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 | B | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 233 | 156 | 295 | 435 | 522 | 3806 | 204 | 478 | 0 |
N.S. |
1 | 1.27 | 0.85 | 1.61 | 2.38 | 2.85 | 20.80 | 1.11 | 2.61 | 0.00 |
time (sec) |
N/A | 0.829 | 1.548 | 0.691 | 0.061 | 0.110 | 27.137 | 0.128 | 0.252 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 178 | 127 | 334 | 447 | 467 | 3448 | 138 | 467 | 0 |
N.S. |
1 | 1.03 | 0.74 | 1.94 | 2.60 | 2.72 | 20.05 | 0.80 | 2.72 | 0.00 |
time (sec) |
N/A | 0.599 | 1.238 | 0.571 | 0.061 | 0.108 | 38.259 | 0.137 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 154 | 89 | 95 | 240 | 137 | 740 | 112 | 244 | 196 |
N.S. |
1 | 1.14 | 0.66 | 0.70 | 1.78 | 1.01 | 5.48 | 0.83 | 1.81 | 1.45 |
time (sec) |
N/A | 0.535 | 0.901 | 0.580 | 0.039 | 0.091 | 22.793 | 0.140 | 1.101 | 2.567 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 162 | 79 | 76 | 253 | 122 | 575 | 81 | 265 | 186 |
N.S. |
1 | 1.57 | 0.77 | 0.74 | 2.46 | 1.18 | 5.58 | 0.79 | 2.57 | 1.81 |
time (sec) |
N/A | 0.477 | 0.995 | 0.562 | 0.039 | 0.088 | 35.014 | 0.136 | 0.244 | 2.430 |
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 | 120 | 145 | 84 | 85 | 179 | 131 | 660 | 95 | 224 | 133 |
N.S. |
1 | 1.21 | 0.70 | 0.71 | 1.49 | 1.09 | 5.50 | 0.79 | 1.87 | 1.11 |
time (sec) |
N/A | 0.380 | 1.237 | 0.543 | 0.036 | 0.088 | 23.243 | 0.130 | 0.172 | 2.294 |
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 | 133 | 139 | 87 | 88 | 197 | 134 | 904 | 94 | 285 | 133 |
N.S. |
1 | 1.05 | 0.65 | 0.66 | 1.48 | 1.01 | 6.80 | 0.71 | 2.14 | 1.00 |
time (sec) |
N/A | 0.365 | 0.933 | 0.574 | 0.041 | 0.092 | 37.441 | 0.135 | 0.226 | 2.241 |
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 | 108 | 125 | 76 | 73 | 123 | 119 | 796 | 82 | 204 | 99 |
N.S. |
1 | 1.16 | 0.70 | 0.68 | 1.14 | 1.10 | 7.37 | 0.76 | 1.89 | 0.92 |
time (sec) |
N/A | 0.298 | 1.109 | 0.620 | 0.032 | 0.096 | 24.766 | 0.133 | 0.166 | 2.219 |
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 | 127 | 121 | 92 | 96 | 153 | 137 | 1880 | 112 | 303 | 115 |
N.S. |
1 | 0.95 | 0.72 | 0.76 | 1.20 | 1.08 | 14.80 | 0.88 | 2.39 | 0.91 |
time (sec) |
N/A | 0.264 | 0.826 | 0.508 | 0.036 | 0.085 | 31.186 | 0.136 | 0.162 | 2.226 |
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 | 138 | 156 | 130 | 193 | 157 | 468 | 6613 | 152 | 588 | 159 |
N.S. |
1 | 1.13 | 0.94 | 1.40 | 1.14 | 3.39 | 47.92 | 1.10 | 4.26 | 1.15 |
time (sec) |
N/A | 0.382 | 1.326 | 0.546 | 0.037 | 0.115 | 39.147 | 0.138 | 0.185 | 2.833 |
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 | 207 | 212 | 168 | 277 | 228 | 528 | 6922 | 239 | 746 | 225 |
N.S. |
1 | 1.02 | 0.81 | 1.34 | 1.10 | 2.55 | 33.44 | 1.15 | 3.60 | 1.09 |
time (sec) |
N/A | 0.807 | 1.304 | 0.562 | 0.045 | 0.119 | 54.802 | 0.135 | 0.196 | 3.308 |
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 | 230 | 246 | 173 | 327 | 265 | 691 | 11198 | 325 | 1029 | 279 |
N.S. |
1 | 1.07 | 0.75 | 1.42 | 1.15 | 3.00 | 48.69 | 1.41 | 4.47 | 1.21 |
time (sec) |
N/A | 1.010 | 1.661 | 0.559 | 0.039 | 0.142 | 87.983 | 0.135 | 0.513 | 3.596 |
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 | 65 | 65 | 65 | 54 | 53 | 53 | 60 | 57 | 59 | 57 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.82 | 0.82 | 0.92 | 0.88 | 0.91 | 0.88 |
time (sec) |
N/A | 0.275 | 0.018 | 0.122 | 0.027 | 0.066 | 0.030 | 0.124 | 0.152 | 2.382 |
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 | 65 | 65 | 65 | 54 | 53 | 53 | 60 | 57 | 59 | 57 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.82 | 0.82 | 0.92 | 0.88 | 0.91 | 0.88 |
time (sec) |
N/A | 0.270 | 0.018 | 0.112 | 0.031 | 0.062 | 0.025 | 0.121 | 0.153 | 2.361 |
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 | 65 | 65 | 65 | 54 | 53 | 53 | 60 | 57 | 59 | 57 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.82 | 0.82 | 0.92 | 0.88 | 0.91 | 0.88 |
time (sec) |
N/A | 0.253 | 0.010 | 0.110 | 0.028 | 0.064 | 0.028 | 0.118 | 0.153 | 2.291 |
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 | 60 | 60 | 60 | 51 | 50 | 50 | 56 | 54 | 57 | 54 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.83 | 0.83 | 0.93 | 0.90 | 0.95 | 0.90 |
time (sec) |
N/A | 0.249 | 0.011 | 0.096 | 0.031 | 0.065 | 0.024 | 0.122 | 0.152 | 2.345 |
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 | 56 | 56 | 56 | 51 | 48 | 48 | 54 | 53 | 54 | 52 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.86 | 0.86 | 0.96 | 0.95 | 0.96 | 0.93 |
time (sec) |
N/A | 0.242 | 0.015 | 0.056 | 0.025 | 0.064 | 0.098 | 0.120 | 0.151 | 2.299 |
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 | 54 | 54 | 54 | 50 | 48 | 55 | 49 | 50 | 61 | 49 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.89 | 1.02 | 0.91 | 0.93 | 1.13 | 0.91 |
time (sec) |
N/A | 0.250 | 0.036 | 0.045 | 0.025 | 0.069 | 0.104 | 0.121 | 0.155 | 2.397 |
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 | 54 | 54 | 51 | 48 | 48 | 55 | 51 | 48 | 63 | 47 |
N.S. |
1 | 1.00 | 0.94 | 0.89 | 0.89 | 1.02 | 0.94 | 0.89 | 1.17 | 0.87 |
time (sec) |
N/A | 0.248 | 0.027 | 0.046 | 0.029 | 0.064 | 0.183 | 0.118 | 0.157 | 2.252 |
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 | 54 | 54 | 55 | 49 | 49 | 55 | 54 | 50 | 63 | 50 |
N.S. |
1 | 1.00 | 1.02 | 0.91 | 0.91 | 1.02 | 1.00 | 0.93 | 1.17 | 0.93 |
time (sec) |
N/A | 0.252 | 0.020 | 0.043 | 0.027 | 0.062 | 0.463 | 0.109 | 0.156 | 2.304 |
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 | 109 | 109 | 98 | 102 | 101 | 101 | 110 | 105 | 105 | 108 |
N.S. |
1 | 1.00 | 0.90 | 0.94 | 0.93 | 0.93 | 1.01 | 0.96 | 0.96 | 0.99 |
time (sec) |
N/A | 0.347 | 0.047 | 0.383 | 0.028 | 0.061 | 0.034 | 0.121 | 0.155 | 2.308 |
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 | 109 | 109 | 92 | 102 | 101 | 101 | 110 | 105 | 105 | 108 |
N.S. |
1 | 1.00 | 0.84 | 0.94 | 0.93 | 0.93 | 1.01 | 0.96 | 0.96 | 0.99 |
time (sec) |
N/A | 0.331 | 0.052 | 0.393 | 0.033 | 0.064 | 0.028 | 0.115 | 0.153 | 2.213 |
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 | 104 | 104 | 92 | 102 | 101 | 101 | 110 | 105 | 105 | 107 |
N.S. |
1 | 1.00 | 0.88 | 0.98 | 0.97 | 0.97 | 1.06 | 1.01 | 1.01 | 1.03 |
time (sec) |
N/A | 0.316 | 0.041 | 0.380 | 0.037 | 0.066 | 0.037 | 0.123 | 0.155 | 2.295 |
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 | 99 | 99 | 88 | 99 | 98 | 98 | 107 | 102 | 103 | 105 |
N.S. |
1 | 1.00 | 0.89 | 1.00 | 0.99 | 0.99 | 1.08 | 1.03 | 1.04 | 1.06 |
time (sec) |
N/A | 0.324 | 0.034 | 0.378 | 0.033 | 0.064 | 0.038 | 0.124 | 0.153 | 2.262 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 88 | 96 | 96 | 96 | 104 | 100 | 99 | 103 |
N.S. |
1 | 1.00 | 0.96 | 1.04 | 1.04 | 1.04 | 1.13 | 1.09 | 1.08 | 1.12 |
time (sec) |
N/A | 0.309 | 0.043 | 0.378 | 0.029 | 0.071 | 0.110 | 0.122 | 0.153 | 2.250 |
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 | 90 | 90 | 88 | 98 | 96 | 103 | 99 | 98 | 107 | 92 |
N.S. |
1 | 1.00 | 0.98 | 1.09 | 1.07 | 1.14 | 1.10 | 1.09 | 1.19 | 1.02 |
time (sec) |
N/A | 0.337 | 0.063 | 0.374 | 0.032 | 0.066 | 0.140 | 0.125 | 0.152 | 2.286 |
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 | 98 | 98 | 87 | 95 | 96 | 103 | 100 | 97 | 109 | 103 |
N.S. |
1 | 1.00 | 0.89 | 0.97 | 0.98 | 1.05 | 1.02 | 0.99 | 1.11 | 1.05 |
time (sec) |
N/A | 0.301 | 0.039 | 0.471 | 0.038 | 0.065 | 0.231 | 0.127 | 0.152 | 2.274 |
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 | 98 | 98 | 83 | 92 | 97 | 103 | 100 | 97 | 109 | 106 |
N.S. |
1 | 1.00 | 0.85 | 0.94 | 0.99 | 1.05 | 1.02 | 0.99 | 1.11 | 1.08 |
time (sec) |
N/A | 0.320 | 0.054 | 0.379 | 0.030 | 0.068 | 0.574 | 0.116 | 0.150 | 2.425 |
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 | 149 | 149 | 149 | 148 | 145 | 145 | 163 | 153 | 151 | 153 |
N.S. |
1 | 1.00 | 1.00 | 0.99 | 0.97 | 0.97 | 1.09 | 1.03 | 1.01 | 1.03 |
time (sec) |
N/A | 0.435 | 0.032 | 0.525 | 0.033 | 0.062 | 0.041 | 0.127 | 0.151 | 2.524 |
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 | 149 | 149 | 125 | 148 | 145 | 145 | 165 | 153 | 151 | 153 |
N.S. |
1 | 1.00 | 0.84 | 0.99 | 0.97 | 0.97 | 1.11 | 1.03 | 1.01 | 1.03 |
time (sec) |
N/A | 0.387 | 0.068 | 0.377 | 0.030 | 0.065 | 0.037 | 0.121 | 0.151 | 2.542 |
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 | 138 | 138 | 124 | 148 | 145 | 145 | 163 | 153 | 151 | 153 |
N.S. |
1 | 1.00 | 0.90 | 1.07 | 1.05 | 1.05 | 1.18 | 1.11 | 1.09 | 1.11 |
time (sec) |
N/A | 0.365 | 0.062 | 0.472 | 0.029 | 0.070 | 0.041 | 0.120 | 0.154 | 2.561 |
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 | 133 | 133 | 121 | 144 | 142 | 142 | 158 | 149 | 149 | 149 |
N.S. |
1 | 1.00 | 0.91 | 1.08 | 1.07 | 1.07 | 1.19 | 1.12 | 1.12 | 1.12 |
time (sec) |
N/A | 0.354 | 0.051 | 0.378 | 0.026 | 0.067 | 0.040 | 0.123 | 0.152 | 2.494 |
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 | 121 | 142 | 140 | 140 | 158 | 148 | 145 | 147 |
N.S. |
1 | 1.00 | 0.94 | 1.10 | 1.09 | 1.09 | 1.22 | 1.15 | 1.12 | 1.14 |
time (sec) |
N/A | 0.340 | 0.062 | 0.372 | 0.029 | 0.071 | 0.160 | 0.119 | 0.155 | 2.438 |
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 | 124 | 123 | 145 | 139 | 147 | 150 | 145 | 153 | 121 |
N.S. |
1 | 1.00 | 0.99 | 1.17 | 1.12 | 1.19 | 1.21 | 1.17 | 1.23 | 0.98 |
time (sec) |
N/A | 0.366 | 0.091 | 0.377 | 0.032 | 0.069 | 0.180 | 0.118 | 0.156 | 2.297 |
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 | 135 | 135 | 124 | 142 | 139 | 147 | 151 | 144 | 155 | 143 |
N.S. |
1 | 1.00 | 0.92 | 1.05 | 1.03 | 1.09 | 1.12 | 1.07 | 1.15 | 1.06 |
time (sec) |
N/A | 0.358 | 0.068 | 0.381 | 0.037 | 0.070 | 0.283 | 0.120 | 0.151 | 2.387 |
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 | 139 | 139 | 124 | 141 | 142 | 147 | 155 | 146 | 155 | 148 |
N.S. |
1 | 1.00 | 0.89 | 1.01 | 1.02 | 1.06 | 1.12 | 1.05 | 1.12 | 1.06 |
time (sec) |
N/A | 0.360 | 0.050 | 0.380 | 0.028 | 0.069 | 0.589 | 0.117 | 0.154 | 2.529 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 130 | 114 | 128 | 127 | 270 | 274 | 137 | 151 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.98 | 0.98 | 2.08 | 2.11 | 1.05 | 1.16 | 0.00 |
time (sec) |
N/A | 0.359 | 0.096 | 0.454 | 0.109 | 0.095 | 0.691 | 0.120 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 95 | 95 | 98 | 238 | 245 | 112 | 121 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.86 | 0.88 | 2.14 | 2.21 | 1.01 | 1.09 | 0.00 |
time (sec) |
N/A | 0.322 | 0.054 | 0.452 | 0.120 | 0.084 | 0.647 | 0.120 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 81 | 85 | 82 | 180 | 211 | 88 | 104 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.92 | 0.89 | 1.96 | 2.29 | 0.96 | 1.13 | 0.00 |
time (sec) |
N/A | 0.293 | 0.062 | 0.486 | 0.111 | 0.080 | 0.564 | 0.122 | 0.149 | 0.000 |
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 | 73 | 73 | 68 | 65 | 64 | 157 | 219 | 66 | 79 | 79 |
N.S. |
1 | 1.00 | 0.93 | 0.89 | 0.88 | 2.15 | 3.00 | 0.90 | 1.08 | 1.08 |
time (sec) |
N/A | 0.255 | 0.043 | 0.450 | 0.108 | 0.083 | 0.523 | 0.122 | 0.152 | 2.297 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 73 | 73 | 65 | 157 | 0 | 66 | 90 | 0 |
N.S. |
1 | 1.00 | 1.01 | 1.01 | 0.90 | 2.18 | 0.00 | 0.92 | 1.25 | 0.00 |
time (sec) |
N/A | 0.291 | 0.056 | 0.441 | 0.115 | 0.107 | 0.000 | 0.123 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 75 | 67 | 67 | 165 | 0 | 68 | 90 | 78 |
N.S. |
1 | 1.00 | 0.99 | 0.88 | 0.88 | 2.17 | 0.00 | 0.89 | 1.18 | 1.03 |
time (sec) |
N/A | 0.306 | 0.052 | 0.492 | 0.108 | 0.098 | 0.000 | 0.120 | 0.150 | 2.337 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 84 | 89 | 76 | 207 | 0 | 80 | 125 | 97 |
N.S. |
1 | 1.00 | 0.91 | 0.97 | 0.83 | 2.25 | 0.00 | 0.87 | 1.36 | 1.05 |
time (sec) |
N/A | 0.321 | 0.079 | 0.459 | 0.120 | 0.112 | 0.000 | 0.122 | 0.151 | 2.434 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 108 | 103 | 100 | 97 | 218 | 0 | 98 | 127 | 118 |
N.S. |
1 | 1.00 | 0.95 | 0.93 | 0.90 | 2.02 | 0.00 | 0.91 | 1.18 | 1.09 |
time (sec) |
N/A | 0.333 | 0.090 | 0.455 | 0.115 | 0.111 | 0.000 | 0.127 | 0.153 | 2.298 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 127 | 113 | 124 | 117 | 282 | 0 | 128 | 158 | 145 |
N.S. |
1 | 1.00 | 0.89 | 0.98 | 0.92 | 2.22 | 0.00 | 1.01 | 1.24 | 1.14 |
time (sec) |
N/A | 0.361 | 0.140 | 0.458 | 0.113 | 0.113 | 0.000 | 0.122 | 0.155 | 2.393 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 179 | 139 | 134 | 150 | 468 | 335 | 159 | 264 | 0 |
N.S. |
1 | 1.15 | 0.90 | 0.86 | 0.97 | 3.02 | 2.16 | 1.03 | 1.70 | 0.00 |
time (sec) |
N/A | 0.568 | 0.137 | 0.543 | 0.118 | 0.082 | 2.424 | 0.127 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 155 | 128 | 124 | 127 | 372 | 289 | 131 | 243 | 0 |
N.S. |
1 | 1.19 | 0.98 | 0.95 | 0.98 | 2.86 | 2.22 | 1.01 | 1.87 | 0.00 |
time (sec) |
N/A | 0.526 | 0.080 | 0.471 | 0.127 | 0.080 | 2.216 | 0.121 | 0.157 | 0.000 |
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 | 115 | 131 | 100 | 103 | 108 | 357 | 284 | 111 | 204 | 152 |
N.S. |
1 | 1.14 | 0.87 | 0.90 | 0.94 | 3.10 | 2.47 | 0.97 | 1.77 | 1.32 |
time (sec) |
N/A | 0.505 | 0.078 | 0.461 | 0.111 | 0.084 | 2.178 | 0.125 | 0.153 | 2.352 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 109 | 92 | 78 | 84 | 286 | 212 | 81 | 182 | 0 |
N.S. |
1 | 1.18 | 1.00 | 0.85 | 0.91 | 3.11 | 2.30 | 0.88 | 1.98 | 0.00 |
time (sec) |
N/A | 0.373 | 0.052 | 0.450 | 0.110 | 0.076 | 1.658 | 0.122 | 0.153 | 0.000 |
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 | 93 | 99 | 83 | 88 | 89 | 257 | 233 | 88 | 156 | 110 |
N.S. |
1 | 1.06 | 0.89 | 0.95 | 0.96 | 2.76 | 2.51 | 0.95 | 1.68 | 1.18 |
time (sec) |
N/A | 0.271 | 0.083 | 0.467 | 0.105 | 0.080 | 1.800 | 0.118 | 0.153 | 2.262 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 104 | 85 | 99 | 87 | 296 | 0 | 93 | 192 | 0 |
N.S. |
1 | 1.09 | 0.89 | 1.04 | 0.92 | 3.12 | 0.00 | 0.98 | 2.02 | 0.00 |
time (sec) |
N/A | 0.359 | 0.081 | 0.470 | 0.110 | 0.097 | 0.000 | 0.120 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 115 | 110 | 96 | 105 | 336 | 0 | 103 | 195 | 133 |
N.S. |
1 | 1.04 | 0.99 | 0.86 | 0.95 | 3.03 | 0.00 | 0.93 | 1.76 | 1.20 |
time (sec) |
N/A | 0.417 | 0.071 | 0.558 | 0.112 | 0.094 | 0.000 | 0.120 | 0.151 | 2.431 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 136 | 112 | 127 | 117 | 442 | 0 | 126 | 289 | 158 |
N.S. |
1 | 1.04 | 0.85 | 0.97 | 0.89 | 3.37 | 0.00 | 0.96 | 2.21 | 1.21 |
time (sec) |
N/A | 0.489 | 0.101 | 0.468 | 0.113 | 0.115 | 0.000 | 0.124 | 0.153 | 2.405 |
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 | 158 | 186 | 139 | 140 | 165 | 574 | 357 | 157 | 353 | 232 |
N.S. |
1 | 1.18 | 0.88 | 0.89 | 1.04 | 3.63 | 2.26 | 0.99 | 2.23 | 1.47 |
time (sec) |
N/A | 0.608 | 0.112 | 0.464 | 0.109 | 0.084 | 12.231 | 0.126 | 0.152 | 2.522 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 161 | 126 | 115 | 136 | 480 | 282 | 122 | 303 | 0 |
N.S. |
1 | 1.23 | 0.96 | 0.88 | 1.04 | 3.66 | 2.15 | 0.93 | 2.31 | 0.00 |
time (sec) |
N/A | 0.550 | 0.079 | 0.457 | 0.108 | 0.083 | 11.331 | 0.122 | 0.157 | 0.000 |
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 | 134 | 148 | 122 | 123 | 146 | 447 | 304 | 128 | 278 | 195 |
N.S. |
1 | 1.10 | 0.91 | 0.92 | 1.09 | 3.34 | 2.27 | 0.96 | 2.07 | 1.46 |
time (sec) |
N/A | 0.510 | 0.096 | 0.463 | 0.106 | 0.084 | 10.080 | 0.123 | 0.148 | 2.438 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 127 | 99 | 97 | 111 | 357 | 178 | 97 | 229 | 0 |
N.S. |
1 | 1.21 | 0.94 | 0.92 | 1.06 | 3.40 | 1.70 | 0.92 | 2.18 | 0.00 |
time (sec) |
N/A | 0.388 | 0.114 | 0.600 | 0.114 | 0.080 | 6.734 | 0.121 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 127 | 104 | 98 | 122 | 346 | 184 | 106 | 222 | 163 |
N.S. |
1 | 1.09 | 0.90 | 0.84 | 1.05 | 2.98 | 1.59 | 0.91 | 1.91 | 1.41 |
time (sec) |
N/A | 0.292 | 0.112 | 0.461 | 0.110 | 0.084 | 3.771 | 0.122 | 0.156 | 2.450 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 144 | 117 | 130 | 133 | 488 | 0 | 128 | 321 | 0 |
N.S. |
1 | 1.11 | 0.90 | 1.00 | 1.02 | 3.75 | 0.00 | 0.98 | 2.47 | 0.00 |
time (sec) |
N/A | 0.402 | 0.112 | 0.460 | 0.118 | 0.102 | 0.000 | 0.127 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 157 | 141 | 125 | 152 | 524 | 0 | 141 | 328 | 202 |
N.S. |
1 | 1.09 | 0.98 | 0.87 | 1.06 | 3.64 | 0.00 | 0.98 | 2.28 | 1.40 |
time (sec) |
N/A | 0.602 | 0.097 | 0.481 | 0.117 | 0.099 | 0.000 | 0.120 | 0.153 | 2.559 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 188 | 147 | 169 | 172 | 696 | 0 | 162 | 468 | 229 |
N.S. |
1 | 1.11 | 0.86 | 0.99 | 1.01 | 4.09 | 0.00 | 0.95 | 2.75 | 1.35 |
time (sec) |
N/A | 0.704 | 0.162 | 0.476 | 0.107 | 0.126 | 0.000 | 0.124 | 0.154 | 2.587 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 244 | 160 | 286 | 255 | 387 | 264 | 207 | 305 | 0 |
N.S. |
1 | 1.07 | 0.70 | 1.26 | 1.12 | 1.70 | 1.16 | 0.91 | 1.34 | 0.00 |
time (sec) |
N/A | 0.644 | 0.793 | 0.586 | 0.033 | 0.097 | 0.797 | 0.123 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 208 | 141 | 238 | 213 | 326 | 228 | 177 | 261 | 0 |
N.S. |
1 | 1.07 | 0.73 | 1.23 | 1.10 | 1.68 | 1.18 | 0.91 | 1.35 | 0.00 |
time (sec) |
N/A | 0.557 | 0.646 | 0.599 | 0.033 | 0.094 | 0.694 | 0.126 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 173 | 128 | 194 | 173 | 288 | 196 | 149 | 227 | 0 |
N.S. |
1 | 1.04 | 0.77 | 1.16 | 1.04 | 1.72 | 1.17 | 0.89 | 1.36 | 0.00 |
time (sec) |
N/A | 0.464 | 0.638 | 0.561 | 0.035 | 0.095 | 0.663 | 0.123 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 137 | 108 | 148 | 130 | 231 | 160 | 121 | 183 | 0 |
N.S. |
1 | 1.04 | 0.82 | 1.12 | 0.98 | 1.75 | 1.21 | 0.92 | 1.39 | 0.00 |
time (sec) |
N/A | 0.344 | 0.523 | 0.511 | 0.051 | 0.089 | 0.477 | 0.120 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 143 | 127 | 153 | 125 | 533 | 265 | 0 | 209 | 0 |
N.S. |
1 | 1.04 | 0.92 | 1.11 | 0.91 | 3.86 | 1.92 | 0.00 | 1.51 | 0.00 |
time (sec) |
N/A | 0.449 | 0.671 | 0.513 | 0.030 | 0.108 | 3.420 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 141 | 131 | 155 | 103 | 477 | 235 | 133 | 204 | 166 |
N.S. |
1 | 1.04 | 0.97 | 1.15 | 0.76 | 3.53 | 1.74 | 0.99 | 1.51 | 1.23 |
time (sec) |
N/A | 0.478 | 0.767 | 0.532 | 0.028 | 0.103 | 2.656 | 0.140 | 0.163 | 3.105 |
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 | 150 | 147 | 119 | 204 | 141 | 539 | 238 | 194 | 245 | 161 |
N.S. |
1 | 0.98 | 0.79 | 1.36 | 0.94 | 3.59 | 1.59 | 1.29 | 1.63 | 1.07 |
time (sec) |
N/A | 0.490 | 0.829 | 0.527 | 0.029 | 0.121 | 3.399 | 0.147 | 0.164 | 3.185 |
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 | 143 | 145 | 120 | 185 | 130 | 494 | 216 | 247 | 400 | 143 |
N.S. |
1 | 1.01 | 0.84 | 1.29 | 0.91 | 3.45 | 1.51 | 1.73 | 2.80 | 1.00 |
time (sec) |
N/A | 0.470 | 0.796 | 0.550 | 0.034 | 0.099 | 3.606 | 0.141 | 0.187 | 3.348 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 148 | 133 | 233 | 177 | 582 | 253 | 492 | 269 | 168 |
N.S. |
1 | 1.05 | 0.94 | 1.65 | 1.26 | 4.13 | 1.79 | 3.49 | 1.91 | 1.19 |
time (sec) |
N/A | 0.487 | 1.097 | 0.566 | 0.036 | 0.109 | 4.812 | 0.137 | 0.168 | 3.524 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 140 | 125 | 210 | 185 | 257 | 265 | 494 | 287 | 149 |
N.S. |
1 | 1.00 | 0.89 | 1.50 | 1.32 | 1.84 | 1.89 | 3.53 | 2.05 | 1.06 |
time (sec) |
N/A | 0.435 | 1.086 | 0.585 | 0.038 | 0.094 | 4.463 | 0.125 | 0.174 | 3.396 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 175 | 140 | 258 | 229 | 314 | 347 | 648 | 310 | 0 |
N.S. |
1 | 1.02 | 0.81 | 1.50 | 1.33 | 1.83 | 2.02 | 3.77 | 1.80 | 0.00 |
time (sec) |
N/A | 0.501 | 1.472 | 0.602 | 0.034 | 0.103 | 9.082 | 0.129 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 210 | 160 | 302 | 269 | 353 | 670 | 676 | 369 | 248 |
N.S. |
1 | 1.05 | 0.80 | 1.51 | 1.34 | 1.76 | 3.35 | 3.38 | 1.84 | 1.24 |
time (sec) |
N/A | 0.559 | 1.475 | 0.635 | 0.036 | 0.116 | 9.740 | 0.140 | 0.202 | 3.743 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 248 | 176 | 350 | 311 | 410 | 729 | 844 | 400 | 0 |
N.S. |
1 | 1.06 | 0.75 | 1.49 | 1.32 | 1.74 | 3.10 | 3.59 | 1.70 | 0.00 |
time (sec) |
N/A | 0.614 | 1.993 | 0.783 | 0.037 | 0.134 | 30.784 | 0.128 | 0.241 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 260 | 266 | 189 | 318 | 293 | 477 | 483 | 261 | 383 | 0 |
N.S. |
1 | 1.02 | 0.73 | 1.22 | 1.13 | 1.83 | 1.86 | 1.00 | 1.47 | 0.00 |
time (sec) |
N/A | 0.663 | 0.890 | 0.843 | 0.036 | 0.102 | 0.883 | 0.143 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 230 | 174 | 270 | 251 | 428 | 422 | 238 | 339 | 0 |
N.S. |
1 | 1.01 | 0.77 | 1.19 | 1.11 | 1.89 | 1.86 | 1.05 | 1.49 | 0.00 |
time (sec) |
N/A | 0.597 | 0.770 | 0.543 | 0.046 | 0.100 | 0.827 | 0.128 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 195 | 161 | 226 | 211 | 390 | 364 | 210 | 305 | 0 |
N.S. |
1 | 0.98 | 0.80 | 1.13 | 1.06 | 1.95 | 1.82 | 1.05 | 1.52 | 0.00 |
time (sec) |
N/A | 0.487 | 0.726 | 0.635 | 0.037 | 0.103 | 0.771 | 0.130 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 159 | 141 | 180 | 165 | 327 | 303 | 180 | 261 | 0 |
N.S. |
1 | 0.98 | 0.87 | 1.10 | 1.01 | 2.01 | 1.86 | 1.10 | 1.60 | 0.00 |
time (sec) |
N/A | 0.373 | 0.714 | 0.510 | 0.039 | 0.095 | 0.612 | 0.137 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 180 | 163 | 199 | 173 | 719 | 600 | 0 | 291 | 0 |
N.S. |
1 | 1.03 | 0.93 | 1.14 | 0.99 | 4.11 | 3.43 | 0.00 | 1.66 | 0.00 |
time (sec) |
N/A | 0.529 | 0.901 | 0.517 | 0.037 | 0.120 | 6.098 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 180 | 157 | 201 | 148 | 663 | 520 | 197 | 288 | 165 |
N.S. |
1 | 1.07 | 0.93 | 1.20 | 0.88 | 3.95 | 3.10 | 1.17 | 1.71 | 0.98 |
time (sec) |
N/A | 0.528 | 0.841 | 0.524 | 0.034 | 0.113 | 3.948 | 0.143 | 0.176 | 3.037 |
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 | 195 | 204 | 150 | 264 | 199 | 683 | 500 | 254 | 327 | 173 |
N.S. |
1 | 1.05 | 0.77 | 1.35 | 1.02 | 3.50 | 2.56 | 1.30 | 1.68 | 0.89 |
time (sec) |
N/A | 0.575 | 1.024 | 0.519 | 0.045 | 0.132 | 5.497 | 0.143 | 0.181 | 3.212 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 204 | 150 | 312 | 223 | 603 | 447 | 323 | 314 | 0 |
N.S. |
1 | 1.00 | 0.73 | 1.52 | 1.09 | 2.94 | 2.18 | 1.58 | 1.53 | 0.00 |
time (sec) |
N/A | 0.587 | 1.041 | 0.630 | 0.034 | 0.126 | 6.260 | 0.141 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 208 | 150 | 360 | 275 | 682 | 462 | 515 | 325 | 0 |
N.S. |
1 | 1.02 | 0.74 | 1.76 | 1.35 | 3.34 | 2.26 | 2.52 | 1.59 | 0.00 |
time (sec) |
N/A | 0.582 | 1.167 | 0.599 | 0.034 | 0.128 | 8.356 | 0.147 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 185 | 160 | 301 | 248 | 680 | 401 | 494 | 332 | 0 |
N.S. |
1 | 1.02 | 0.88 | 1.65 | 1.36 | 3.74 | 2.20 | 2.71 | 1.82 | 0.00 |
time (sec) |
N/A | 0.523 | 1.237 | 0.577 | 0.037 | 0.108 | 8.433 | 0.153 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 185 | 168 | 349 | 297 | 772 | 439 | 726 | 349 | 0 |
N.S. |
1 | 1.04 | 0.94 | 1.96 | 1.67 | 4.34 | 2.47 | 4.08 | 1.96 | 0.00 |
time (sec) |
N/A | 0.525 | 1.608 | 0.691 | 0.040 | 0.126 | 14.386 | 0.164 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 164 | 174 | 286 | 265 | 353 | 774 | 728 | 369 | 0 |
N.S. |
1 | 0.97 | 1.03 | 1.69 | 1.57 | 2.09 | 4.58 | 4.31 | 2.18 | 0.00 |
time (sec) |
N/A | 0.469 | 0.839 | 0.625 | 0.036 | 0.116 | 14.976 | 0.146 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 201 | 177 | 334 | 307 | 412 | 808 | 872 | 400 | 0 |
N.S. |
1 | 0.98 | 0.86 | 1.63 | 1.50 | 2.01 | 3.94 | 4.25 | 1.95 | 0.00 |
time (sec) |
N/A | 0.503 | 2.103 | 0.678 | 0.039 | 0.142 | 39.960 | 0.144 | 0.253 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 236 | 192 | 378 | 347 | 451 | 1697 | 900 | 447 | 0 |
N.S. |
1 | 1.01 | 0.82 | 1.62 | 1.49 | 1.94 | 7.28 | 3.86 | 1.92 | 0.00 |
time (sec) |
N/A | 0.568 | 2.005 | 0.723 | 0.037 | 0.154 | 39.191 | 0.145 | 0.252 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 262 | 269 | 206 | 426 | 389 | 506 | 0 | 1068 | 478 | 0 |
N.S. |
1 | 1.03 | 0.79 | 1.63 | 1.48 | 1.93 | 0.00 | 4.08 | 1.82 | 0.00 |
time (sec) |
N/A | 0.643 | 2.722 | 0.760 | 0.041 | 0.204 | 0.000 | 0.142 | 0.422 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 255 | 141 | 296 | 259 | 333 | 218 | 187 | 261 | 0 |
N.S. |
1 | 1.15 | 0.64 | 1.34 | 1.17 | 1.51 | 0.99 | 0.85 | 1.18 | 0.00 |
time (sec) |
N/A | 0.674 | 0.737 | 0.606 | 0.035 | 0.095 | 0.709 | 0.132 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 220 | 128 | 248 | 217 | 295 | 194 | 159 | 227 | 0 |
N.S. |
1 | 1.15 | 0.67 | 1.29 | 1.13 | 1.54 | 1.01 | 0.83 | 1.18 | 0.00 |
time (sec) |
N/A | 0.611 | 0.632 | 0.680 | 0.034 | 0.092 | 0.629 | 0.136 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 184 | 118 | 200 | 175 | 238 | 167 | 132 | 183 | 0 |
N.S. |
1 | 1.16 | 0.74 | 1.26 | 1.10 | 1.50 | 1.05 | 0.83 | 1.15 | 0.00 |
time (sec) |
N/A | 0.559 | 0.928 | 0.556 | 0.029 | 0.093 | 0.608 | 0.134 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 149 | 92 | 155 | 134 | 204 | 143 | 106 | 149 | 0 |
N.S. |
1 | 1.14 | 0.70 | 1.18 | 1.02 | 1.56 | 1.09 | 0.81 | 1.14 | 0.00 |
time (sec) |
N/A | 0.455 | 0.487 | 0.540 | 0.036 | 0.086 | 0.635 | 0.126 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 113 | 78 | 112 | 95 | 147 | 116 | 77 | 109 | 149 |
N.S. |
1 | 1.13 | 0.78 | 1.12 | 0.95 | 1.47 | 1.16 | 0.77 | 1.09 | 1.49 |
time (sec) |
N/A | 0.324 | 0.430 | 0.621 | 0.033 | 0.086 | 0.455 | 0.124 | 0.155 | 3.125 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 104 | 107 | 106 | 79 | 410 | 168 | 0 | 139 | 137 |
N.S. |
1 | 1.04 | 1.07 | 1.06 | 0.79 | 4.10 | 1.68 | 0.00 | 1.39 | 1.37 |
time (sec) |
N/A | 0.426 | 0.616 | 0.522 | 0.029 | 0.104 | 1.966 | 0.000 | 0.153 | 3.147 |
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 | 98 | 96 | 84 | 65 | 379 | 114 | 103 | 203 | 103 |
N.S. |
1 | 1.10 | 1.08 | 0.94 | 0.73 | 4.26 | 1.28 | 1.16 | 2.28 | 1.16 |
time (sec) |
N/A | 0.400 | 0.509 | 0.523 | 0.029 | 0.096 | 1.399 | 0.138 | 0.154 | 2.561 |
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 | 104 | 108 | 102 | 119 | 88 | 451 | 138 | 176 | 191 | 99 |
N.S. |
1 | 1.04 | 0.98 | 1.14 | 0.85 | 4.34 | 1.33 | 1.69 | 1.84 | 0.95 |
time (sec) |
N/A | 0.438 | 0.653 | 0.519 | 0.029 | 0.099 | 2.492 | 0.137 | 0.160 | 2.715 |
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 | 110 | 116 | 89 | 136 | 111 | 173 | 138 | 220 | 209 | 107 |
N.S. |
1 | 1.05 | 0.81 | 1.24 | 1.01 | 1.57 | 1.25 | 2.00 | 1.90 | 0.97 |
time (sec) |
N/A | 0.433 | 0.608 | 0.537 | 0.043 | 0.086 | 2.755 | 0.136 | 0.159 | 3.059 |
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 | 142 | 153 | 104 | 180 | 151 | 226 | 221 | 442 | 241 | 143 |
N.S. |
1 | 1.08 | 0.73 | 1.27 | 1.06 | 1.59 | 1.56 | 3.11 | 1.70 | 1.01 |
time (sec) |
N/A | 0.498 | 0.831 | 0.555 | 0.028 | 0.095 | 5.089 | 0.132 | 0.166 | 2.960 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 188 | 125 | 224 | 191 | 261 | 507 | 442 | 287 | 164 |
N.S. |
1 | 1.09 | 0.72 | 1.29 | 1.10 | 1.51 | 2.93 | 2.55 | 1.66 | 0.95 |
time (sec) |
N/A | 0.541 | 0.928 | 0.573 | 0.029 | 0.096 | 5.148 | 0.135 | 0.168 | 3.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 212 | 124 | 242 | 214 | 358 | 292 | 156 | 338 | 0 |
N.S. |
1 | 1.28 | 0.75 | 1.47 | 1.30 | 2.17 | 1.77 | 0.95 | 2.05 | 0.00 |
time (sec) |
N/A | 0.623 | 0.711 | 0.683 | 0.035 | 0.092 | 11.456 | 0.128 | 0.165 | 0.000 |