1 | 1.41 | 0.59 | 0.75 | 1.25 | 1.83 | 0.00 | 1.13 | 3.17 | 0.66 |
time (sec) |
N/A | 1.126 | 0.711 | 14.665 | 0.115 | 0.161 | 0.000 | 0.119 | 0.188 | 17.758 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 317 | 439 | 186 | 236 | 385 | 577 | 0 | 355 | 996 | 207 |
N.S. |
1 | 1.38 | 0.59 | 0.74 | 1.21 | 1.82 | 0.00 | 1.12 | 3.14 | 0.65 |
time (sec) |
N/A | 1.093 | 0.666 | 14.628 | 0.124 | 0.121 | 0.000 | 0.125 | 0.186 | 0.121 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 317 | 443 | 186 | 236 | 394 | 576 | 0 | 354 | 995 | 207 |
N.S. |
1 | 1.40 | 0.59 | 0.74 | 1.24 | 1.82 | 0.00 | 1.12 | 3.14 | 0.65 |
time (sec) |
N/A | 1.098 | 0.705 | 14.567 | 0.118 | 0.187 | 0.000 | 0.118 | 0.187 | 0.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 312 | 438 | 183 | 238 | 383 | 567 | 0 | 355 | 996 | 209 |
N.S. |
1 | 1.40 | 0.59 | 0.76 | 1.23 | 1.82 | 0.00 | 1.14 | 3.19 | 0.67 |
time (sec) |
N/A | 1.134 | 0.580 | 14.545 | 0.122 | 0.110 | 0.000 | 0.125 | 0.190 | 17.755 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 312 | 442 | 183 | 238 | 392 | 540 | 0 | 354 | 993 | 209 |
N.S. |
1 | 1.42 | 0.59 | 0.76 | 1.26 | 1.73 | 0.00 | 1.13 | 3.18 | 0.67 |
time (sec) |
N/A | 1.098 | 0.523 | 0.586 | 0.126 | 0.119 | 0.000 | 0.160 | 0.189 | 0.140 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 310 | 437 | 183 | 244 | 377 | 526 | 0 | 340 | 993 | 210 |
N.S. |
1 | 1.41 | 0.59 | 0.79 | 1.22 | 1.70 | 0.00 | 1.10 | 3.20 | 0.68 |
time (sec) |
N/A | 1.093 | 0.386 | 0.668 | 0.117 | 0.124 | 0.000 | 0.145 | 0.190 | 0.132 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 310 | 441 | 183 | 237 | 382 | 537 | 0 | 346 | 995 | 210 |
N.S. |
1 | 1.42 | 0.59 | 0.76 | 1.23 | 1.73 | 0.00 | 1.12 | 3.21 | 0.68 |
time (sec) |
N/A | 1.076 | 0.389 | 0.668 | 0.123 | 0.134 | 0.000 | 0.138 | 0.182 | 17.757 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 327 | 461 | 195 | 249 | 388 | 618 | 0 | 365 | 1042 | 226 |
N.S. |
1 | 1.41 | 0.60 | 0.76 | 1.19 | 1.89 | 0.00 | 1.12 | 3.19 | 0.69 |
time (sec) |
N/A | 1.158 | 0.873 | 0.752 | 0.128 | 0.228 | 0.000 | 0.133 | 0.193 | 0.218 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 327 | 465 | 195 | 254 | 395 | 644 | 0 | 356 | 1049 | 226 |
N.S. |
1 | 1.42 | 0.60 | 0.78 | 1.21 | 1.97 | 0.00 | 1.09 | 3.21 | 0.69 |
time (sec) |
N/A | 1.129 | 0.843 | 0.840 | 0.122 | 0.246 | 0.000 | 0.160 | 0.190 | 17.828 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 345 | 488 | 211 | 261 | 410 | 663 | 0 | 362 | 1068 | 239 |
N.S. |
1 | 1.41 | 0.61 | 0.76 | 1.19 | 1.92 | 0.00 | 1.05 | 3.10 | 0.69 |
time (sec) |
N/A | 1.287 | 0.861 | 0.918 | 0.131 | 0.220 | 0.000 | 0.149 | 0.190 | 17.902 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 49 | 91 | 24 | 13 | 13 | 0 | 29 | 15 | 71 |
N.S. |
1 | 0.62 | 1.15 | 0.30 | 0.16 | 0.16 | 0.00 | 0.37 | 0.19 | 0.90 |
time (sec) |
N/A | 0.329 | 0.327 | 0.174 | 0.026 | 0.090 | 0.000 | 0.114 | 0.169 | 18.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 71 | 39 | 24 | 13 | 13 | 0 | 23 | 15 | 59 |
N.S. |
1 | 1.06 | 0.58 | 0.36 | 0.19 | 0.19 | 0.00 | 0.34 | 0.22 | 0.88 |
time (sec) |
N/A | 0.342 | 1.009 | 0.131 | 0.031 | 0.097 | 0.000 | 0.155 | 0.172 | 18.716 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 88 | 23 | 14 | 13 | 0 | 22 | 14 | 33 |
N.S. |
1 | 1.00 | 2.44 | 0.64 | 0.39 | 0.36 | 0.00 | 0.61 | 0.39 | 0.92 |
time (sec) |
N/A | 0.284 | 0.269 | 0.127 | 0.025 | 0.120 | 0.000 | 0.141 | 0.168 | 18.328 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 45 | 454 | 26 | 14 | 11 | 0 | 30 | 11 | 109 |
N.S. |
1 | 0.60 | 6.05 | 0.35 | 0.19 | 0.15 | 0.00 | 0.40 | 0.15 | 1.45 |
time (sec) |
N/A | 0.314 | 0.557 | 0.142 | 0.031 | 0.091 | 0.000 | 0.148 | 0.168 | 17.863 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 45 | 178 | 28 | 14 | 17 | 0 | 45 | 17 | 112 |
N.S. |
1 | 0.60 | 2.37 | 0.37 | 0.19 | 0.23 | 0.00 | 0.60 | 0.23 | 1.49 |
time (sec) |
N/A | 0.321 | 0.197 | 0.123 | 0.025 | 0.074 | 0.000 | 0.142 | 0.171 | 17.881 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 37 | 22 | 13 | 13 | 0 | 30 | 15 | 33 |
N.S. |
1 | 1.00 | 0.95 | 0.56 | 0.33 | 0.33 | 0.00 | 0.77 | 0.38 | 0.85 |
time (sec) |
N/A | 0.304 | 1.011 | 0.104 | 0.031 | 0.131 | 0.000 | 0.119 | 0.169 | 17.488 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 49 | 39 | 24 | 15 | 15 | 0 | 31 | 15 | 35 |
N.S. |
1 | 0.62 | 0.49 | 0.30 | 0.19 | 0.19 | 0.00 | 0.39 | 0.19 | 0.44 |
time (sec) |
N/A | 0.320 | 1.007 | 0.105 | 0.030 | 0.107 | 0.000 | 0.145 | 0.165 | 17.508 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 49 | 39 | 24 | 15 | 15 | 0 | 31 | 15 | 35 |
N.S. |
1 | 0.62 | 0.49 | 0.30 | 0.19 | 0.19 | 0.00 | 0.39 | 0.19 | 0.44 |
time (sec) |
N/A | 0.325 | 1.013 | 0.107 | 0.032 | 0.151 | 0.000 | 0.149 | 0.168 | 17.547 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 49 | 39 | 24 | 15 | 15 | 0 | 31 | 15 | 35 |
N.S. |
1 | 0.62 | 0.49 | 0.30 | 0.19 | 0.19 | 0.00 | 0.39 | 0.19 | 0.44 |
time (sec) |
N/A | 0.323 | 1.009 | 0.111 | 0.027 | 0.122 | 0.000 | 0.102 | 0.175 | 17.817 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 49 | 39 | 36 | 13 | 13 | 0 | 29 | 15 | 0 |
N.S. |
1 | 0.62 | 0.49 | 0.46 | 0.16 | 0.16 | 0.00 | 0.37 | 0.19 | 0.00 |
time (sec) |
N/A | 0.325 | 1.008 | 1.546 | 0.030 | 0.123 | 0.000 | 0.156 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 49 | 39 | 36 | 13 | 13 | 0 | 29 | 15 | 0 |
N.S. |
1 | 0.62 | 0.49 | 0.46 | 0.16 | 0.16 | 0.00 | 0.37 | 0.19 | 0.00 |
time (sec) |
N/A | 0.328 | 1.007 | 1.043 | 0.030 | 0.075 | 0.000 | 0.111 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 50 | 36 | 33 | 10 | 10 | 0 | 20 | 12 | 0 |
N.S. |
1 | 0.68 | 0.49 | 0.45 | 0.14 | 0.14 | 0.00 | 0.27 | 0.16 | 0.00 |
time (sec) |
N/A | 0.306 | 0.005 | 0.648 | 0.029 | 0.144 | 0.000 | 0.118 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 42 | 35 | 34 | 10 | 13 | 0 | 26 | 13 | 0 |
N.S. |
1 | 0.58 | 0.49 | 0.47 | 0.14 | 0.18 | 0.00 | 0.36 | 0.18 | 0.00 |
time (sec) |
N/A | 0.325 | 1.007 | 0.998 | 0.027 | 0.083 | 0.000 | 0.140 | 0.166 | 0.000 |