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 | C | A | F | F(-1) | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 324 | 372 | 48 | 159 | 0 | 0 | 0 | 207 | 0 |
N.S. |
1 | 1.15 | 0.15 | 0.49 | 0.00 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.690 | 10.087 | 1.812 | 0.000 | 0.000 | 0.000 | 0.362 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 412 | 478 | 48 | 192 | 0 | 0 | 0 | 258 | 0 |
N.S. |
1 | 1.16 | 0.12 | 0.47 | 0.00 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.925 | 10.096 | 1.991 | 0.000 | 0.000 | 0.000 | 0.382 | 0.000 |
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 | 17 | 14 | 13 | 13 | 12 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 0.76 | 0.71 | 0.76 | 0.76 |
time (sec) |
N/A | 0.153 | 0.003 | 0.038 | 0.198 | 0.279 | 0.017 | 0.281 | 0.023 |
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 | 17 | 14 | 13 | 13 | 12 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 0.76 | 0.71 | 0.76 | 0.76 |
time (sec) |
N/A | 0.151 | 0.001 | 0.034 | 0.192 | 0.289 | 0.016 | 0.281 | 0.021 |
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 | 17 | 14 | 13 | 13 | 12 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 0.76 | 0.71 | 0.76 | 0.76 |
time (sec) |
N/A | 0.148 | 0.000 | 0.030 | 0.186 | 0.271 | 0.016 | 0.279 | 0.021 |
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 | 17 | 14 | 13 | 13 | 12 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 0.76 | 0.71 | 0.76 | 0.76 |
time (sec) |
N/A | 0.148 | 0.001 | 0.027 | 0.202 | 0.277 | 0.018 | 0.284 | 0.021 |
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 | 12 | 14 | 12 | 11 | 10 | 10 | 8 | 10 | 10 |
N.S. |
1 | 1.17 | 1.00 | 0.92 | 0.83 | 0.83 | 0.67 | 0.83 | 0.83 |
time (sec) |
N/A | 0.132 | 0.001 | 0.024 | 0.193 | 0.257 | 0.017 | 0.276 | 0.018 |
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 | 30 | 30 | 30 | 25 | 24 | 24 | 24 | 24 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.80 | 0.80 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.163 | 0.003 | 1.820 | 0.193 | 0.235 | 0.017 | 0.283 | 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 | 30 | 30 | 30 | 25 | 24 | 24 | 26 | 24 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.80 | 0.80 | 0.87 | 0.80 | 0.80 |
time (sec) |
N/A | 0.170 | 0.003 | 1.877 | 0.197 | 0.246 | 0.017 | 0.265 | 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 | 30 | 30 | 30 | 25 | 24 | 24 | 24 | 24 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.80 | 0.80 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.179 | 0.004 | 1.769 | 0.199 | 0.240 | 0.018 | 0.272 | 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 | 30 | 30 | 30 | 25 | 24 | 24 | 26 | 24 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.80 | 0.80 | 0.87 | 0.80 | 0.80 |
time (sec) |
N/A | 0.164 | 0.002 | 2.625 | 0.198 | 0.250 | 0.018 | 0.276 | 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 | 30 | 30 | 30 | 25 | 24 | 24 | 24 | 24 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.80 | 0.80 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.162 | 0.002 | 2.598 | 0.202 | 0.249 | 0.018 | 0.273 | 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 | 57 | 57 | 57 | 52 | 52 | 52 | 49 | 53 | 51 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.91 | 0.91 | 0.86 | 0.93 | 0.89 |
time (sec) |
N/A | 0.196 | 0.006 | 2.537 | 0.216 | 0.251 | 0.060 | 0.276 | 8.831 |
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 | 44 | 41 | 42 | 41 | 37 | 43 | 40 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.95 | 0.93 | 0.84 | 0.98 | 0.91 |
time (sec) |
N/A | 0.189 | 0.004 | 2.158 | 0.204 | 0.246 | 0.052 | 0.287 | 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 | 31 | 31 | 31 | 30 | 29 | 29 | 26 | 30 | 29 |
N.S. |
1 | 1.00 | 1.00 | 0.97 | 0.94 | 0.94 | 0.84 | 0.97 | 0.94 |
time (sec) |
N/A | 0.175 | 0.004 | 1.780 | 0.193 | 0.242 | 0.050 | 0.290 | 0.041 |
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 | 19 | 18 | 17 | 14 | 19 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 0.94 | 0.78 | 1.06 | 1.00 |
time (sec) |
N/A | 0.161 | 0.003 | 1.815 | 0.215 | 0.243 | 0.040 | 0.275 | 0.036 |
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 | 10 | 10 | 10 | 11 | 10 | 10 | 7 | 11 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 1.00 | 1.00 | 0.70 | 1.10 | 1.00 |
time (sec) |
N/A | 0.135 | 0.001 | 1.767 | 0.202 | 0.240 | 0.018 | 0.286 | 0.021 |
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 | 16 | 18 | 16 | 10 | 20 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 1.00 | 0.89 | 0.56 | 1.11 | 0.83 |
time (sec) |
N/A | 0.145 | 0.004 | 2.029 | 0.201 | 0.261 | 0.059 | 0.271 | 8.898 |
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 | 28 | 28 | 28 | 26 | 28 | 26 | 19 | 30 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 1.00 | 0.93 | 0.68 | 1.07 | 0.89 |
time (sec) |
N/A | 0.183 | 0.005 | 1.862 | 0.203 | 0.258 | 0.074 | 0.268 | 0.055 |
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 | 42 | 42 | 42 | 41 | 40 | 41 | 31 | 45 | 38 |
N.S. |
1 | 1.00 | 1.00 | 0.98 | 0.95 | 0.98 | 0.74 | 1.07 | 0.90 |
time (sec) |
N/A | 0.184 | 0.006 | 1.751 | 0.221 | 0.280 | 0.097 | 0.288 | 0.058 |
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 | 56 | 56 | 56 | 53 | 51 | 54 | 44 | 56 | 48 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.91 | 0.96 | 0.79 | 1.00 | 0.86 |
time (sec) |
N/A | 0.198 | 0.007 | 1.783 | 0.204 | 0.275 | 0.118 | 0.270 | 0.060 |
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 | 58 | 58 | 54 | 57 | 59 | 73 | 54 | 62 | 62 |
N.S. |
1 | 1.00 | 0.93 | 0.98 | 1.02 | 1.26 | 0.93 | 1.07 | 1.07 |
time (sec) |
N/A | 0.211 | 0.030 | 1.907 | 0.219 | 0.245 | 0.093 | 0.266 | 0.039 |
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 | 46 | 46 | 43 | 45 | 47 | 62 | 44 | 48 | 50 |
N.S. |
1 | 1.00 | 0.93 | 0.98 | 1.02 | 1.35 | 0.96 | 1.04 | 1.09 |
time (sec) |
N/A | 0.195 | 0.015 | 1.968 | 0.202 | 0.248 | 0.088 | 0.266 | 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 | 33 | 33 | 29 | 34 | 36 | 47 | 31 | 34 | 36 |
N.S. |
1 | 1.00 | 0.88 | 1.03 | 1.09 | 1.42 | 0.94 | 1.03 | 1.09 |
time (sec) |
N/A | 0.176 | 0.015 | 1.828 | 0.199 | 0.266 | 0.071 | 0.295 | 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 | 23 | 23 | 20 | 24 | 26 | 28 | 20 | 24 | 23 |
N.S. |
1 | 1.00 | 0.87 | 1.04 | 1.13 | 1.22 | 0.87 | 1.04 | 1.00 |
time (sec) |
N/A | 0.167 | 0.009 | 2.178 | 0.201 | 0.247 | 0.056 | 0.277 | 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 | 12 | 12 | 12 | 13 | 13 | 13 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.08 | 1.08 | 0.83 | 1.00 | 1.00 |
time (sec) |
N/A | 0.137 | 0.002 | 2.295 | 0.210 | 0.246 | 0.053 | 0.283 | 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 | 29 | 29 | 24 | 30 | 28 | 39 | 22 | 31 | 26 |
N.S. |
1 | 1.00 | 0.83 | 1.03 | 0.97 | 1.34 | 0.76 | 1.07 | 0.90 |
time (sec) |
N/A | 0.173 | 0.012 | 2.312 | 0.204 | 0.277 | 0.095 | 0.284 | 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 | 42 | 42 | 35 | 43 | 45 | 63 | 37 | 45 | 41 |
N.S. |
1 | 1.00 | 0.83 | 1.02 | 1.07 | 1.50 | 0.88 | 1.07 | 0.98 |
time (sec) |
N/A | 0.191 | 0.043 | 2.358 | 0.210 | 0.260 | 0.126 | 0.280 | 8.845 |
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 | 58 | 58 | 53 | 57 | 64 | 86 | 54 | 64 | 57 |
N.S. |
1 | 1.00 | 0.91 | 0.98 | 1.10 | 1.48 | 0.93 | 1.10 | 0.98 |
time (sec) |
N/A | 0.204 | 0.052 | 1.974 | 0.205 | 0.248 | 0.146 | 0.278 | 8.858 |
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 | 69 | 69 | 66 | 68 | 73 | 95 | 66 | 73 | 69 |
N.S. |
1 | 1.00 | 0.96 | 0.99 | 1.06 | 1.38 | 0.96 | 1.06 | 1.00 |
time (sec) |
N/A | 0.227 | 0.062 | 4.385 | 0.199 | 0.261 | 0.156 | 0.286 | 0.069 |
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 | 84 | 84 | 79 | 79 | 86 | 108 | 80 | 86 | 79 |
N.S. |
1 | 1.00 | 0.94 | 0.94 | 1.02 | 1.29 | 0.95 | 1.02 | 0.94 |
time (sec) |
N/A | 0.231 | 0.050 | 4.141 | 0.217 | 0.269 | 0.171 | 0.281 | 0.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 105 | 117 | 53 | 32 | 53 | 62 | 0 | 131 | 62 |
N.S. |
1 | 1.11 | 0.50 | 0.30 | 0.50 | 0.59 | 0.00 | 1.25 | 0.59 |
time (sec) |
N/A | 0.284 | 0.019 | 2.575 | 0.212 | 0.252 | 0.000 | 0.263 | 9.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 86 | 42 | 21 | 42 | 51 | 0 | 108 | 51 |
N.S. |
1 | 1.08 | 0.52 | 0.26 | 0.52 | 0.64 | 0.00 | 1.35 | 0.64 |
time (sec) |
N/A | 0.228 | 0.013 | 1.864 | 0.218 | 0.263 | 0.000 | 0.273 | 9.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 41 | 13 | 30 | 39 | 0 | 81 | 39 |
N.S. |
1 | 1.00 | 0.79 | 0.25 | 0.58 | 0.75 | 0.00 | 1.56 | 0.75 |
time (sec) |
N/A | 0.193 | 0.008 | 1.914 | 0.212 | 0.263 | 0.000 | 0.285 | 8.936 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 23 | 25 | 12 | 26 | 0 | 50 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.00 | 0.48 | 1.04 | 0.00 | 2.00 | 0.00 |
time (sec) |
N/A | 0.157 | 0.008 | 1.890 | 0.211 | 0.264 | 0.000 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 53 | 36 | 0 | 111 | 0 | 67 | 73 |
N.S. |
1 | 1.00 | 1.04 | 0.71 | 0.00 | 2.18 | 0.00 | 1.31 | 1.43 |
time (sec) |
N/A | 0.194 | 0.030 | 1.909 | 0.000 | 0.250 | 0.000 | 0.288 | 9.147 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 64 | 50 | 0 | 127 | 0 | 45 | 0 |
N.S. |
1 | 1.00 | 1.23 | 0.96 | 0.00 | 2.44 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.189 | 0.026 | 1.971 | 0.000 | 0.256 | 0.000 | 0.294 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 84 | 82 | 81 | 61 | 0 | 149 | 0 | 72 | 0 |
N.S. |
1 | 0.98 | 0.96 | 0.73 | 0.00 | 1.77 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.235 | 0.039 | 2.392 | 0.000 | 0.270 | 0.000 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 116 | 93 | 72 | 0 | 175 | 0 | 92 | 0 |
N.S. |
1 | 1.04 | 0.83 | 0.64 | 0.00 | 1.56 | 0.00 | 0.82 | 0.00 |
time (sec) |
N/A | 0.284 | 0.040 | 1.998 | 0.000 | 0.271 | 0.000 | 0.316 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 161 | 185 | 80 | 32 | 86 | 95 | 0 | 282 | 80 |
N.S. |
1 | 1.15 | 0.50 | 0.20 | 0.53 | 0.59 | 0.00 | 1.75 | 0.50 |
time (sec) |
N/A | 0.375 | 0.056 | 1.891 | 0.223 | 0.274 | 0.000 | 0.276 | 9.139 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 136 | 154 | 69 | 21 | 75 | 84 | 0 | 246 | 69 |
N.S. |
1 | 1.13 | 0.51 | 0.15 | 0.55 | 0.62 | 0.00 | 1.81 | 0.51 |
time (sec) |
N/A | 0.329 | 0.048 | 1.855 | 0.217 | 0.262 | 0.000 | 0.282 | 9.010 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 120 | 58 | 13 | 64 | 73 | 0 | 210 | 58 |
N.S. |
1 | 1.11 | 0.54 | 0.12 | 0.59 | 0.68 | 0.00 | 1.94 | 0.54 |
time (sec) |
N/A | 0.269 | 0.019 | 1.818 | 0.216 | 0.256 | 0.000 | 0.290 | 9.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 86 | 47 | 35 | 53 | 62 | 0 | 173 | 47 |
N.S. |
1 | 1.08 | 0.59 | 0.44 | 0.66 | 0.78 | 0.00 | 2.16 | 0.59 |
time (sec) |
N/A | 0.240 | 0.018 | 1.823 | 0.220 | 0.263 | 0.000 | 0.290 | 9.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 31 | 35 | 41 | 50 | 0 | 136 | 36 |
N.S. |
1 | 1.00 | 0.60 | 0.67 | 0.79 | 0.96 | 0.00 | 2.62 | 0.69 |
time (sec) |
N/A | 0.193 | 0.015 | 1.838 | 0.208 | 0.252 | 0.000 | 0.292 | 8.923 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 23 | 27 | 28 | 37 | 0 | 89 | 28 |
N.S. |
1 | 1.00 | 0.92 | 1.08 | 1.12 | 1.48 | 0.00 | 3.56 | 1.12 |
time (sec) |
N/A | 0.159 | 0.010 | 2.421 | 0.221 | 0.254 | 0.000 | 0.277 | 9.287 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 76 | 68 | 61 | 0 | 130 | 0 | 85 | 0 |
N.S. |
1 | 1.03 | 0.92 | 0.82 | 0.00 | 1.76 | 0.00 | 1.15 | 0.00 |
time (sec) |
N/A | 0.231 | 0.048 | 2.020 | 0.000 | 0.282 | 0.000 | 0.280 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 77 | 66 | 70 | 0 | 136 | 0 | 62 | 0 |
N.S. |
1 | 1.05 | 0.90 | 0.96 | 0.00 | 1.86 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.230 | 0.045 | 1.888 | 0.000 | 0.284 | 0.000 | 0.299 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 80 | 82 | 67 | 0 | 154 | 0 | 70 | 0 |
N.S. |
1 | 0.99 | 1.01 | 0.83 | 0.00 | 1.90 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.229 | 0.039 | 1.943 | 0.000 | 0.273 | 0.000 | 0.336 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 109 | 110 | 94 | 81 | 0 | 175 | 0 | 92 | 0 |
N.S. |
1 | 1.01 | 0.86 | 0.74 | 0.00 | 1.61 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.281 | 0.050 | 2.248 | 0.000 | 0.281 | 0.000 | 0.297 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 144 | 104 | 92 | 0 | 197 | 0 | 109 | 0 |
N.S. |
1 | 1.05 | 0.76 | 0.67 | 0.00 | 1.44 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.324 | 0.236 | 2.148 | 0.000 | 0.276 | 0.000 | 0.304 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 165 | 178 | 116 | 103 | 0 | 219 | 0 | 126 | 0 |
N.S. |
1 | 1.08 | 0.70 | 0.62 | 0.00 | 1.33 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.379 | 0.252 | 2.873 | 0.000 | 0.277 | 0.000 | 0.313 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 103 | 115 | 53 | 52 | 53 | 51 | 0 | 64 | 51 |
N.S. |
1 | 1.12 | 0.51 | 0.50 | 0.51 | 0.50 | 0.00 | 0.62 | 0.50 |
time (sec) |
N/A | 0.271 | 0.018 | 1.877 | 0.232 | 0.263 | 0.000 | 0.272 | 8.919 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 81 | 42 | 41 | 42 | 40 | 0 | 52 | 40 |
N.S. |
1 | 1.08 | 0.56 | 0.55 | 0.56 | 0.53 | 0.00 | 0.69 | 0.53 |
time (sec) |
N/A | 0.226 | 0.014 | 1.834 | 0.213 | 0.260 | 0.000 | 0.282 | 8.878 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 30 | 30 | 30 | 28 | 0 | 38 | 31 |
N.S. |
1 | 1.00 | 0.61 | 0.61 | 0.61 | 0.57 | 0.00 | 0.78 | 0.63 |
time (sec) |
N/A | 0.184 | 0.011 | 1.846 | 0.251 | 0.262 | 0.000 | 0.272 | 8.866 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 21 | 21 | 12 | 21 | 0 | 27 | 17 |
N.S. |
1 | 1.00 | 0.91 | 0.91 | 0.52 | 0.91 | 0.00 | 1.17 | 0.74 |
time (sec) |
N/A | 0.151 | 0.006 | 2.034 | 0.216 | 0.268 | 0.000 | 0.271 | 8.878 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 46 | 13 | 0 | 74 | 0 | 45 | 0 |
N.S. |
1 | 1.00 | 1.53 | 0.43 | 0.00 | 2.47 | 0.00 | 1.50 | 0.00 |
time (sec) |
N/A | 0.155 | 0.010 | 1.830 | 0.000 | 0.265 | 0.000 | 0.276 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 60 | 18 | 0 | 127 | 0 | 51 | 0 |
N.S. |
1 | 1.00 | 1.11 | 0.33 | 0.00 | 2.35 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 0.190 | 0.021 | 2.158 | 0.000 | 0.259 | 0.000 | 0.312 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 88 | 83 | 36 | 0 | 153 | 0 | 73 | 44 |
N.S. |
1 | 1.01 | 0.95 | 0.41 | 0.00 | 1.76 | 0.00 | 0.84 | 0.51 |
time (sec) |
N/A | 0.233 | 0.031 | 2.494 | 0.000 | 0.268 | 0.000 | 0.293 | 9.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 122 | 96 | 56 | 0 | 175 | 0 | 88 | 0 |
N.S. |
1 | 1.06 | 0.83 | 0.49 | 0.00 | 1.52 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 0.286 | 0.031 | 2.027 | 0.000 | 0.280 | 0.000 | 0.304 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 110 | 50 | 56 | 41 | 60 | 0 | 79 | 57 |
N.S. |
1 | 1.12 | 0.51 | 0.57 | 0.42 | 0.61 | 0.00 | 0.81 | 0.58 |
time (sec) |
N/A | 0.270 | 0.013 | 1.916 | 0.201 | 0.263 | 0.000 | 0.284 | 9.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 78 | 39 | 46 | 30 | 49 | 0 | 64 | 47 |
N.S. |
1 | 1.08 | 0.54 | 0.64 | 0.42 | 0.68 | 0.00 | 0.89 | 0.65 |
time (sec) |
N/A | 0.228 | 0.011 | 1.991 | 0.209 | 0.260 | 0.000 | 0.269 | 9.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 26 | 34 | 19 | 38 | 0 | 48 | 35 |
N.S. |
1 | 1.00 | 0.55 | 0.72 | 0.40 | 0.81 | 0.00 | 1.02 | 0.74 |
time (sec) |
N/A | 0.187 | 0.010 | 1.849 | 0.287 | 0.283 | 0.000 | 0.280 | 8.991 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 19 | 27 | 12 | 29 | 0 | 27 | 28 |
N.S. |
1 | 1.00 | 0.90 | 1.29 | 0.57 | 1.38 | 0.00 | 1.29 | 1.33 |
time (sec) |
N/A | 0.151 | 0.005 | 1.885 | 0.251 | 0.251 | 0.000 | 0.286 | 8.936 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 54 | 31 | 0 | 156 | 0 | 77 | 0 |
N.S. |
1 | 1.00 | 1.04 | 0.60 | 0.00 | 3.00 | 0.00 | 1.48 | 0.00 |
time (sec) |
N/A | 0.193 | 0.015 | 1.774 | 0.000 | 0.271 | 0.000 | 0.271 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 80 | 62 | 20 | 0 | 189 | 0 | 72 | 0 |
N.S. |
1 | 1.07 | 0.83 | 0.27 | 0.00 | 2.52 | 0.00 | 0.96 | 0.00 |
time (sec) |
N/A | 0.234 | 0.023 | 1.824 | 0.000 | 0.275 | 0.000 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 117 | 84 | 13 | 0 | 219 | 0 | 92 | 42 |
N.S. |
1 | 1.06 | 0.76 | 0.12 | 0.00 | 1.99 | 0.00 | 0.84 | 0.38 |
time (sec) |
N/A | 0.275 | 0.027 | 1.829 | 0.000 | 0.279 | 0.000 | 0.311 | 9.139 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 138 | 151 | 96 | 31 | 0 | 241 | 0 | 107 | 0 |
N.S. |
1 | 1.09 | 0.70 | 0.22 | 0.00 | 1.75 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.329 | 0.184 | 1.851 | 0.000 | 0.272 | 0.000 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 166 | 185 | 106 | 51 | 0 | 263 | 0 | 122 | 44 |
N.S. |
1 | 1.11 | 0.64 | 0.31 | 0.00 | 1.58 | 0.00 | 0.73 | 0.27 |
time (sec) |
N/A | 0.394 | 0.243 | 1.866 | 0.000 | 0.296 | 0.000 | 0.313 | 9.888 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 125 | 132 | 110 | 100 | 0 | 180 | 0 | 83 | 0 |
N.S. |
1 | 1.06 | 0.88 | 0.80 | 0.00 | 1.44 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.289 | 0.061 | 1.936 | 0.000 | 0.280 | 0.000 | 0.303 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 95 | 96 | 99 | 89 | 0 | 159 | 0 | 71 | 0 |
N.S. |
1 | 1.01 | 1.04 | 0.94 | 0.00 | 1.67 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 0.245 | 0.032 | 2.066 | 0.000 | 0.272 | 0.000 | 0.280 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 80 | 78 | 0 | 131 | 0 | 55 | 0 |
N.S. |
1 | 1.00 | 1.33 | 1.30 | 0.00 | 2.18 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.200 | 0.032 | 1.836 | 0.000 | 0.277 | 0.000 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 53 | 58 | 0 | 77 | 0 | 37 | 0 |
N.S. |
1 | 1.00 | 1.56 | 1.71 | 0.00 | 2.26 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.162 | 0.014 | 1.769 | 0.000 | 0.267 | 0.000 | 0.283 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 23 | 25 | 0 | 21 | 0 | 34 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.00 | 0.00 | 0.84 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.150 | 0.011 | 1.871 | 0.000 | 0.264 | 0.000 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 31 | 31 | 0 | 29 | 0 | 54 | 0 |
N.S. |
1 | 1.00 | 0.55 | 0.55 | 0.00 | 0.52 | 0.00 | 0.96 | 0.00 |
time (sec) |
N/A | 0.185 | 0.014 | 1.804 | 0.000 | 0.269 | 0.000 | 0.310 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 92 | 44 | 44 | 0 | 40 | 0 | 81 | 0 |
N.S. |
1 | 1.07 | 0.51 | 0.51 | 0.00 | 0.47 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 0.229 | 0.016 | 1.816 | 0.000 | 0.265 | 0.000 | 0.292 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 116 | 128 | 55 | 55 | 0 | 51 | 0 | 107 | 0 |
N.S. |
1 | 1.10 | 0.47 | 0.47 | 0.00 | 0.44 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.275 | 0.019 | 2.790 | 0.000 | 0.268 | 0.000 | 0.314 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 59 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.196 | 0.048 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 48 | 61 | 59 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.27 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.193 | 0.038 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 52 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.192 | 0.037 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 30 | 36 | 0 | 38 | 0 | 0 | 54 |
N.S. |
1 | 1.00 | 0.94 | 1.12 | 0.00 | 1.19 | 0.00 | 0.00 | 1.69 |
time (sec) |
N/A | 0.165 | 0.044 | 1.934 | 0.000 | 0.274 | 0.000 | 0.000 | 9.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 44 | 50 | 0 | 70 | 0 | 0 | 98 |
N.S. |
1 | 1.00 | 0.63 | 0.71 | 0.00 | 1.00 | 0.00 | 0.00 | 1.40 |
time (sec) |
N/A | 0.221 | 0.070 | 1.921 | 0.000 | 0.272 | 0.000 | 0.000 | 9.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 116 | 114 | 72 | 84 | 0 | 111 | 0 | 0 | 157 |
N.S. |
1 | 0.98 | 0.62 | 0.72 | 0.00 | 0.96 | 0.00 | 0.00 | 1.35 |
time (sec) |
N/A | 0.288 | 0.061 | 1.937 | 0.000 | 0.274 | 0.000 | 0.000 | 9.126 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 24 | 23 | 36 | 36 | 36 | 22 | 37 |
N.S. |
1 | 1.00 | 1.26 | 1.21 | 1.89 | 1.89 | 1.89 | 1.16 | 1.95 |
time (sec) |
N/A | 0.148 | 0.011 | 1.803 | 0.196 | 0.258 | 0.168 | 0.289 | 8.945 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 86 | 46 | 43 | 46 | 42 | 0 | 65 | 42 |
N.S. |
1 | 1.08 | 0.58 | 0.54 | 0.58 | 0.52 | 0.00 | 0.81 | 0.52 |
time (sec) |
N/A | 0.246 | 0.017 | 2.506 | 0.226 | 0.270 | 0.000 | 0.283 | 9.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 34 | 32 | 34 | 30 | 0 | 48 | 33 |
N.S. |
1 | 1.00 | 0.65 | 0.62 | 0.65 | 0.58 | 0.00 | 0.92 | 0.63 |
time (sec) |
N/A | 0.200 | 0.012 | 2.275 | 0.208 | 0.256 | 0.000 | 0.275 | 8.999 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 22 | 14 | 21 | 0 | 29 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.56 | 0.84 | 0.00 | 1.16 | 0.84 |
time (sec) |
N/A | 0.158 | 0.010 | 2.218 | 0.219 | 0.264 | 0.000 | 0.275 | 9.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 54 | 43 | 0 | 75 | 0 | 47 | 0 |
N.S. |
1 | 1.00 | 1.69 | 1.34 | 0.00 | 2.34 | 0.00 | 1.47 | 0.00 |
time (sec) |
N/A | 0.161 | 0.012 | 2.144 | 0.000 | 0.274 | 0.000 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 76 | 66 | 0 | 127 | 0 | 55 | 0 |
N.S. |
1 | 1.00 | 1.29 | 1.12 | 0.00 | 2.15 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.200 | 0.025 | 2.311 | 0.000 | 0.275 | 0.000 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 238 | 238 | 68 | 248 | 0 | 37 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.29 | 1.04 | 0.00 | 0.16 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.311 | 10.036 | 2.256 | 0.000 | 0.074 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 212 | 212 | 52 | 231 | 0 | 14 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.25 | 1.09 | 0.00 | 0.07 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.256 | 10.018 | 1.945 | 0.000 | 0.072 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 243 | 243 | 55 | 248 | 0 | 38 | 0 | 0 | 44 |
N.S. |
1 | 1.00 | 0.23 | 1.02 | 0.00 | 0.16 | 0.00 | 0.00 | 0.18 |
time (sec) |
N/A | 0.307 | 10.016 | 2.025 | 0.000 | 0.077 | 0.000 | 0.000 | 9.711 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 514 | 543 | 68 | 25 | 0 | 45 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.13 | 0.05 | 0.00 | 0.09 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.572 | 10.039 | 1.995 | 0.000 | 0.075 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 484 | 512 | 55 | 15 | 0 | 22 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.11 | 0.03 | 0.00 | 0.05 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.513 | 10.021 | 1.859 | 0.000 | 0.076 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 510 | 543 | 50 | 20 | 0 | 46 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.10 | 0.04 | 0.00 | 0.09 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.575 | 10.020 | 1.825 | 0.000 | 0.077 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 265 | 273 | 86 | 742 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.32 | 2.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.409 | 10.038 | 2.232 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 525 | 536 | 70 | 1115 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.13 | 2.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.658 | 10.031 | 2.248 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 82 | 79 | 0 | 148 | 0 | 52 | 0 |
N.S. |
1 | 1.00 | 1.26 | 1.22 | 0.00 | 2.28 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.215 | 0.034 | 1.872 | 0.000 | 0.361 | 0.000 | 0.313 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 237 | 237 | 70 | 727 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.30 | 3.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.344 | 10.034 | 2.080 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 492 | 502 | 57 | 2374 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.12 | 4.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.566 | 10.024 | 1.977 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 60 | 59 | 0 | 101 | 0 | 40 | 0 |
N.S. |
1 | 1.00 | 1.67 | 1.64 | 0.00 | 2.81 | 0.00 | 1.11 | 0.00 |
time (sec) |
N/A | 0.177 | 0.012 | 1.780 | 0.000 | 0.353 | 0.000 | 0.299 | 0.000 |