Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 26 | 23 | 30 | 22 | 486 | 29 | 29 |
N.S. |
1 | 1.00 | 0.68 | 0.61 | 0.79 | 0.58 | 12.79 | 0.76 | 0.76 |
time (sec) |
N/A | 0.160 | 0.014 | 0.067 | 0.201 | 0.219 | 0.791 | 0.306 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 15 | 14 | 14 | 12 | 14 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.78 | 0.78 | 0.67 | 0.78 | 0.78 |
time (sec) |
N/A | 0.128 | 0.001 | 0.064 | 0.214 | 0.218 | 0.050 | 0.312 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 78 | 100 | 79 | 86 | 285 | 160 | 112 | 117 |
N.S. |
1 | 0.95 | 1.22 | 0.96 | 1.05 | 3.48 | 1.95 | 1.37 | 1.43 |
time (sec) |
N/A | 0.178 | 0.062 | 0.436 | 0.296 | 0.235 | 1.626 | 0.583 | 0.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 103 | 105 | 128 | 103 | 116 | 328 | 838 | 144 | 133 |
N.S. |
1 | 1.02 | 1.24 | 1.00 | 1.13 | 3.18 | 8.14 | 1.40 | 1.29 |
time (sec) |
N/A | 0.198 | 0.113 | 0.167 | 0.297 | 0.239 | 1.884 | 0.533 | 0.195 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 136 | 135 | 160 | 124 | 159 | 374 | 2744 | 167 | 216 |
N.S. |
1 | 0.99 | 1.18 | 0.91 | 1.17 | 2.75 | 20.18 | 1.23 | 1.59 |
time (sec) |
N/A | 0.220 | 0.117 | 0.278 | 0.290 | 0.235 | 3.858 | 0.537 | 0.248 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 46 | 43 | 56 | 42 | 1640 | 49 | 56 |
N.S. |
1 | 1.00 | 0.66 | 0.61 | 0.80 | 0.60 | 23.43 | 0.70 | 0.80 |
time (sec) |
N/A | 0.187 | 0.023 | 0.076 | 0.223 | 0.225 | 1.619 | 0.300 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 35 | 32 | 41 | 31 | 600 | 37 | 37 |
N.S. |
1 | 1.00 | 0.69 | 0.63 | 0.80 | 0.61 | 11.76 | 0.73 | 0.73 |
time (sec) |
N/A | 0.167 | 0.021 | 0.070 | 0.219 | 0.228 | 1.062 | 0.313 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 23 | 21 | 26 | 19 | 162 | 23 | 25 |
N.S. |
1 | 1.00 | 0.72 | 0.66 | 0.81 | 0.59 | 5.06 | 0.72 | 0.78 |
time (sec) |
N/A | 0.156 | 0.012 | 0.069 | 0.194 | 0.229 | 1.097 | 0.288 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 12 | 12 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.86 | 0.86 | 0.71 | 0.86 | 0.86 |
time (sec) |
N/A | 0.131 | 0.001 | 0.064 | 0.212 | 0.216 | 0.036 | 0.287 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 76 | 93 | 75 | 77 | 115 | 150 | 78 | 95 |
N.S. |
1 | 0.95 | 1.16 | 0.94 | 0.96 | 1.44 | 1.88 | 0.98 | 1.19 |
time (sec) |
N/A | 0.180 | 0.056 | 0.081 | 0.279 | 0.225 | 1.686 | 0.543 | 0.201 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 102 | 119 | 95 | 106 | 166 | 830 | 108 | 122 |
N.S. |
1 | 1.04 | 1.21 | 0.97 | 1.08 | 1.69 | 8.47 | 1.10 | 1.24 |
time (sec) |
N/A | 0.196 | 0.123 | 0.119 | 0.286 | 0.224 | 2.637 | 0.531 | 0.145 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 130 | 130 | 149 | 122 | 142 | 162 | 2728 | 130 | 175 |
N.S. |
1 | 1.00 | 1.15 | 0.94 | 1.09 | 1.25 | 20.98 | 1.00 | 1.35 |
time (sec) |
N/A | 0.211 | 0.127 | 0.131 | 0.290 | 0.234 | 3.099 | 0.496 | 0.181 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 46 | 43 | 56 | 52 | 1538 | 62 | 56 |
N.S. |
1 | 1.00 | 0.66 | 0.61 | 0.80 | 0.74 | 21.97 | 0.89 | 0.80 |
time (sec) |
N/A | 0.179 | 0.024 | 0.088 | 0.201 | 0.220 | 2.224 | 0.311 | 0.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 34 | 31 | 41 | 40 | 534 | 46 | 35 |
N.S. |
1 | 1.00 | 0.69 | 0.63 | 0.84 | 0.82 | 10.90 | 0.94 | 0.71 |
time (sec) |
N/A | 0.170 | 0.023 | 0.078 | 0.200 | 0.218 | 1.513 | 0.322 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 23 | 20 | 26 | 29 | 41 | 30 | 20 |
N.S. |
1 | 1.00 | 0.72 | 0.62 | 0.81 | 0.91 | 1.28 | 0.94 | 0.62 |
time (sec) |
N/A | 0.155 | 0.015 | 0.075 | 0.203 | 0.218 | 0.350 | 0.451 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 12 | 20 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.86 | 1.43 | 0.86 | 0.86 | 0.86 |
time (sec) |
N/A | 0.128 | 0.002 | 0.067 | 0.211 | 0.226 | 0.045 | 0.367 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 93 | 94 | 111 | 92 | 88 | 285 | 184 | 89 | 114 |
N.S. |
1 | 1.01 | 1.19 | 0.99 | 0.95 | 3.06 | 1.98 | 0.96 | 1.23 |
time (sec) |
N/A | 0.197 | 0.089 | 0.100 | 0.291 | 0.234 | 2.041 | 0.731 | 0.163 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 120 | 123 | 108 | 122 | 407 | 857 | 120 | 173 |
N.S. |
1 | 1.06 | 1.09 | 0.96 | 1.08 | 3.60 | 7.58 | 1.06 | 1.53 |
time (sec) |
N/A | 0.208 | 0.202 | 0.113 | 0.290 | 0.236 | 3.686 | 0.518 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 149 | 148 | 142 | 118 | 158 | 407 | 2793 | 140 | 221 |
N.S. |
1 | 0.99 | 0.95 | 0.79 | 1.06 | 2.73 | 18.74 | 0.94 | 1.48 |
time (sec) |
N/A | 0.234 | 0.266 | 0.130 | 0.288 | 0.235 | 4.534 | 0.522 | 0.148 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 97 | 85 | 86 | 88 | 138 | 87 | 105 |
N.S. |
1 | 1.00 | 1.37 | 1.20 | 1.21 | 1.24 | 1.94 | 1.23 | 1.48 |
time (sec) |
N/A | 0.192 | 0.051 | 0.395 | 0.301 | 0.223 | 1.338 | 0.292 | 0.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 101 | 89 | 90 | 92 | 136 | 91 | 108 |
N.S. |
1 | 1.00 | 1.38 | 1.22 | 1.23 | 1.26 | 1.86 | 1.25 | 1.48 |
time (sec) |
N/A | 0.198 | 0.052 | 0.381 | 0.333 | 0.229 | 1.469 | 0.294 | 0.136 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 102 | 90 | 94 | 93 | 134 | 95 | 112 |
N.S. |
1 | 1.00 | 1.38 | 1.22 | 1.27 | 1.26 | 1.81 | 1.28 | 1.51 |
time (sec) |
N/A | 0.190 | 0.055 | 0.400 | 0.315 | 0.230 | 1.303 | 0.326 | 0.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 106 | 94 | 98 | 97 | 139 | 99 | 115 |
N.S. |
1 | 1.00 | 1.39 | 1.24 | 1.29 | 1.28 | 1.83 | 1.30 | 1.51 |
time (sec) |
N/A | 0.189 | 0.065 | 0.393 | 0.317 | 0.227 | 2.558 | 0.314 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 95 | 85 | 87 | 86 | 134 | 88 | 101 |
N.S. |
1 | 1.00 | 1.32 | 1.18 | 1.21 | 1.19 | 1.86 | 1.22 | 1.40 |
time (sec) |
N/A | 0.187 | 0.043 | 0.096 | 0.319 | 0.231 | 1.295 | 0.302 | 0.153 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 99 | 89 | 91 | 90 | 136 | 92 | 104 |
N.S. |
1 | 1.00 | 1.34 | 1.20 | 1.23 | 1.22 | 1.84 | 1.24 | 1.41 |
time (sec) |
N/A | 0.190 | 0.043 | 0.093 | 0.301 | 0.232 | 1.306 | 0.307 | 0.129 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 102 | 92 | 93 | 95 | 134 | 94 | 107 |
N.S. |
1 | 1.00 | 1.38 | 1.24 | 1.26 | 1.28 | 1.81 | 1.27 | 1.45 |
time (sec) |
N/A | 0.185 | 0.042 | 0.091 | 0.312 | 0.228 | 2.282 | 0.326 | 0.174 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 106 | 96 | 97 | 99 | 133 | 98 | 110 |
N.S. |
1 | 1.00 | 1.39 | 1.26 | 1.28 | 1.30 | 1.75 | 1.29 | 1.45 |
time (sec) |
N/A | 0.184 | 0.044 | 0.089 | 0.289 | 0.231 | 2.027 | 0.289 | 0.179 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 22 | 30 | 25 | 33 | 87 | 43 | 30 |
N.S. |
1 | 1.00 | 0.88 | 1.20 | 1.00 | 1.32 | 3.48 | 1.72 | 1.20 |
time (sec) |
N/A | 0.159 | 0.022 | 0.021 | 0.209 | 0.224 | 0.357 | 0.292 | 0.362 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 17 | 14 | 13 | 18 | 19 | 13 | 13 |
N.S. |
1 | 1.00 | 0.81 | 0.67 | 0.62 | 0.86 | 0.90 | 0.62 | 0.62 |
time (sec) |
N/A | 0.142 | 0.011 | 0.065 | 0.203 | 0.224 | 0.212 | 0.302 | 0.148 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 17 | 14 | 13 | 18 | 19 | 13 | 13 |
N.S. |
1 | 1.00 | 0.81 | 0.67 | 0.62 | 0.86 | 0.90 | 0.62 | 0.62 |
time (sec) |
N/A | 0.145 | 0.010 | 0.063 | 0.203 | 0.218 | 0.183 | 0.314 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 17 | 14 | 13 | 16 | 19 | 13 | 13 |
N.S. |
1 | 1.00 | 0.81 | 0.67 | 0.62 | 0.76 | 0.90 | 0.62 | 0.62 |
time (sec) |
N/A | 0.143 | 0.009 | 0.060 | 0.201 | 0.220 | 0.869 | 0.276 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 16 | 13 | 13 | 12 | 17 | 13 | 12 |
N.S. |
1 | 1.00 | 0.84 | 0.68 | 0.68 | 0.63 | 0.89 | 0.68 | 0.63 |
time (sec) |
N/A | 0.142 | 0.010 | 0.023 | 0.206 | 0.221 | 0.070 | 0.294 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 13 | 12 | 13 | 12 | 15 | 13 | 11 |
N.S. |
1 | 1.00 | 0.76 | 0.71 | 0.76 | 0.71 | 0.88 | 0.76 | 0.65 |
time (sec) |
N/A | 0.143 | 0.011 | 0.029 | 0.213 | 0.225 | 0.259 | 0.304 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 15 | 12 | 11 | 11 | 19 | 11 | 13 |
N.S. |
1 | 1.00 | 0.79 | 0.63 | 0.58 | 0.58 | 1.00 | 0.58 | 0.68 |
time (sec) |
N/A | 0.145 | 0.012 | 0.032 | 0.213 | 0.228 | 0.262 | 0.289 | 0.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 38 | 51 | 43 | 85 | 299 | 117 | 93 |
N.S. |
1 | 1.00 | 0.88 | 1.19 | 1.00 | 1.98 | 6.95 | 2.72 | 2.16 |
time (sec) |
N/A | 0.176 | 0.037 | 0.059 | 0.201 | 0.223 | 0.374 | 0.286 | 0.469 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 28 | 25 | 24 | 29 | 34 | 24 | 24 |
N.S. |
1 | 1.00 | 0.78 | 0.69 | 0.67 | 0.81 | 0.94 | 0.67 | 0.67 |
time (sec) |
N/A | 0.157 | 0.014 | 0.079 | 0.208 | 0.225 | 0.317 | 0.288 | 0.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 28 | 25 | 24 | 29 | 34 | 24 | 24 |
N.S. |
1 | 1.00 | 0.78 | 0.69 | 0.67 | 0.81 | 0.94 | 0.67 | 0.67 |
time (sec) |
N/A | 0.155 | 0.013 | 0.071 | 0.201 | 0.225 | 0.263 | 0.303 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 28 | 25 | 24 | 27 | 1851 | 24 | 24 |
N.S. |
1 | 1.00 | 0.78 | 0.69 | 0.67 | 0.75 | 51.42 | 0.67 | 0.67 |
time (sec) |
N/A | 0.154 | 0.013 | 0.071 | 0.203 | 0.216 | 81.194 | 0.281 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 28 | 24 | 24 | 24 | 32 | 24 | 24 |
N.S. |
1 | 1.00 | 0.82 | 0.71 | 0.71 | 0.71 | 0.94 | 0.71 | 0.71 |
time (sec) |
N/A | 0.153 | 0.013 | 0.053 | 0.216 | 0.215 | 0.105 | 0.288 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 28 | 25 | 24 | 23 | 31 | 24 | 24 |
N.S. |
1 | 1.00 | 0.88 | 0.78 | 0.75 | 0.72 | 0.97 | 0.75 | 0.75 |
time (sec) |
N/A | 0.153 | 0.015 | 0.054 | 0.211 | 0.227 | 0.190 | 0.303 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 26 | 23 | 23 | 24 | 31 | 23 | 24 |
N.S. |
1 | 1.00 | 0.81 | 0.72 | 0.72 | 0.75 | 0.97 | 0.72 | 0.75 |
time (sec) |
N/A | 0.154 | 0.016 | 0.057 | 0.222 | 0.224 | 0.231 | 0.282 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 54 | 72 | 61 | 157 | 663 | 224 | 167 |
N.S. |
1 | 1.00 | 0.89 | 1.18 | 1.00 | 2.57 | 10.87 | 3.67 | 2.74 |
time (sec) |
N/A | 0.189 | 0.040 | 0.067 | 0.200 | 0.227 | 0.390 | 0.287 | 0.444 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 39 | 36 | 35 | 40 | 49 | 35 | 35 |
N.S. |
1 | 1.00 | 0.76 | 0.71 | 0.69 | 0.78 | 0.96 | 0.69 | 0.69 |
time (sec) |
N/A | 0.162 | 0.016 | 0.087 | 0.202 | 0.219 | 0.373 | 0.290 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 39 | 36 | 35 | 40 | 49 | 35 | 35 |
N.S. |
1 | 1.00 | 0.76 | 0.71 | 0.69 | 0.78 | 0.96 | 0.69 | 0.69 |
time (sec) |
N/A | 0.164 | 0.016 | 0.073 | 0.245 | 0.230 | 0.271 | 0.273 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 39 | 36 | 35 | 38 | 0 | 35 | 35 |
N.S. |
1 | 1.00 | 0.76 | 0.71 | 0.69 | 0.75 | 0.00 | 0.69 | 0.69 |
time (sec) |
N/A | 0.165 | 0.015 | 0.074 | 0.205 | 0.219 | 0.000 | 0.282 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 39 | 35 | 35 | 35 | 46 | 35 | 35 |
N.S. |
1 | 1.00 | 0.83 | 0.74 | 0.74 | 0.74 | 0.98 | 0.74 | 0.74 |
time (sec) |
N/A | 0.166 | 0.015 | 0.055 | 0.203 | 0.222 | 0.119 | 0.280 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 39 | 36 | 35 | 34 | 44 | 35 | 35 |
N.S. |
1 | 1.00 | 0.87 | 0.80 | 0.78 | 0.76 | 0.98 | 0.78 | 0.78 |
time (sec) |
N/A | 0.173 | 0.017 | 0.056 | 0.205 | 0.222 | 0.214 | 0.294 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 38 | 34 | 34 | 34 | 46 | 34 | 35 |
N.S. |
1 | 1.00 | 0.81 | 0.72 | 0.72 | 0.72 | 0.98 | 0.72 | 0.74 |
time (sec) |
N/A | 0.173 | 0.019 | 0.058 | 0.214 | 0.223 | 0.246 | 0.288 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 68 | 78 | 61 | 53 | 54 | 132 | 122 | 59 | 48 |
N.S. |
1 | 1.15 | 0.90 | 0.78 | 0.79 | 1.94 | 1.79 | 0.87 | 0.71 |
time (sec) |
N/A | 0.184 | 0.048 | 0.084 | 0.277 | 0.230 | 2.462 | 0.281 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 59 | 49 | 42 | 42 | 103 | 107 | 45 | 37 |
N.S. |
1 | 1.11 | 0.92 | 0.79 | 0.79 | 1.94 | 2.02 | 0.85 | 0.70 |
time (sec) |
N/A | 0.167 | 0.037 | 0.072 | 0.286 | 0.231 | 1.129 | 0.293 | 0.087 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 40 | 32 | 31 | 85 | 88 | 31 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.78 | 2.12 | 2.20 | 0.78 | 0.70 |
time (sec) |
N/A | 0.152 | 0.022 | 0.072 | 0.297 | 0.225 | 0.316 | 0.314 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 19 | 18 | 68 | 73 | 18 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.66 | 0.62 | 2.34 | 2.52 | 0.62 | 0.66 |
time (sec) |
N/A | 0.145 | 0.015 | 0.068 | 0.278 | 0.225 | 0.481 | 0.292 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 40 | 32 | 31 | 93 | 85 | 31 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.78 | 2.32 | 2.12 | 0.78 | 0.70 |
time (sec) |
N/A | 0.151 | 0.026 | 0.075 | 0.299 | 0.226 | 0.948 | 0.302 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 59 | 48 | 40 | 41 | 118 | 107 | 41 | 38 |
N.S. |
1 | 1.11 | 0.91 | 0.75 | 0.77 | 2.23 | 2.02 | 0.77 | 0.72 |
time (sec) |
N/A | 0.160 | 0.040 | 0.075 | 0.314 | 0.237 | 2.431 | 0.294 | 0.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 68 | 78 | 61 | 53 | 52 | 144 | 126 | 52 | 49 |
N.S. |
1 | 1.15 | 0.90 | 0.78 | 0.76 | 2.12 | 1.85 | 0.76 | 0.72 |
time (sec) |
N/A | 0.174 | 0.049 | 0.076 | 0.333 | 0.227 | 9.822 | 0.295 | 0.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 84 | 68 | 56 | 63 | 161 | 389 | 65 | 58 |
N.S. |
1 | 1.20 | 0.97 | 0.80 | 0.90 | 2.30 | 5.56 | 0.93 | 0.83 |
time (sec) |
N/A | 0.176 | 0.077 | 0.098 | 0.303 | 0.233 | 12.894 | 0.291 | 0.116 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 65 | 54 | 47 | 49 | 134 | 332 | 46 | 46 |
N.S. |
1 | 1.14 | 0.95 | 0.82 | 0.86 | 2.35 | 5.82 | 0.81 | 0.81 |
time (sec) |
N/A | 0.155 | 0.067 | 0.083 | 0.294 | 0.241 | 3.558 | 0.295 | 0.126 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 46 | 37 | 37 | 115 | 269 | 36 | 34 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.80 | 2.50 | 5.85 | 0.78 | 0.74 |
time (sec) |
N/A | 0.149 | 0.056 | 0.070 | 0.282 | 0.227 | 1.961 | 0.278 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 45 | 36 | 35 | 116 | 277 | 35 | 33 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.78 | 2.58 | 6.16 | 0.78 | 0.73 |
time (sec) |
N/A | 0.148 | 0.050 | 0.068 | 0.287 | 0.224 | 3.189 | 0.298 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 64 | 54 | 47 | 51 | 147 | 384 | 49 | 48 |
N.S. |
1 | 1.14 | 0.96 | 0.84 | 0.91 | 2.62 | 6.86 | 0.88 | 0.86 |
time (sec) |
N/A | 0.157 | 0.071 | 0.086 | 0.294 | 0.233 | 8.012 | 0.312 | 0.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 69 | 83 | 68 | 53 | 64 | 184 | 452 | 58 | 58 |
N.S. |
1 | 1.20 | 0.99 | 0.77 | 0.93 | 2.67 | 6.55 | 0.84 | 0.84 |
time (sec) |
N/A | 0.173 | 0.073 | 0.088 | 0.285 | 0.239 | 20.423 | 0.302 | 0.151 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 95 | 111 | 81 | 66 | 86 | 227 | 762 | 77 | 81 |
N.S. |
1 | 1.17 | 0.85 | 0.69 | 0.91 | 2.39 | 8.02 | 0.81 | 0.85 |
time (sec) |
N/A | 0.182 | 0.122 | 0.124 | 0.293 | 0.236 | 66.065 | 0.330 | 0.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 92 | 70 | 56 | 73 | 200 | 683 | 59 | 69 |
N.S. |
1 | 1.12 | 0.85 | 0.68 | 0.89 | 2.44 | 8.33 | 0.72 | 0.84 |
time (sec) |
N/A | 0.169 | 0.112 | 0.112 | 0.290 | 0.230 | 28.379 | 0.313 | 0.155 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 73 | 59 | 50 | 61 | 185 | 605 | 47 | 58 |
N.S. |
1 | 1.04 | 0.84 | 0.71 | 0.87 | 2.64 | 8.64 | 0.67 | 0.83 |
time (sec) |
N/A | 0.158 | 0.102 | 0.070 | 0.297 | 0.239 | 16.623 | 0.301 | 0.148 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 72 | 60 | 52 | 64 | 186 | 627 | 52 | 56 |
N.S. |
1 | 0.99 | 0.82 | 0.71 | 0.88 | 2.55 | 8.59 | 0.71 | 0.77 |
time (sec) |
N/A | 0.163 | 0.104 | 0.070 | 0.387 | 0.238 | 8.307 | 0.304 | 0.143 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 72 | 59 | 59 | 60 | 186 | 632 | 47 | 57 |
N.S. |
1 | 1.03 | 0.84 | 0.84 | 0.86 | 2.66 | 9.03 | 0.67 | 0.81 |
time (sec) |
N/A | 0.167 | 0.070 | 0.070 | 0.319 | 0.230 | 12.056 | 0.292 | 0.138 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 91 | 70 | 56 | 73 | 214 | 779 | 59 | 70 |
N.S. |
1 | 1.11 | 0.85 | 0.68 | 0.89 | 2.61 | 9.50 | 0.72 | 0.85 |
time (sec) |
N/A | 0.179 | 0.102 | 0.094 | 0.300 | 0.237 | 28.040 | 0.312 | 0.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 95 | 110 | 81 | 64 | 86 | 250 | 869 | 71 | 80 |
N.S. |
1 | 1.16 | 0.85 | 0.67 | 0.91 | 2.63 | 9.15 | 0.75 | 0.84 |
time (sec) |
N/A | 0.186 | 0.107 | 0.109 | 0.312 | 0.238 | 65.484 | 0.317 | 0.235 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 68 | 77 | 61 | 53 | 70 | 131 | 117 | 61 | 51 |
N.S. |
1 | 1.13 | 0.90 | 0.78 | 1.03 | 1.93 | 1.72 | 0.90 | 0.75 |
time (sec) |
N/A | 0.173 | 0.049 | 0.082 | 0.301 | 0.231 | 2.432 | 0.295 | 0.167 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 59 | 49 | 41 | 58 | 103 | 102 | 47 | 37 |
N.S. |
1 | 1.11 | 0.92 | 0.77 | 1.09 | 1.94 | 1.92 | 0.89 | 0.70 |
time (sec) |
N/A | 0.164 | 0.038 | 0.073 | 0.293 | 0.237 | 1.248 | 0.293 | 0.127 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 40 | 32 | 47 | 83 | 83 | 33 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 1.18 | 2.08 | 2.08 | 0.82 | 0.70 |
time (sec) |
N/A | 0.152 | 0.032 | 0.078 | 0.311 | 0.231 | 0.471 | 0.301 | 0.148 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 19 | 34 | 67 | 68 | 20 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.66 | 1.17 | 2.31 | 2.34 | 0.69 | 0.66 |
time (sec) |
N/A | 0.142 | 0.022 | 0.072 | 0.308 | 0.226 | 0.525 | 0.301 | 0.150 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 40 | 32 | 47 | 91 | 76 | 33 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 1.18 | 2.28 | 1.90 | 0.82 | 0.70 |
time (sec) |
N/A | 0.155 | 0.034 | 0.077 | 0.279 | 0.228 | 1.343 | 0.298 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 59 | 48 | 40 | 55 | 113 | 99 | 41 | 37 |
N.S. |
1 | 1.11 | 0.91 | 0.75 | 1.04 | 2.13 | 1.87 | 0.77 | 0.70 |
time (sec) |
N/A | 0.162 | 0.061 | 0.082 | 0.298 | 0.236 | 2.706 | 0.310 | 0.138 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 68 | 77 | 61 | 53 | 68 | 143 | 117 | 54 | 48 |
N.S. |
1 | 1.13 | 0.90 | 0.78 | 1.00 | 2.10 | 1.72 | 0.79 | 0.71 |
time (sec) |
N/A | 0.175 | 0.062 | 0.080 | 0.296 | 0.238 | 7.932 | 0.293 | 0.152 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 83 | 70 | 57 | 81 | 167 | 354 | 69 | 61 |
N.S. |
1 | 1.19 | 1.00 | 0.81 | 1.16 | 2.39 | 5.06 | 0.99 | 0.87 |
time (sec) |
N/A | 0.175 | 0.100 | 0.104 | 0.305 | 0.227 | 12.462 | 0.297 | 0.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 65 | 56 | 48 | 68 | 138 | 301 | 51 | 47 |
N.S. |
1 | 1.14 | 0.98 | 0.84 | 1.19 | 2.42 | 5.28 | 0.89 | 0.82 |
time (sec) |
N/A | 0.162 | 0.073 | 0.091 | 0.304 | 0.233 | 5.086 | 0.303 | 0.138 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 49 | 38 | 56 | 123 | 243 | 40 | 35 |
N.S. |
1 | 1.00 | 1.04 | 0.81 | 1.19 | 2.62 | 5.17 | 0.85 | 0.74 |
time (sec) |
N/A | 0.156 | 0.067 | 0.074 | 0.289 | 0.226 | 2.613 | 0.303 | 0.130 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 46 | 37 | 56 | 122 | 252 | 41 | 34 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 1.22 | 2.65 | 5.48 | 0.89 | 0.74 |
time (sec) |
N/A | 0.154 | 0.060 | 0.075 | 0.284 | 0.227 | 3.180 | 0.315 | 0.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 65 | 55 | 48 | 69 | 151 | 354 | 52 | 49 |
N.S. |
1 | 1.14 | 0.96 | 0.84 | 1.21 | 2.65 | 6.21 | 0.91 | 0.86 |
time (sec) |
N/A | 0.168 | 0.075 | 0.092 | 0.279 | 0.232 | 12.416 | 0.299 | 0.087 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 83 | 69 | 56 | 82 | 187 | 416 | 61 | 60 |
N.S. |
1 | 1.19 | 0.99 | 0.80 | 1.17 | 2.67 | 5.94 | 0.87 | 0.86 |
time (sec) |
N/A | 0.177 | 0.092 | 0.094 | 0.291 | 0.238 | 22.124 | 0.295 | 0.162 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 111 | 82 | 67 | 103 | 227 | 695 | 81 | 83 |
N.S. |
1 | 1.14 | 0.85 | 0.69 | 1.06 | 2.34 | 7.16 | 0.84 | 0.86 |
time (sec) |
N/A | 0.190 | 0.128 | 0.123 | 0.320 | 0.235 | 64.023 | 0.302 | 0.166 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 84 | 93 | 71 | 57 | 90 | 199 | 624 | 63 | 69 |
N.S. |
1 | 1.11 | 0.85 | 0.68 | 1.07 | 2.37 | 7.43 | 0.75 | 0.82 |
time (sec) |
N/A | 0.186 | 0.123 | 0.118 | 0.317 | 0.233 | 22.943 | 0.297 | 0.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 75 | 60 | 51 | 78 | 186 | 552 | 51 | 58 |
N.S. |
1 | 1.04 | 0.83 | 0.71 | 1.08 | 2.58 | 7.67 | 0.71 | 0.81 |
time (sec) |
N/A | 0.168 | 0.121 | 0.075 | 0.291 | 0.242 | 15.788 | 0.290 | 0.171 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 74 | 60 | 53 | 80 | 183 | 575 | 55 | 57 |
N.S. |
1 | 0.99 | 0.80 | 0.71 | 1.07 | 2.44 | 7.67 | 0.73 | 0.76 |
time (sec) |
N/A | 0.165 | 0.102 | 0.076 | 0.308 | 0.233 | 10.405 | 0.304 | 0.190 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 74 | 60 | 61 | 77 | 185 | 580 | 51 | 58 |
N.S. |
1 | 1.03 | 0.83 | 0.85 | 1.07 | 2.57 | 8.06 | 0.71 | 0.81 |
time (sec) |
N/A | 0.165 | 0.087 | 0.077 | 0.300 | 0.237 | 14.766 | 0.303 | 0.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 84 | 93 | 71 | 57 | 90 | 213 | 716 | 63 | 69 |
N.S. |
1 | 1.11 | 0.85 | 0.68 | 1.07 | 2.54 | 8.52 | 0.75 | 0.82 |
time (sec) |
N/A | 0.177 | 0.114 | 0.099 | 0.322 | 0.240 | 24.368 | 0.295 | 0.180 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 111 | 82 | 66 | 103 | 249 | 799 | 73 | 80 |
N.S. |
1 | 1.14 | 0.85 | 0.68 | 1.06 | 2.57 | 8.24 | 0.75 | 0.82 |
time (sec) |
N/A | 0.195 | 0.122 | 0.111 | 0.300 | 0.243 | 59.596 | 0.295 | 0.354 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 122 | 132 | 96 | 98 | 178 | 162 | 153 | 224 | 0 |
N.S. |
1 | 1.08 | 0.79 | 0.80 | 1.46 | 1.33 | 1.25 | 1.84 | 0.00 |
time (sec) |
N/A | 0.199 | 0.321 | 0.090 | 0.298 | 0.241 | 29.003 | 152.739 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 102 | 85 | 87 | 146 | 141 | 122 | 182 | 0 |
N.S. |
1 | 1.04 | 0.87 | 0.89 | 1.49 | 1.44 | 1.24 | 1.86 | 0.00 |
time (sec) |
N/A | 0.183 | 0.253 | 0.077 | 0.304 | 0.227 | 8.043 | 158.636 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 72 | 71 | 74 | 108 | 114 | 97 | 147 | 52 |
N.S. |
1 | 0.97 | 0.96 | 1.00 | 1.46 | 1.54 | 1.31 | 1.99 | 0.70 |
time (sec) |
N/A | 0.170 | 0.179 | 0.076 | 0.294 | 0.233 | 2.676 | 153.614 | 0.177 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 47 | 62 | 70 | 93 | 42 | 68 | 41 |
N.S. |
1 | 1.00 | 1.07 | 1.41 | 1.59 | 2.11 | 0.95 | 1.55 | 0.93 |
time (sec) |
N/A | 0.151 | 0.055 | 0.077 | 0.312 | 0.226 | 1.553 | 76.153 | 0.761 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 55 | 61 | 54 | 89 | 68 | 65 | 0 |
N.S. |
1 | 1.00 | 1.22 | 1.36 | 1.20 | 1.98 | 1.51 | 1.44 | 0.00 |
time (sec) |
N/A | 0.155 | 0.077 | 0.076 | 0.293 | 0.239 | 1.026 | 79.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 16 | 15 | 15 | 41 | 33 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.76 | 0.71 | 0.71 | 1.95 | 1.57 | 1.00 |
time (sec) |
N/A | 0.136 | 0.022 | 0.076 | 0.224 | 0.233 | 1.021 | 0.315 | 0.275 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 39 | 24 | 31 | 34 | 65 | 50 | 32 |
N.S. |
1 | 1.00 | 0.89 | 0.55 | 0.70 | 0.77 | 1.48 | 1.14 | 0.73 |
time (sec) |
N/A | 0.145 | 0.074 | 0.077 | 0.214 | 0.231 | 3.460 | 0.336 | 0.348 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 68 | 74 | 51 | 35 | 46 | 45 | 347 | 66 | 43 |
N.S. |
1 | 1.09 | 0.75 | 0.51 | 0.68 | 0.66 | 5.10 | 0.97 | 0.63 |
time (sec) |
N/A | 0.164 | 0.080 | 0.076 | 0.239 | 0.221 | 9.987 | 0.322 | 0.309 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 137 | 98 | 102 | 170 | 164 | 323 | 257 | 0 |
N.S. |
1 | 1.08 | 0.77 | 0.80 | 1.34 | 1.29 | 2.54 | 2.02 | 0.00 |
time (sec) |
N/A | 0.205 | 0.319 | 0.091 | 0.300 | 0.235 | 30.401 | 157.006 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 106 | 87 | 91 | 135 | 142 | 260 | 207 | 0 |
N.S. |
1 | 1.04 | 0.85 | 0.89 | 1.32 | 1.39 | 2.55 | 2.03 | 0.00 |
time (sec) |
N/A | 0.192 | 0.260 | 0.079 | 0.291 | 0.229 | 6.751 | 156.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 75 | 75 | 78 | 95 | 118 | 207 | 166 | 58 |
N.S. |
1 | 0.97 | 0.97 | 1.01 | 1.23 | 1.53 | 2.69 | 2.16 | 0.75 |
time (sec) |
N/A | 0.171 | 0.202 | 0.076 | 0.280 | 0.236 | 4.627 | 156.001 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 57 | 66 | 52 | 94 | 119 | 74 | 43 |
N.S. |
1 | 1.00 | 1.24 | 1.43 | 1.13 | 2.04 | 2.59 | 1.61 | 0.93 |
time (sec) |
N/A | 0.151 | 0.117 | 0.078 | 0.286 | 0.246 | 1.710 | 76.649 | 0.653 |