Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 34 | 37 | 37 | 37 | 45 | 60 | 37 | 223 | 230 |
N.S. |
1 | 0.81 | 0.88 | 0.88 | 0.88 | 1.07 | 1.43 | 0.88 | 5.31 | 5.48 |
time (sec) |
N/A | 0.268 | 0.012 | 0.566 | 0.029 | 0.108 | 0.634 | 0.128 | 0.215 | 0.786 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F(-2) | A | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 36 | 40 | 140 | 40 | 58 | 0 | 40 | 58 | 58 |
N.S. |
1 | 0.80 | 0.89 | 3.11 | 0.89 | 1.29 | 0.00 | 0.89 | 1.29 | 1.29 |
time (sec) |
N/A | 0.285 | 0.025 | 7.032 | 0.028 | 0.123 | 0.000 | 0.130 | 0.180 | 0.649 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 149 | 86 | 260 | 0 | 76 | 138 | 94 | 159 | 0 |
N.S. |
1 | 1.03 | 0.60 | 1.81 | 0.00 | 0.53 | 0.96 | 0.65 | 1.10 | 0.00 |
time (sec) |
N/A | 0.306 | 0.051 | 0.514 | 0.000 | 0.101 | 0.988 | 0.219 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 119 | 74 | 212 | 0 | 65 | 107 | 80 | 137 | 0 |
N.S. |
1 | 1.03 | 0.64 | 1.83 | 0.00 | 0.56 | 0.92 | 0.69 | 1.18 | 0.00 |
time (sec) |
N/A | 0.262 | 0.036 | 0.023 | 0.000 | 0.103 | 0.432 | 0.218 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 89 | 59 | 164 | 0 | 49 | 73 | 63 | 138 | 0 |
N.S. |
1 | 1.01 | 0.67 | 1.86 | 0.00 | 0.56 | 0.83 | 0.72 | 1.57 | 0.00 |
time (sec) |
N/A | 0.242 | 0.028 | 0.023 | 0.000 | 0.104 | 0.150 | 0.189 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 288 | 189 | 171 | 0 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.66 | 0.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.754 | 1.651 | 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 | B | A | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 54 | 122 | 58 | 44 | 53 | 104 | 69 | 0 |
N.S. |
1 | 1.00 | 0.95 | 2.14 | 1.02 | 0.77 | 0.93 | 1.82 | 1.21 | 0.00 |
time (sec) |
N/A | 0.223 | 0.025 | 0.026 | 0.092 | 0.119 | 1.855 | 0.230 | 0.197 | 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 | 85 | 84 | 67 | 69 | 68 | 58 | 83 | 198 | 98 | 0 |
N.S. |
1 | 0.99 | 0.79 | 0.81 | 0.80 | 0.68 | 0.98 | 2.33 | 1.15 | 0.00 |
time (sec) |
N/A | 0.232 | 0.032 | 0.030 | 0.050 | 0.114 | 2.273 | 0.238 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 114 | 78 | 117 | 109 | 68 | 352 | 275 | 120 | 0 |
N.S. |
1 | 1.01 | 0.69 | 1.04 | 0.96 | 0.60 | 3.12 | 2.43 | 1.06 | 0.00 |
time (sec) |
N/A | 0.260 | 0.040 | 0.028 | 0.056 | 0.125 | 2.905 | 0.244 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 144 | 89 | 165 | 132 | 80 | 575 | 351 | 142 | 0 |
N.S. |
1 | 1.02 | 0.63 | 1.17 | 0.94 | 0.57 | 4.08 | 2.49 | 1.01 | 0.00 |
time (sec) |
N/A | 0.284 | 0.044 | 0.030 | 0.042 | 0.146 | 3.912 | 0.245 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 116 | 83 | 231 | 167 | 79 | 136 | 137 | 132 | 0 |
N.S. |
1 | 0.94 | 0.67 | 1.86 | 1.35 | 0.64 | 1.10 | 1.10 | 1.06 | 0.00 |
time (sec) |
N/A | 0.284 | 0.067 | 0.030 | 0.041 | 0.157 | 1.645 | 0.199 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 97 | 72 | 183 | 139 | 68 | 105 | 101 | 110 | 0 |
N.S. |
1 | 0.98 | 0.73 | 1.85 | 1.40 | 0.69 | 1.06 | 1.02 | 1.11 | 0.00 |
time (sec) |
N/A | 0.260 | 0.058 | 0.024 | 0.048 | 0.157 | 0.705 | 0.205 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 76 | 60 | 135 | 111 | 56 | 75 | 64 | 88 | 0 |
N.S. |
1 | 1.03 | 0.81 | 1.82 | 1.50 | 0.76 | 1.01 | 0.86 | 1.19 | 0.00 |
time (sec) |
N/A | 0.243 | 0.052 | 0.023 | 0.053 | 0.169 | 0.335 | 0.191 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 47 | 43 | 86 | 77 | 41 | 41 | 40 | 64 | 35 |
N.S. |
1 | 1.09 | 1.00 | 2.00 | 1.79 | 0.95 | 0.95 | 0.93 | 1.49 | 0.81 |
time (sec) |
N/A | 0.203 | 0.012 | 0.017 | 0.048 | 0.095 | 0.135 | 0.161 | 0.181 | 0.637 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 86 | 90 | 0 | 148 | 66 | 53 | 113 | 0 |
N.S. |
1 | 1.00 | 1.46 | 1.53 | 0.00 | 2.51 | 1.12 | 0.90 | 1.92 | 0.00 |
time (sec) |
N/A | 0.229 | 0.040 | 0.030 | 0.000 | 0.121 | 2.075 | 0.200 | 0.192 | 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 | 91 | 85 | 101 | 130 | 0 | 198 | 82 | 89 | 137 | 0 |
N.S. |
1 | 0.93 | 1.11 | 1.43 | 0.00 | 2.18 | 0.90 | 0.98 | 1.51 | 0.00 |
time (sec) |
N/A | 0.240 | 0.060 | 0.027 | 0.000 | 0.137 | 4.028 | 0.198 | 0.199 | 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 | 119 | 115 | 114 | 178 | 0 | 228 | 148 | 116 | 162 | 0 |
N.S. |
1 | 0.97 | 0.96 | 1.50 | 0.00 | 1.92 | 1.24 | 0.97 | 1.36 | 0.00 |
time (sec) |
N/A | 0.251 | 0.075 | 0.029 | 0.000 | 0.143 | 6.659 | 0.192 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 218 | 170 | 0 | 0 | 96 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.03 | 0.81 | 0.00 | 0.00 | 0.45 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.321 | 11.391 | 0.000 | 0.000 | 0.146 | 0.000 | 0.000 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 186 | 158 | 0 | 0 | 85 | 75 | 0 | 24 | 0 |
N.S. |
1 | 1.03 | 0.87 | 0.00 | 0.00 | 0.47 | 0.41 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.306 | 0.296 | 0.000 | 0.000 | 0.135 | 41.386 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 154 | 147 | 0 | 0 | 71 | 75 | 0 | 21 | 0 |
N.S. |
1 | 1.01 | 0.96 | 0.00 | 0.00 | 0.46 | 0.49 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.278 | 0.202 | 0.000 | 0.000 | 0.129 | 9.094 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 122 | 115 | 0 | 0 | 52 | 71 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.00 | 0.00 | 0.43 | 0.58 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.252 | 0.096 | 0.000 | 0.000 | 0.110 | 8.789 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 154 | 150 | 0 | 0 | 73 | 78 | 0 | 24 | 0 |
N.S. |
1 | 0.99 | 0.96 | 0.00 | 0.00 | 0.47 | 0.50 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.279 | 0.191 | 0.000 | 0.000 | 0.121 | 43.998 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 186 | 162 | 0 | 0 | 86 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.46 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.309 | 0.222 | 0.000 | 0.000 | 0.109 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 218 | 171 | 0 | 0 | 97 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.01 | 0.79 | 0.00 | 0.00 | 0.45 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.328 | 0.402 | 0.000 | 0.000 | 0.122 | 0.000 | 0.000 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 326 | 321 | 139 | 0 | 0 | 94 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.98 | 0.43 | 0.00 | 0.00 | 0.29 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.442 | 10.112 | 0.000 | 0.000 | 0.138 | 0.000 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 296 | 289 | 119 | 0 | 0 | 79 | 75 | 0 | 22 | 0 |
N.S. |
1 | 0.98 | 0.40 | 0.00 | 0.00 | 0.27 | 0.25 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.391 | 0.076 | 0.000 | 0.000 | 0.127 | 10.341 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 260 | 253 | 89 | 0 | 0 | 55 | 71 | 0 | 24 | 0 |
N.S. |
1 | 0.97 | 0.34 | 0.00 | 0.00 | 0.21 | 0.27 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.350 | 0.072 | 0.000 | 0.000 | 0.118 | 9.590 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 298 | 285 | 121 | 0 | 0 | 80 | 78 | 0 | 24 | 0 |
N.S. |
1 | 0.96 | 0.41 | 0.00 | 0.00 | 0.27 | 0.26 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.399 | 0.091 | 0.000 | 0.000 | 0.122 | 10.401 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 331 | 317 | 137 | 0 | 0 | 94 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.96 | 0.41 | 0.00 | 0.00 | 0.28 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.426 | 0.082 | 0.000 | 0.000 | 0.110 | 0.000 | 0.000 | 0.221 | 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 | 50 | 50 | 50 | 43 | 42 | 47 | 41 | 43 | 55 | 42 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.84 | 0.94 | 0.82 | 0.86 | 1.10 | 0.84 |
time (sec) |
N/A | 0.290 | 0.013 | 1.006 | 0.117 | 0.093 | 0.288 | 0.127 | 0.182 | 0.735 |
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 | 40 | 40 | 42 | 36 | 39 | 38 | 34 | 38 | 39 | 39 |
N.S. |
1 | 1.00 | 1.05 | 0.90 | 0.98 | 0.95 | 0.85 | 0.95 | 0.98 | 0.98 |
time (sec) |
N/A | 0.247 | 0.130 | 1.234 | 0.872 | 0.125 | 4.157 | 0.347 | 0.621 | 0.850 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 431 | 429 | 0 | 1664 | 0 | 0 | 0 | 0 | 150 | 0 |
N.S. |
1 | 1.00 | 0.00 | 3.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 1.105 | 0.000 | 1.542 | 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 | F | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 283 | 285 | 0 | 916 | 0 | 0 | 0 | 0 | 108 | 0 |
N.S. |
1 | 1.01 | 0.00 | 3.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.802 | 0.000 | 0.121 | 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 | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 93 | 93 | 368 | 0 | 0 | 0 | 0 | 64 | 0 |
N.S. |
1 | 0.95 | 0.95 | 3.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.324 | 0.028 | 0.109 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 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 | 40 | 40 | 42 | 36 | 39 | 48 | 61 | 38 | 63 | 39 |
N.S. |
1 | 1.00 | 1.05 | 0.90 | 0.98 | 1.20 | 1.52 | 0.95 | 1.58 | 0.98 |
time (sec) |
N/A | 0.241 | 0.196 | 0.651 | 0.338 | 0.089 | 3.309 | 0.204 | 0.190 | 0.596 |
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 | 40 | 40 | 42 | 36 | 163 | 91 | 126 | 38 | 123 | 39 |
N.S. |
1 | 1.00 | 1.05 | 0.90 | 4.08 | 2.28 | 3.15 | 0.95 | 3.08 | 0.98 |
time (sec) |
N/A | 0.249 | 0.893 | 0.612 | 0.429 | 0.085 | 7.168 | 0.322 | 0.213 | 1.415 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 34 | 41 | 38 | 33 | 158 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.11 | 1.03 | 0.89 | 4.27 | 0.00 | 1.03 | 0.00 |
time (sec) |
N/A | 0.187 | 0.045 | 0.440 | 0.049 | 0.093 | 0.811 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 20 | 20 | 81 | 13 | 32 | 0 | 13 | 19 |
N.S. |
1 | 1.00 | 0.87 | 0.87 | 3.52 | 0.57 | 1.39 | 0.00 | 0.57 | 0.83 |
time (sec) |
N/A | 0.167 | 0.013 | 0.091 | 0.039 | 0.077 | 0.156 | 0.000 | 0.196 | 0.139 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 20 | 20 | 57 | 13 | 32 | 0 | 11 | 19 |
N.S. |
1 | 1.00 | 0.87 | 0.87 | 2.48 | 0.57 | 1.39 | 0.00 | 0.48 | 0.83 |
time (sec) |
N/A | 0.177 | 0.011 | 0.041 | 0.030 | 0.078 | 0.097 | 0.000 | 0.188 | 0.071 |
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 | 16 | 16 | 18 | 15 | 12 | 10 | 42 | 26 | 14 | 16 |
N.S. |
1 | 1.00 | 1.12 | 0.94 | 0.75 | 0.62 | 2.62 | 1.62 | 0.88 | 1.00 |
time (sec) |
N/A | 0.153 | 0.005 | 0.097 | 0.032 | 0.074 | 0.076 | 0.121 | 0.188 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 19 | 23 | 42 | 8 | 34 | 0 | 13 | 0 |
N.S. |
1 | 1.00 | 0.90 | 1.10 | 2.00 | 0.38 | 1.62 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.190 | 0.011 | 0.071 | 0.113 | 0.102 | 0.388 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 31 | 56 | 40 | 42 | 160 | 62 | 47 | 0 |
N.S. |
1 | 1.00 | 0.86 | 1.56 | 1.11 | 1.17 | 4.44 | 1.72 | 1.31 | 0.00 |
time (sec) |
N/A | 0.181 | 0.035 | 0.523 | 0.027 | 0.087 | 2.049 | 0.134 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 20 | 26 | 17 | 17 | 26 | 19 | 22 | 25 |
N.S. |
1 | 1.00 | 0.87 | 1.13 | 0.74 | 0.74 | 1.13 | 0.83 | 0.96 | 1.09 |
time (sec) |
N/A | 0.163 | 0.013 | 0.278 | 0.051 | 0.088 | 0.130 | 0.129 | 0.192 | 0.502 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 20 | 26 | 17 | 17 | 26 | 19 | 20 | 25 |
N.S. |
1 | 1.00 | 0.87 | 1.13 | 0.74 | 0.74 | 1.13 | 0.83 | 0.87 | 1.09 |
time (sec) |
N/A | 0.182 | 0.012 | 0.077 | 0.026 | 0.079 | 0.093 | 0.129 | 0.182 | 0.080 |
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 | 16 | 16 | 18 | 22 | 15 | 15 | 24 | 15 | 21 | 21 |
N.S. |
1 | 1.00 | 1.12 | 1.38 | 0.94 | 0.94 | 1.50 | 0.94 | 1.31 | 1.31 |
time (sec) |
N/A | 0.159 | 0.006 | 0.091 | 0.044 | 0.070 | 0.103 | 0.127 | 0.186 | 0.450 |
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 | 19 | 19 | 19 | 27 | 14 | 14 | 27 | 15 | 21 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.42 | 0.74 | 0.74 | 1.42 | 0.79 | 1.11 | 0.00 |
time (sec) |
N/A | 0.182 | 0.013 | 0.093 | 0.033 | 0.084 | 1.615 | 0.126 | 0.185 | 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 | 16 | 16 | 18 | 15 | 12 | 10 | 42 | 26 | 14 | 16 |
N.S. |
1 | 1.00 | 1.12 | 0.94 | 0.75 | 0.62 | 2.62 | 1.62 | 0.88 | 1.00 |
time (sec) |
N/A | 0.158 | 0.000 | 0.000 | 0.028 | 0.092 | 0.089 | 0.129 | 0.180 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 403 | 519 | 371 | 8039 | 0 | 1965 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.29 | 0.92 | 19.95 | 0.00 | 4.88 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.567 | 2.878 | 49.339 | 0.000 | 0.183 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 305 | 396 | 281 | 7647 | 0 | 1545 | 0 | 0 | 15 | 0 |
N.S. |
1 | 1.30 | 0.92 | 25.07 | 0.00 | 5.07 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.148 | 2.576 | 3.917 | 0.000 | 0.164 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 277 | 549 | 1001 | 433 | 1101 | 0 | 0 | 13 | 0 |
N.S. |
1 | 1.40 | 2.77 | 5.06 | 2.19 | 5.56 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.707 | 5.102 | 2.898 | 0.205 | 0.167 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-1) | 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 | 15 | 15 | 17 | 15 | 0 | 17 | 14 | 17 | 17 | 17 |
N.S. |
1 | 1.00 | 1.13 | 1.00 | 0.00 | 1.13 | 0.93 | 1.13 | 1.13 | 1.13 |
time (sec) |
N/A | 0.312 | 1.858 | 0.441 | 0.000 | 0.091 | 71.748 | 0.776 | 0.200 | 0.577 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | B | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 198 | 140 | 1487 | 310 | 322 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.29 | 0.91 | 9.66 | 2.01 | 2.09 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.837 | 0.259 | 4.920 | 0.058 | 0.127 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | B | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 155 | 110 | 1452 | 218 | 271 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.26 | 0.89 | 11.80 | 1.77 | 2.20 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.660 | 0.156 | 1.335 | 0.059 | 0.103 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 107 | 967 | 563 | 448 | 202 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.26 | 11.38 | 6.62 | 5.27 | 2.38 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.449 | 8.552 | 1.550 | 0.170 | 0.102 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 23 | 19 | 0 | 37 | 0 | 21 | 24 | 22 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 0.00 | 1.76 | 0.00 | 1.00 | 1.14 | 1.05 |
time (sec) |
N/A | 0.312 | 0.443 | 0.552 | 0.000 | 0.090 | 0.000 | 0.692 | 0.194 | 0.703 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | B | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 199 | 137 | 1488 | 310 | 322 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.28 | 0.88 | 9.60 | 2.00 | 2.08 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.804 | 0.269 | 5.005 | 0.070 | 0.110 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | B | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 156 | 111 | 1453 | 218 | 271 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.26 | 0.90 | 11.72 | 1.76 | 2.19 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.623 | 0.176 | 1.498 | 0.055 | 0.098 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 108 | 847 | 594 | 448 | 200 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.26 | 9.85 | 6.91 | 5.21 | 2.33 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.454 | 6.252 | 1.592 | 0.198 | 0.091 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 23 | 19 | 0 | 37 | 0 | 21 | 26 | 22 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 0.00 | 1.76 | 0.00 | 1.00 | 1.24 | 1.05 |
time (sec) |
N/A | 0.320 | 0.734 | 0.451 | 0.000 | 0.098 | 0.000 | 0.857 | 0.190 | 0.854 |
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 | 16 | 16 | 18 | 22 | 15 | 15 | 24 | 15 | 21 | 21 |
N.S. |
1 | 1.00 | 1.12 | 1.38 | 0.94 | 0.94 | 1.50 | 0.94 | 1.31 | 1.31 |
time (sec) |
N/A | 0.156 | 0.001 | 0.017 | 0.038 | 0.069 | 0.080 | 0.120 | 0.186 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 399 | 515 | 360 | 7869 | 0 | 1589 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.29 | 0.90 | 19.72 | 0.00 | 3.98 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.555 | 2.655 | 60.347 | 0.000 | 0.271 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 303 | 394 | 275 | 7501 | 0 | 1289 | 0 | 0 | 15 | 0 |
N.S. |
1 | 1.30 | 0.91 | 24.76 | 0.00 | 4.25 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.133 | 2.107 | 4.211 | 0.000 | 0.236 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 277 | 702 | 1145 | 532 | 965 | 0 | 0 | 13 | 0 |
N.S. |
1 | 1.40 | 3.55 | 5.78 | 2.69 | 4.87 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.689 | 9.774 | 4.129 | 0.212 | 0.220 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-1) | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 17 | 15 | 0 | 17 | 0 | 17 | 17 | 17 |
N.S. |
1 | 1.00 | 1.13 | 1.00 | 0.00 | 1.13 | 0.00 | 1.13 | 1.13 | 1.13 |
time (sec) |
N/A | 0.298 | 1.692 | 0.493 | 0.000 | 0.092 | 0.000 | 2.654 | 0.194 | 0.631 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 198 | 136 | 1487 | 309 | 166 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.29 | 0.88 | 9.66 | 2.01 | 1.08 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.811 | 0.240 | 5.201 | 0.083 | 0.094 | 0.000 | 0.000 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 155 | 110 | 1452 | 217 | 144 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.26 | 0.89 | 11.80 | 1.76 | 1.17 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.675 | 0.160 | 1.483 | 0.065 | 0.099 | 0.000 | 0.000 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | A | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 107 | 929 | 584 | 458 | 112 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.26 | 10.93 | 6.87 | 5.39 | 1.32 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.463 | 9.465 | 1.727 | 0.145 | 0.093 | 0.000 | 0.000 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 23 | 23 | 0 | 37 | 0 | 25 | 30 | 23 |
N.S. |
1 | 1.00 | 1.10 | 1.10 | 0.00 | 1.76 | 0.00 | 1.19 | 1.43 | 1.10 |
time (sec) |
N/A | 0.302 | 0.473 | 0.865 | 0.000 | 0.086 | 0.000 | 1.540 | 0.194 | 0.883 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 199 | 140 | 1488 | 311 | 166 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.28 | 0.90 | 9.60 | 2.01 | 1.07 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.848 | 0.250 | 4.981 | 0.058 | 0.098 | 0.000 | 0.000 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 156 | 110 | 1453 | 219 | 144 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.26 | 0.89 | 11.72 | 1.77 | 1.16 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.644 | 0.163 | 1.536 | 0.067 | 0.092 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | A | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 108 | 872 | 625 | 458 | 112 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.26 | 10.14 | 7.27 | 5.33 | 1.30 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.448 | 5.750 | 1.597 | 0.155 | 0.083 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 23 | 23 | 0 | 37 | 0 | 25 | 28 | 23 |
N.S. |
1 | 1.00 | 1.10 | 1.10 | 0.00 | 1.76 | 0.00 | 1.19 | 1.33 | 1.10 |
time (sec) |
N/A | 0.304 | 0.481 | 0.825 | 0.000 | 0.086 | 0.000 | 1.750 | 0.200 | 0.944 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 56 | 52 | 0 | 58 | 0 | 0 | 5 | 0 |
N.S. |
1 | 1.00 | 1.44 | 1.33 | 0.00 | 1.49 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.302 | 0.038 | 2.021 | 0.000 | 0.116 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 77 | 93 | 632 | 0 | 93 | 0 | 0 | 7 | 0 |
N.S. |
1 | 1.04 | 1.26 | 8.54 | 0.00 | 1.26 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.434 | 0.035 | 1.305 | 0.000 | 0.108 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 113 | 121 | 658 | 0 | 125 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.05 | 1.12 | 6.09 | 0.00 | 1.16 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.576 | 0.064 | 1.911 | 0.000 | 0.095 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 327 | 600 | 3570 | 0 | 1460 | 0 | 0 | 67 | 0 |
N.S. |
1 | 1.09 | 2.01 | 11.94 | 0.00 | 4.88 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 1.150 | 0.671 | 38.757 | 0.000 | 0.206 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 251 | 375 | 2668 | 0 | 1002 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.10 | 1.64 | 11.65 | 0.00 | 4.38 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.869 | 0.349 | 26.380 | 0.000 | 0.164 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 175 | 237 | 1776 | 0 | 600 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.10 | 1.49 | 11.17 | 0.00 | 3.77 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.588 | 0.194 | 2.996 | 0.000 | 0.134 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 80 | 91 | 107 | 0 | 334 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.08 | 1.23 | 1.45 | 0.00 | 4.51 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.350 | 0.020 | 1.533 | 0.000 | 0.147 | 0.000 | 0.000 | 0.180 | 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 | 15 | 15 | 17 | 15 | 17 | 17 | 14 | 3 | 17 | 17 |
N.S. |
1 | 1.00 | 1.13 | 1.00 | 1.13 | 1.13 | 0.93 | 0.20 | 1.13 | 1.13 |
time (sec) |
N/A | 0.213 | 10.976 | 0.768 | 1.617 | 0.094 | 3.796 | 87.325 | 0.190 | 0.508 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 355 | 441 | 438 | 6917 | 0 | 1289 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.24 | 1.23 | 19.48 | 0.00 | 3.63 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.448 | 0.853 | 50.624 | 0.000 | 0.180 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 267 | 343 | 330 | 6567 | 0 | 1067 | 0 | 0 | 15 | 0 |
N.S. |
1 | 1.28 | 1.24 | 24.60 | 0.00 | 4.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.104 | 0.726 | 3.451 | 0.000 | 0.170 | 0.000 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 237 | 288 | 352 | 0 | 825 | 0 | 0 | 13 | 0 |
N.S. |
1 | 1.36 | 1.66 | 2.02 | 0.00 | 4.74 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.664 | 2.217 | 1.431 | 0.000 | 0.250 | 0.000 | 0.000 | 0.199 | 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 | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 17 | 15 | 17 | 17 | 0 | 17 | 17 | 17 |
N.S. |
1 | 1.00 | 1.13 | 1.00 | 1.13 | 1.13 | 0.00 | 1.13 | 1.13 | 1.13 |
time (sec) |
N/A | 0.295 | 5.830 | 0.135 | 1.049 | 0.091 | 0.000 | 0.354 | 0.188 | 0.610 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 167 | 134 | 1406 | 129 | 293 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.18 | 0.94 | 9.90 | 0.91 | 2.06 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.902 | 0.145 | 1.135 | 1.372 | 0.137 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 132 | 103 | 1370 | 106 | 247 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.17 | 0.91 | 12.12 | 0.94 | 2.19 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.668 | 0.074 | 0.542 | 1.463 | 0.126 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 92 | 71 | 545 | 80 | 187 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.16 | 0.90 | 6.90 | 1.01 | 2.37 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.434 | 1.441 | 0.536 | 1.526 | 0.112 | 0.000 | 0.000 | 0.207 | 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 | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 21 | 17 | 72 | 37 | 0 | 19 | 25 | 20 |
N.S. |
1 | 1.00 | 1.11 | 0.89 | 3.79 | 1.95 | 0.00 | 1.00 | 1.32 | 1.05 |
time (sec) |
N/A | 0.294 | 2.933 | 0.189 | 0.583 | 0.111 | 0.000 | 0.173 | 0.197 | 0.943 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 170 | 134 | 1417 | 129 | 293 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.17 | 0.92 | 9.77 | 0.89 | 2.02 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.797 | 0.151 | 1.291 | 1.423 | 0.109 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 136 | 103 | 1381 | 107 | 247 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.17 | 0.89 | 11.91 | 0.92 | 2.13 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.646 | 0.084 | 0.680 | 1.362 | 0.105 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 96 | 71 | 516 | 80 | 187 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.17 | 0.87 | 6.29 | 0.98 | 2.28 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.452 | 1.472 | 0.698 | 1.368 | 0.101 | 0.000 | 0.000 | 0.217 | 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 | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 77 | 37 | 0 | 19 | 26 | 20 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 3.50 | 1.68 | 0.00 | 0.86 | 1.18 | 0.91 |
time (sec) |
N/A | 0.292 | 2.955 | 0.260 | 0.513 | 0.077 | 0.000 | 0.174 | 0.205 | 0.943 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 327 | 600 | 3570 | 0 | 1460 | 0 | 0 | 67 | 0 |
N.S. |
1 | 1.09 | 2.01 | 11.94 | 0.00 | 4.88 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 1.182 | 0.267 | 7.812 | 0.000 | 0.189 | 0.000 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 251 | 375 | 2668 | 0 | 1002 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.10 | 1.64 | 11.65 | 0.00 | 4.38 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.856 | 0.162 | 4.629 | 0.000 | 0.154 | 0.000 | 0.000 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 175 | 237 | 1777 | 0 | 600 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.10 | 1.49 | 11.18 | 0.00 | 3.77 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.589 | 0.105 | 0.605 | 0.000 | 0.159 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 79 | 91 | 106 | 0 | 334 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.08 | 1.25 | 1.45 | 0.00 | 4.58 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.378 | 0.019 | 0.293 | 0.000 | 0.141 | 0.000 | 0.000 | 0.194 | 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 | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 17 | 15 | 17 | 17 | 0 | 3 | 17 | 17 |
N.S. |
1 | 1.00 | 1.13 | 1.00 | 1.13 | 1.13 | 0.00 | 0.20 | 1.13 | 1.13 |
time (sec) |
N/A | 0.244 | 0.657 | 0.092 | 1.958 | 0.082 | 0.000 | 73.997 | 0.209 | 0.547 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 351 | 437 | 442 | 6845 | 0 | 1269 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.25 | 1.26 | 19.50 | 0.00 | 3.62 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.506 | 0.872 | 16.229 | 0.000 | 0.188 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 265 | 339 | 334 | 6495 | 0 | 1051 | 0 | 0 | 15 | 0 |
N.S. |
1 | 1.28 | 1.26 | 24.51 | 0.00 | 3.97 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.175 | 0.634 | 2.719 | 0.000 | 0.251 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 237 | 287 | 352 | 0 | 813 | 0 | 0 | 13 | 0 |
N.S. |
1 | 1.36 | 1.65 | 2.02 | 0.00 | 4.67 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.689 | 1.919 | 1.568 | 0.000 | 0.221 | 0.000 | 0.000 | 0.189 | 0.000 |