Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 84 | 58 | 80 | 80 | 63 | 88 | 125 | 82 | 0 |
N.S. |
1 | 1.02 | 0.71 | 0.98 | 0.98 | 0.77 | 1.07 | 1.52 | 1.00 | 0.00 |
time (sec) |
N/A | 0.242 | 0.031 | 0.053 | 0.106 | 0.092 | 0.348 | 0.115 | 0.194 | 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 | 76 | 88 | 81 | 68 | 70 | 61 | 80 | 95 | 71 | 0 |
N.S. |
1 | 1.16 | 1.07 | 0.89 | 0.92 | 0.80 | 1.05 | 1.25 | 0.93 | 0.00 |
time (sec) |
N/A | 0.230 | 0.018 | 0.050 | 0.110 | 0.081 | 0.279 | 0.126 | 0.229 | 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 | 60 | 63 | 49 | 60 | 59 | 53 | 65 | 74 | 61 | 0 |
N.S. |
1 | 1.05 | 0.82 | 1.00 | 0.98 | 0.88 | 1.08 | 1.23 | 1.02 | 0.00 |
time (sec) |
N/A | 0.239 | 0.024 | 0.050 | 0.108 | 0.094 | 0.210 | 0.116 | 0.179 | 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 | 51 | 56 | 56 | 48 | 49 | 49 | 54 | 64 | 50 | 45 |
N.S. |
1 | 1.10 | 1.10 | 0.94 | 0.96 | 0.96 | 1.06 | 1.25 | 0.98 | 0.88 |
time (sec) |
N/A | 0.194 | 0.013 | 0.046 | 0.103 | 0.088 | 0.166 | 0.114 | 0.188 | 0.163 |
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 | 30 | 30 | 30 | 30 | 29 | 31 | 26 | 29 | 30 | 28 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.97 | 1.03 | 0.87 | 0.97 | 1.00 | 0.93 |
time (sec) |
N/A | 0.153 | 0.004 | 0.000 | 0.112 | 0.084 | 0.075 | 0.118 | 0.225 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 71 | 52 | 118 | 0 | 0 | 0 | 0 | 17 | 48 |
N.S. |
1 | 1.13 | 0.83 | 1.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.76 |
time (sec) |
N/A | 0.365 | 0.054 | 0.101 | 0.000 | 0.000 | 0.000 | 0.000 | 0.205 | 0.168 |
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 | 33 | 33 | 36 | 39 | 47 | 55 | 39 | 325 | 27 | 34 |
N.S. |
1 | 1.00 | 1.09 | 1.18 | 1.42 | 1.67 | 1.18 | 9.85 | 0.82 | 1.03 |
time (sec) |
N/A | 0.240 | 0.003 | 0.050 | 0.105 | 0.096 | 0.985 | 0.171 | 0.196 | 0.144 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 44 | 46 | 36 | 35 | 61 | 163 | 32 | 0 |
N.S. |
1 | 1.00 | 1.13 | 1.18 | 0.92 | 0.90 | 1.56 | 4.18 | 0.82 | 0.00 |
time (sec) |
N/A | 0.226 | 0.009 | 0.049 | 0.104 | 0.087 | 0.740 | 0.132 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 67 | 61 | 69 | 80 | 117 | 284 | 48 | 0 |
N.S. |
1 | 1.00 | 1.08 | 0.98 | 1.11 | 1.29 | 1.89 | 4.58 | 0.77 | 0.00 |
time (sec) |
N/A | 0.211 | 0.011 | 0.053 | 0.116 | 0.114 | 1.606 | 0.297 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 68 | 54 | 66 | 59 | 50 | 110 | 321 | 52 | 0 |
N.S. |
1 | 1.06 | 0.84 | 1.03 | 0.92 | 0.78 | 1.72 | 5.02 | 0.81 | 0.00 |
time (sec) |
N/A | 0.203 | 0.019 | 0.054 | 0.105 | 0.096 | 0.998 | 0.142 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 91 | 61 | 81 | 91 | 93 | 192 | 442 | 69 | 0 |
N.S. |
1 | 1.05 | 0.70 | 0.93 | 1.05 | 1.07 | 2.21 | 5.08 | 0.79 | 0.00 |
time (sec) |
N/A | 0.223 | 0.013 | 0.052 | 0.111 | 0.108 | 3.082 | 0.722 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 137 | 137 | 165 | 0 | 135 | 201 | 257 | 97 | 0 |
N.S. |
1 | 1.12 | 1.12 | 1.35 | 0.00 | 1.11 | 1.65 | 2.11 | 0.80 | 0.00 |
time (sec) |
N/A | 0.559 | 0.046 | 0.131 | 0.000 | 0.083 | 0.397 | 0.128 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 109 | 95 | 125 | 142 | 111 | 170 | 194 | 87 | 0 |
N.S. |
1 | 1.07 | 0.93 | 1.23 | 1.39 | 1.09 | 1.67 | 1.90 | 0.85 | 0.00 |
time (sec) |
N/A | 0.429 | 0.106 | 0.118 | 0.110 | 0.107 | 0.279 | 0.135 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 84 | 73 | 97 | 0 | 99 | 126 | 155 | 117 | 0 |
N.S. |
1 | 1.11 | 0.96 | 1.28 | 0.00 | 1.30 | 1.66 | 2.04 | 1.54 | 0.00 |
time (sec) |
N/A | 0.388 | 0.044 | 0.135 | 0.000 | 0.082 | 0.234 | 0.128 | 0.179 | 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 | 47 | 51 | 47 | 72 | 72 | 65 | 82 | 75 | 75 | 142 |
N.S. |
1 | 1.09 | 1.00 | 1.53 | 1.53 | 1.38 | 1.74 | 1.60 | 1.60 | 3.02 |
time (sec) |
N/A | 0.261 | 0.016 | 0.002 | 0.103 | 0.089 | 0.106 | 0.119 | 0.196 | 0.006 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 105 | 143 | 294 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.17 | 1.59 | 3.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.490 | 0.097 | 0.132 | 0.000 | 0.000 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 78 | 126 | 165 | 0 | 0 | 0 | 0 | 49 | 0 |
N.S. |
1 | 0.96 | 1.56 | 2.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.464 | 0.158 | 0.123 | 0.000 | 0.000 | 0.000 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 54 | 81 | 100 | 86 | 73 | 0 | 377 | 56 | 0 |
N.S. |
1 | 0.96 | 1.45 | 1.79 | 1.54 | 1.30 | 0.00 | 6.73 | 1.00 | 0.00 |
time (sec) |
N/A | 0.363 | 0.050 | 0.126 | 0.111 | 0.099 | 0.000 | 0.188 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 128 | 215 | 216 | 0 | 0 | 0 | 0 | 73 | 0 |
N.S. |
1 | 0.92 | 1.55 | 1.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.667 | 0.472 | 0.224 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 103 | 130 | 154 | 143 | 107 | 0 | 735 | 77 | 0 |
N.S. |
1 | 0.96 | 1.21 | 1.44 | 1.34 | 1.00 | 0.00 | 6.87 | 0.72 | 0.00 |
time (sec) |
N/A | 0.454 | 0.075 | 0.136 | 0.110 | 0.111 | 0.000 | 0.238 | 0.281 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | B | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 276 | 255 | 323 | 0 | 244 | 416 | 490 | 126 | 0 |
N.S. |
1 | 1.33 | 1.23 | 1.55 | 0.00 | 1.17 | 2.00 | 2.36 | 0.61 | 0.00 |
time (sec) |
N/A | 1.188 | 0.094 | 0.195 | 0.000 | 0.092 | 0.584 | 0.148 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 201 | 163 | 235 | 273 | 194 | 328 | 368 | 112 | 0 |
N.S. |
1 | 1.18 | 0.96 | 1.38 | 1.61 | 1.14 | 1.93 | 2.16 | 0.66 | 0.00 |
time (sec) |
N/A | 0.847 | 0.225 | 0.183 | 0.124 | 0.091 | 0.405 | 0.138 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 138 | 114 | 159 | 0 | 169 | 264 | 285 | 221 | 0 |
N.S. |
1 | 1.10 | 0.91 | 1.27 | 0.00 | 1.35 | 2.11 | 2.28 | 1.77 | 0.00 |
time (sec) |
N/A | 0.616 | 0.084 | 0.194 | 0.000 | 0.084 | 0.348 | 0.140 | 0.173 | 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 | 79 | 83 | 77 | 132 | 141 | 108 | 160 | 150 | 144 | 242 |
N.S. |
1 | 1.05 | 0.97 | 1.67 | 1.78 | 1.37 | 2.03 | 1.90 | 1.82 | 3.06 |
time (sec) |
N/A | 0.335 | 0.049 | 0.000 | 0.109 | 0.084 | 0.159 | 0.125 | 0.205 | 0.006 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 141 | 244 | 530 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.15 | 1.98 | 4.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.616 | 0.147 | 0.200 | 0.000 | 0.000 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 134 | 283 | 349 | 0 | 0 | 0 | 0 | 72 | 0 |
N.S. |
1 | 0.98 | 2.07 | 2.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.653 | 0.210 | 0.222 | 0.000 | 0.000 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 129 | 179 | 265 | 0 | 0 | 0 | 0 | 81 | 0 |
N.S. |
1 | 1.02 | 1.42 | 2.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.740 | 0.347 | 0.223 | 0.000 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 210 | 567 | 454 | 0 | 0 | 0 | 0 | 101 | 0 |
N.S. |
1 | 0.94 | 2.54 | 2.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 1.530 | 7.175 | 0.298 | 0.000 | 0.000 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 213 | 287 | 389 | 0 | 0 | 0 | 0 | 104 | 0 |
N.S. |
1 | 1.02 | 1.38 | 1.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 1.172 | 0.606 | 0.316 | 0.000 | 0.000 | 0.000 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 412 | 150 | 197 | 207 | 134 | 241 | 305 | 12 | 0 |
N.S. |
1 | 1.65 | 0.60 | 0.79 | 0.83 | 0.54 | 0.96 | 1.22 | 0.05 | 0.00 |
time (sec) |
N/A | 2.318 | 0.046 | 0.329 | 0.133 | 0.099 | 1.177 | 0.129 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 293 | 135 | 215 | 0 | 121 | 190 | 234 | 12 | 0 |
N.S. |
1 | 1.48 | 0.68 | 1.09 | 0.00 | 0.61 | 0.96 | 1.18 | 0.06 | 0.00 |
time (sec) |
N/A | 1.684 | 0.037 | 0.253 | 0.000 | 0.085 | 0.722 | 0.126 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 227 | 114 | 130 | 147 | 99 | 158 | 176 | 12 | 0 |
N.S. |
1 | 1.37 | 0.69 | 0.78 | 0.89 | 0.60 | 0.95 | 1.06 | 0.07 | 0.00 |
time (sec) |
N/A | 1.356 | 0.030 | 0.239 | 0.113 | 0.113 | 0.512 | 0.125 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 133 | 96 | 73 | 0 | 82 | 104 | 127 | 98 | 0 |
N.S. |
1 | 1.20 | 0.86 | 0.66 | 0.00 | 0.74 | 0.94 | 1.14 | 0.88 | 0.00 |
time (sec) |
N/A | 0.808 | 0.019 | 0.251 | 0.000 | 0.085 | 0.337 | 0.121 | 0.220 | 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 | 69 | 84 | 69 | 67 | 75 | 55 | 65 | 65 | 64 | 48 |
N.S. |
1 | 1.22 | 1.00 | 0.97 | 1.09 | 0.80 | 0.94 | 0.94 | 0.93 | 0.70 |
time (sec) |
N/A | 0.471 | 0.011 | 0.186 | 0.120 | 0.084 | 0.188 | 0.121 | 0.181 | 0.227 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 148 | 113 | 287 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.31 | 1.00 | 2.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.674 | 0.030 | 0.263 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 165 | 198 | 238 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.06 | 1.27 | 1.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.767 | 0.179 | 0.281 | 0.000 | 0.000 | 0.000 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 134 | 124 | 219 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.13 | 1.04 | 1.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.877 | 0.211 | 0.290 | 0.000 | 0.000 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 276 | 276 | 399 | 377 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.00 | 1.45 | 1.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.747 | 2.786 | 0.342 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 154 | 135 | 154 | 0 | 0 | 0 | 359 | 16 | 0 |
N.S. |
1 | 0.84 | 0.74 | 0.84 | 0.00 | 0.00 | 0.00 | 1.96 | 0.09 | 0.00 |
time (sec) |
N/A | 0.727 | 0.280 | 0.052 | 0.000 | 0.000 | 0.000 | 0.137 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 108 | 98 | 110 | 0 | 0 | 0 | 237 | 16 | 0 |
N.S. |
1 | 0.86 | 0.78 | 0.88 | 0.00 | 0.00 | 0.00 | 1.90 | 0.13 | 0.00 |
time (sec) |
N/A | 0.475 | 0.203 | 0.048 | 0.000 | 0.000 | 0.000 | 0.132 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 104 | 91 | 102 | 0 | 0 | 0 | 173 | 16 | 0 |
N.S. |
1 | 0.86 | 0.75 | 0.84 | 0.00 | 0.00 | 0.00 | 1.43 | 0.13 | 0.00 |
time (sec) |
N/A | 0.419 | 0.168 | 0.043 | 0.000 | 0.000 | 0.000 | 0.127 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 56 | 56 | 58 | 0 | 0 | 0 | 86 | 14 | 0 |
N.S. |
1 | 0.89 | 0.89 | 0.92 | 0.00 | 0.00 | 0.00 | 1.37 | 0.22 | 0.00 |
time (sec) |
N/A | 0.503 | 0.059 | 0.059 | 0.000 | 0.000 | 0.000 | 0.136 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 48 | 44 | 48 | 0 | 0 | 0 | 49 | 12 | 0 |
N.S. |
1 | 0.91 | 0.83 | 0.91 | 0.00 | 0.00 | 0.00 | 0.92 | 0.23 | 0.00 |
time (sec) |
N/A | 0.397 | 0.006 | 0.000 | 0.000 | 0.000 | 0.000 | 0.120 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 14 | 16 | 15 | 12 | 0 | 15 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 1.07 | 0.86 | 0.00 | 1.07 | 1.14 |
time (sec) |
N/A | 0.190 | 0.182 | 0.039 | 0.162 | 0.074 | 0.716 | 0.000 | 0.184 | 0.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 14 | 16 | 19 | 14 | 16 | 19 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 1.36 | 1.00 | 1.14 | 1.36 | 1.14 |
time (sec) |
N/A | 0.189 | 1.472 | 0.133 | 0.173 | 0.076 | 0.730 | 0.586 | 0.179 | 0.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 218 | 190 | 170 | 222 | 0 | 0 | 0 | 1299 | 30 | 0 |
N.S. |
1 | 0.87 | 0.78 | 1.02 | 0.00 | 0.00 | 0.00 | 5.96 | 0.14 | 0.00 |
time (sec) |
N/A | 0.454 | 0.731 | 0.055 | 0.000 | 0.000 | 0.000 | 0.166 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 144 | 201 | 150 | 0 | 0 | 0 | 854 | 30 | 0 |
N.S. |
1 | 0.90 | 1.26 | 0.94 | 0.00 | 0.00 | 0.00 | 5.34 | 0.19 | 0.00 |
time (sec) |
N/A | 0.355 | 0.525 | 0.050 | 0.000 | 0.000 | 0.000 | 0.160 | 0.255 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 140 | 125 | 149 | 0 | 0 | 0 | 646 | 30 | 0 |
N.S. |
1 | 0.90 | 0.80 | 0.96 | 0.00 | 0.00 | 0.00 | 4.14 | 0.19 | 0.00 |
time (sec) |
N/A | 0.366 | 0.467 | 0.051 | 0.000 | 0.000 | 0.000 | 0.162 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 86 | 79 | 77 | 0 | 0 | 0 | 326 | 28 | 0 |
N.S. |
1 | 0.96 | 0.88 | 0.86 | 0.00 | 0.00 | 0.00 | 3.62 | 0.31 | 0.00 |
time (sec) |
N/A | 0.492 | 0.266 | 0.065 | 0.000 | 0.000 | 0.000 | 0.140 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 83 | 72 | 76 | 0 | 0 | 0 | 192 | 26 | 0 |
N.S. |
1 | 0.97 | 0.84 | 0.88 | 0.00 | 0.00 | 0.00 | 2.23 | 0.30 | 0.00 |
time (sec) |
N/A | 0.600 | 0.045 | 0.000 | 0.000 | 0.000 | 0.000 | 0.123 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 14 | 165 | 30 | 14 | 0 | 30 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 11.79 | 2.14 | 1.00 | 0.00 | 2.14 | 1.14 |
time (sec) |
N/A | 0.194 | 3.258 | 0.055 | 0.377 | 0.082 | 1.183 | 0.000 | 0.222 | 0.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 14 | 182 | 36 | 15 | 16 | 36 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 13.00 | 2.57 | 1.07 | 1.14 | 2.57 | 1.14 |
time (sec) |
N/A | 0.194 | 26.764 | 0.123 | 0.556 | 0.084 | 1.045 | 0.995 | 0.235 | 0.116 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 358 | 222 | 442 | 0 | 0 | 0 | 2988 | 44 | 0 |
N.S. |
1 | 1.37 | 0.85 | 1.69 | 0.00 | 0.00 | 0.00 | 11.45 | 0.17 | 0.00 |
time (sec) |
N/A | 1.210 | 0.756 | 0.057 | 0.000 | 0.000 | 0.000 | 0.232 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 260 | 161 | 309 | 0 | 0 | 0 | 2075 | 44 | 0 |
N.S. |
1 | 1.31 | 0.81 | 1.56 | 0.00 | 0.00 | 0.00 | 10.48 | 0.22 | 0.00 |
time (sec) |
N/A | 1.450 | 0.426 | 0.057 | 0.000 | 0.000 | 0.000 | 0.220 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 248 | 168 | 290 | 0 | 0 | 0 | 1539 | 44 | 0 |
N.S. |
1 | 1.26 | 0.85 | 1.47 | 0.00 | 0.00 | 0.00 | 7.81 | 0.22 | 0.00 |
time (sec) |
N/A | 1.716 | 0.469 | 0.054 | 0.000 | 0.000 | 0.000 | 0.216 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 137 | 108 | 157 | 0 | 0 | 0 | 864 | 42 | 0 |
N.S. |
1 | 1.05 | 0.83 | 1.21 | 0.00 | 0.00 | 0.00 | 6.65 | 0.32 | 0.00 |
time (sec) |
N/A | 1.335 | 0.227 | 0.066 | 0.000 | 0.000 | 0.000 | 0.180 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 93 | 138 | 0 | 0 | 0 | 482 | 40 | 0 |
N.S. |
1 | 1.00 | 0.84 | 1.24 | 0.00 | 0.00 | 0.00 | 4.34 | 0.36 | 0.00 |
time (sec) |
N/A | 0.848 | 0.254 | 0.000 | 0.000 | 0.000 | 0.000 | 0.127 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 14 | 254 | 45 | 14 | 0 | 45 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 18.14 | 3.21 | 1.00 | 0.00 | 3.21 | 1.14 |
time (sec) |
N/A | 0.193 | 1.396 | 0.061 | 1.966 | 0.077 | 1.844 | 0.000 | 0.174 | 0.129 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 14 | 283 | 53 | 15 | 16 | 53 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 20.21 | 3.79 | 1.07 | 1.14 | 3.79 | 1.14 |
time (sec) |
N/A | 0.192 | 11.732 | 0.130 | 2.462 | 0.070 | 1.932 | 1.761 | 0.176 | 0.148 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 210 | 159 | 171 | 0 | 0 | 0 | 250 | 12 | 0 |
N.S. |
1 | 1.33 | 1.01 | 1.08 | 0.00 | 0.00 | 0.00 | 1.58 | 0.08 | 0.00 |
time (sec) |
N/A | 0.776 | 0.320 | 0.079 | 0.000 | 0.000 | 0.000 | 0.131 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 177 | 107 | 114 | 0 | 0 | 0 | 174 | 12 | 0 |
N.S. |
1 | 1.23 | 0.74 | 0.79 | 0.00 | 0.00 | 0.00 | 1.21 | 0.08 | 0.00 |
time (sec) |
N/A | 0.793 | 0.293 | 0.060 | 0.000 | 0.000 | 0.000 | 0.130 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 177 | 112 | 117 | 0 | 0 | 0 | 148 | 12 | 0 |
N.S. |
1 | 1.26 | 0.79 | 0.83 | 0.00 | 0.00 | 0.00 | 1.05 | 0.09 | 0.00 |
time (sec) |
N/A | 1.059 | 0.231 | 0.046 | 0.000 | 0.000 | 0.000 | 0.129 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 106 | 86 | 60 | 0 | 0 | 0 | 92 | 10 | 0 |
N.S. |
1 | 1.09 | 0.89 | 0.62 | 0.00 | 0.00 | 0.00 | 0.95 | 0.10 | 0.00 |
time (sec) |
N/A | 0.676 | 0.120 | 0.057 | 0.000 | 0.000 | 0.000 | 0.127 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 91 | 70 | 63 | 0 | 0 | 0 | 66 | 8 | 0 |
N.S. |
1 | 1.17 | 0.90 | 0.81 | 0.00 | 0.00 | 0.00 | 0.85 | 0.10 | 0.00 |
time (sec) |
N/A | 0.553 | 0.070 | 0.034 | 0.000 | 0.000 | 0.000 | 0.122 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 201 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 20.10 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.171 | 2.762 | 0.050 | 3.836 | 0.074 | 0.615 | 0.175 | 0.191 | 0.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 230 | 12 | 12 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 23.00 | 1.20 | 1.20 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.171 | 10.228 | 0.074 | 4.483 | 0.069 | 0.752 | 0.245 | 0.183 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 137 | 100 | 144 | 0 | 99 | 85 | 0 | 31 | 0 |
N.S. |
1 | 1.14 | 0.83 | 1.20 | 0.00 | 0.82 | 0.71 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.291 | 0.023 | 1.397 | 0.000 | 0.108 | 71.051 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 136 | 66 | 138 | 0 | 85 | 85 | 0 | 27 | 0 |
N.S. |
1 | 1.10 | 0.53 | 1.11 | 0.00 | 0.69 | 0.69 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.354 | 0.018 | 0.651 | 0.000 | 0.100 | 11.428 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 97 | 66 | 119 | 0 | 68 | 85 | 0 | 23 | 0 |
N.S. |
1 | 1.10 | 0.75 | 1.35 | 0.00 | 0.77 | 0.97 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.254 | 0.012 | 0.429 | 0.000 | 0.089 | 4.493 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 94 | 45 | 98 | 0 | 53 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.06 | 0.51 | 1.10 | 0.00 | 0.60 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.298 | 0.011 | 0.305 | 0.000 | 0.086 | 0.000 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 40 | 85 | 0 | 49 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.00 | 0.73 | 1.55 | 0.00 | 0.89 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.247 | 0.010 | 0.201 | 0.000 | 0.084 | 0.000 | 0.000 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 133 | 42 | 129 | 0 | 70 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.06 | 0.34 | 1.03 | 0.00 | 0.56 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.391 | 0.012 | 0.332 | 0.000 | 0.090 | 0.000 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 113 | 90 | 0 | 0 | 0 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.04 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.442 | 0.037 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 113 | 90 | 0 | 0 | 0 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.04 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.398 | 0.033 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 109 | 90 | 0 | 0 | 0 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.02 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.401 | 0.033 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 107 | 87 | 0 | 0 | 0 | 0 | 0 | 60 | 0 |
N.S. |
1 | 1.02 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.449 | 0.031 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 87 | 0 | 0 | 0 | 0 | 0 | 67 | 0 |
N.S. |
1 | 1.00 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.414 | 0.034 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 16 | 421 | 53 | 17 | 0 | 67 | 18 |
N.S. |
1 | 1.00 | 1.11 | 0.89 | 23.39 | 2.94 | 0.94 | 0.00 | 3.72 | 1.00 |
time (sec) |
N/A | 0.437 | 52.467 | 0.165 | 3.298 | 0.109 | 86.864 | 0.000 | 0.259 | 0.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 16 | 398 | 44 | 17 | 0 | 61 | 18 |
N.S. |
1 | 1.00 | 1.11 | 0.89 | 22.11 | 2.44 | 0.94 | 0.00 | 3.39 | 1.00 |
time (sec) |
N/A | 0.408 | 118.977 | 0.125 | 3.547 | 0.093 | 9.263 | 0.000 | 0.215 | 0.145 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 16 | 438 | 50 | 0 | 18 | 66 | 18 |
N.S. |
1 | 1.00 | 1.11 | 0.89 | 24.33 | 2.78 | 0.00 | 1.00 | 3.67 | 1.00 |
time (sec) |
N/A | 0.380 | 60.015 | 0.175 | 3.314 | 0.085 | 0.000 | 0.408 | 0.208 | 0.145 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 16 | 469 | 50 | 0 | 18 | 86 | 18 |
N.S. |
1 | 1.00 | 1.11 | 0.89 | 26.06 | 2.78 | 0.00 | 1.00 | 4.78 | 1.00 |
time (sec) |
N/A | 0.374 | 47.672 | 0.164 | 3.325 | 0.086 | 0.000 | 0.477 | 0.226 | 0.140 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 16 | 18 | 20 | 15 | 18 | 20 | 18 |
N.S. |
1 | 1.00 | 1.11 | 0.89 | 1.00 | 1.11 | 0.83 | 1.00 | 1.11 | 1.00 |
time (sec) |
N/A | 0.213 | 1.508 | 0.134 | 0.255 | 0.076 | 4.935 | 0.149 | 0.180 | 0.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 16 | 18 | 18 | 15 | 18 | 18 | 18 |
N.S. |
1 | 1.00 | 1.11 | 0.89 | 1.00 | 1.00 | 0.83 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.217 | 1.347 | 0.148 | 0.251 | 0.067 | 0.615 | 0.148 | 0.176 | 0.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 16 | 18 | 23 | 17 | 18 | 22 | 18 |
N.S. |
1 | 1.00 | 1.11 | 0.89 | 1.00 | 1.28 | 0.94 | 1.00 | 1.22 | 1.00 |
time (sec) |
N/A | 0.199 | 0.752 | 0.148 | 0.324 | 0.069 | 2.257 | 0.129 | 0.194 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 16 | 18 | 31 | 17 | 18 | 27 | 18 |
N.S. |
1 | 1.00 | 1.11 | 0.89 | 1.00 | 1.72 | 0.94 | 1.00 | 1.50 | 1.00 |
time (sec) |
N/A | 0.197 | 0.668 | 0.198 | 0.338 | 0.073 | 3.999 | 0.141 | 0.195 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 16 | 182 | 34 | 17 | 18 | 34 | 18 |
N.S. |
1 | 1.00 | 1.11 | 0.89 | 10.11 | 1.89 | 0.94 | 1.00 | 1.89 | 1.00 |
time (sec) |
N/A | 0.195 | 7.215 | 0.139 | 1.684 | 0.076 | 12.209 | 0.169 | 0.194 | 0.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 16 | 180 | 32 | 17 | 18 | 32 | 18 |
N.S. |
1 | 1.00 | 1.11 | 0.89 | 10.00 | 1.78 | 0.94 | 1.00 | 1.78 | 1.00 |
time (sec) |
N/A | 0.191 | 7.393 | 0.151 | 1.756 | 0.073 | 2.448 | 0.157 | 0.204 | 0.123 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 16 | 195 | 39 | 19 | 18 | 38 | 18 |
N.S. |
1 | 1.00 | 1.11 | 0.89 | 10.83 | 2.17 | 1.06 | 1.00 | 2.11 | 1.00 |
time (sec) |
N/A | 0.197 | 21.046 | 0.151 | 1.574 | 0.087 | 6.471 | 0.138 | 0.196 | 0.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 16 | 219 | 51 | 19 | 18 | 44 | 18 |
N.S. |
1 | 1.00 | 1.11 | 0.89 | 12.17 | 2.83 | 1.06 | 1.00 | 2.44 | 1.00 |
time (sec) |
N/A | 0.195 | 14.385 | 0.212 | 1.772 | 0.083 | 12.941 | 0.140 | 0.199 | 0.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 12 | 115 | 14 | 12 | 14 | 16 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 9.58 | 1.17 | 1.00 | 1.17 | 1.33 | 1.17 |
time (sec) |
N/A | 0.362 | 0.464 | 0.691 | 0.594 | 0.085 | 6.097 | 0.433 | 0.190 | 0.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 12 | 115 | 14 | 12 | 14 | 16 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 9.58 | 1.17 | 1.00 | 1.17 | 1.33 | 1.17 |
time (sec) |
N/A | 0.352 | 0.437 | 0.676 | 0.548 | 0.088 | 4.306 | 0.422 | 0.197 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 148 | 122 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.99 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.378 | 0.030 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 56 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.220 | 0.014 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 12 | 14 | 14 | 10 | 14 | 16 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.17 | 0.83 | 1.17 | 1.33 | 1.17 |
time (sec) |
N/A | 0.186 | 0.237 | 0.455 | 0.192 | 0.073 | 0.448 | 0.281 | 0.178 | 0.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 12 | 157 | 14 | 12 | 14 | 16 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 13.08 | 1.17 | 1.00 | 1.17 | 1.33 | 1.17 |
time (sec) |
N/A | 0.178 | 0.245 | 0.501 | 0.761 | 0.082 | 1.091 | 0.297 | 0.215 | 0.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 120 | 192 | 143 | 0 | 0 | 0 | 247 | 11 | 0 |
N.S. |
1 | 0.99 | 1.59 | 1.18 | 0.00 | 0.00 | 0.00 | 2.04 | 0.09 | 0.00 |
time (sec) |
N/A | 0.507 | 0.043 | 0.137 | 0.000 | 0.000 | 0.000 | 0.177 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 94 | 131 | 90 | 0 | 0 | 0 | 153 | 11 | 0 |
N.S. |
1 | 0.99 | 1.38 | 0.95 | 0.00 | 0.00 | 0.00 | 1.61 | 0.12 | 0.00 |
time (sec) |
N/A | 0.467 | 0.025 | 0.100 | 0.000 | 0.000 | 0.000 | 0.172 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 88 | 126 | 96 | 0 | 0 | 0 | 165 | 11 | 0 |
N.S. |
1 | 1.02 | 1.47 | 1.12 | 0.00 | 0.00 | 0.00 | 1.92 | 0.13 | 0.00 |
time (sec) |
N/A | 0.462 | 0.030 | 0.072 | 0.000 | 0.000 | 0.000 | 0.172 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 57 | 74 | 42 | 0 | 0 | 0 | 71 | 9 | 0 |
N.S. |
1 | 0.97 | 1.25 | 0.71 | 0.00 | 0.00 | 0.00 | 1.20 | 0.15 | 0.00 |
time (sec) |
N/A | 0.409 | 0.014 | 0.054 | 0.000 | 0.000 | 0.000 | 0.160 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 66 | 49 | 0 | 0 | 0 | 83 | 7 | 0 |
N.S. |
1 | 1.00 | 1.50 | 1.11 | 0.00 | 0.00 | 0.00 | 1.89 | 0.16 | 0.00 |
time (sec) |
N/A | 0.420 | 0.019 | 0.046 | 0.000 | 0.000 | 0.000 | 0.143 | 0.177 | 0.000 |