Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 34 | 43 | 130 | 41 | 0 | 0 | 52 | 46 |
N.S. |
1 | 1.00 | 1.00 | 1.26 | 3.82 | 1.21 | 0.00 | 0.00 | 1.53 | 1.35 |
time (sec) |
N/A | 0.239 | 0.078 | 3.508 | 0.139 | 0.079 | 0.000 | 0.000 | 0.187 | 15.922 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 46 | 50 | 210 | 67 | 0 | 0 | 56 | 77 |
N.S. |
1 | 1.00 | 0.61 | 0.66 | 2.76 | 0.88 | 0.00 | 0.00 | 0.74 | 1.01 |
time (sec) |
N/A | 0.408 | 0.073 | 4.908 | 0.144 | 0.122 | 0.000 | 0.000 | 0.193 | 16.598 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 118 | 56 | 119 | 287 | 81 | 0 | 0 | 56 | 120 |
N.S. |
1 | 1.03 | 0.49 | 1.03 | 2.50 | 0.70 | 0.00 | 0.00 | 0.49 | 1.04 |
time (sec) |
N/A | 0.577 | 0.096 | 8.321 | 0.148 | 0.098 | 0.000 | 0.000 | 0.242 | 16.640 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 162 | 66 | 161 | 363 | 93 | 0 | 0 | 56 | 261 |
N.S. |
1 | 1.05 | 0.43 | 1.05 | 2.36 | 0.60 | 0.00 | 0.00 | 0.36 | 1.69 |
time (sec) |
N/A | 0.748 | 0.186 | 12.052 | 0.161 | 0.104 | 0.000 | 0.000 | 0.280 | 20.596 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 247 | 254 | 80 | 712 | 0 | 377 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.03 | 0.32 | 2.88 | 0.00 | 1.53 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 1.032 | 0.155 | 11.435 | 0.000 | 0.199 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 215 | 214 | 80 | 692 | 0 | 481 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.00 | 0.37 | 3.22 | 0.00 | 2.24 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.861 | 0.160 | 9.608 | 0.000 | 0.185 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 236 | 246 | 80 | 864 | 0 | 400 | 0 | 0 | 147 | 0 |
N.S. |
1 | 1.04 | 0.34 | 3.66 | 0.00 | 1.69 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 1.011 | 0.133 | 8.532 | 0.000 | 0.149 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 49 | 96 | 131 | 100 | 0 | 0 | 47 | 82 |
N.S. |
1 | 1.00 | 1.36 | 2.67 | 3.64 | 2.78 | 0.00 | 0.00 | 1.31 | 2.28 |
time (sec) |
N/A | 0.244 | 0.081 | 5.026 | 0.151 | 0.082 | 0.000 | 0.000 | 0.180 | 16.457 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 59 | 133 | 211 | 71 | 0 | 0 | 68 | 95 |
N.S. |
1 | 1.00 | 0.78 | 1.75 | 2.78 | 0.93 | 0.00 | 0.00 | 0.89 | 1.25 |
time (sec) |
N/A | 0.388 | 0.136 | 6.634 | 0.155 | 0.125 | 0.000 | 0.000 | 0.171 | 16.777 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 120 | 56 | 129 | 294 | 99 | 0 | 0 | 74 | 119 |
N.S. |
1 | 1.04 | 0.49 | 1.12 | 2.56 | 0.86 | 0.00 | 0.00 | 0.64 | 1.03 |
time (sec) |
N/A | 0.566 | 0.123 | 8.303 | 0.151 | 0.103 | 0.000 | 0.000 | 0.184 | 17.439 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 162 | 66 | 190 | 373 | 115 | 0 | 0 | 74 | 230 |
N.S. |
1 | 1.05 | 0.43 | 1.23 | 2.42 | 0.75 | 0.00 | 0.00 | 0.48 | 1.49 |
time (sec) |
N/A | 0.747 | 0.182 | 9.091 | 0.168 | 0.089 | 0.000 | 0.000 | 0.169 | 20.147 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 206 | 76 | 216 | 451 | 125 | 0 | 0 | 74 | 413 |
N.S. |
1 | 1.07 | 0.39 | 1.12 | 2.34 | 0.65 | 0.00 | 0.00 | 0.38 | 2.14 |
time (sec) |
N/A | 0.945 | 0.301 | 11.507 | 0.168 | 0.089 | 0.000 | 0.000 | 0.168 | 22.570 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 301 | 80 | 711 | 0 | 510 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.15 | 0.31 | 2.72 | 0.00 | 1.95 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 1.256 | 0.223 | 20.738 | 0.000 | 0.193 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 250 | 80 | 890 | 0 | 428 | 0 | 0 | 416 | 0 |
N.S. |
1 | 1.05 | 0.33 | 3.72 | 0.00 | 1.79 | 0.00 | 0.00 | 1.74 | 0.00 |
time (sec) |
N/A | 1.043 | 0.132 | 14.152 | 0.000 | 0.151 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 218 | 215 | 80 | 984 | 0 | 601 | 0 | 0 | 68 | 0 |
N.S. |
1 | 0.99 | 0.37 | 4.51 | 0.00 | 2.76 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.839 | 0.143 | 12.240 | 0.000 | 0.147 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 49 | 59 | 131 | 70 | 0 | 0 | 264 | 102 |
N.S. |
1 | 1.00 | 1.36 | 1.64 | 3.64 | 1.94 | 0.00 | 0.00 | 7.33 | 2.83 |
time (sec) |
N/A | 0.257 | 0.125 | 6.111 | 0.147 | 0.084 | 0.000 | 0.000 | 0.175 | 17.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 59 | 168 | 207 | 148 | 0 | 0 | 57 | 145 |
N.S. |
1 | 1.00 | 0.78 | 2.21 | 2.72 | 1.95 | 0.00 | 0.00 | 0.75 | 1.91 |
time (sec) |
N/A | 0.394 | 0.111 | 9.187 | 0.142 | 0.086 | 0.000 | 0.000 | 0.164 | 17.419 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 120 | 56 | 207 | 287 | 98 | 0 | 0 | 84 | 137 |
N.S. |
1 | 1.04 | 0.49 | 1.80 | 2.50 | 0.85 | 0.00 | 0.00 | 0.73 | 1.19 |
time (sec) |
N/A | 0.551 | 0.179 | 11.312 | 0.158 | 0.112 | 0.000 | 0.000 | 0.170 | 17.732 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 164 | 66 | 184 | 373 | 130 | 0 | 0 | 92 | 261 |
N.S. |
1 | 1.06 | 0.43 | 1.19 | 2.42 | 0.84 | 0.00 | 0.00 | 0.60 | 1.69 |
time (sec) |
N/A | 0.733 | 0.152 | 12.816 | 0.166 | 0.102 | 0.000 | 0.000 | 0.183 | 20.564 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 206 | 76 | 242 | 451 | 144 | 0 | 0 | 92 | 379 |
N.S. |
1 | 1.07 | 0.39 | 1.25 | 2.34 | 0.75 | 0.00 | 0.00 | 0.48 | 1.96 |
time (sec) |
N/A | 0.951 | 0.293 | 13.293 | 0.157 | 0.116 | 0.000 | 0.000 | 0.167 | 21.634 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 78 | 77 | 0 | 0 | 0 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.01 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.323 | 0.172 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 78 | 77 | 0 | 0 | 0 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.01 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.311 | 0.127 | 0.000 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 78 | 77 | 0 | 0 | 0 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.01 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.322 | 0.091 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.211 | 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 | 77 | 78 | 77 | 0 | 0 | 0 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.01 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.307 | 0.099 | 0.000 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 77 | 0 | 0 | 0 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.299 | 0.092 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 75 | 0 | 0 | 0 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.317 | 0.108 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 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 | 95 | 121 | 94 | 0 | 0 | 0 | 0 | 0 | 145 | 0 |
N.S. |
1 | 1.27 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.53 | 0.00 |
time (sec) |
N/A | 0.313 | 0.130 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 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 | 95 | 121 | 94 | 0 | 0 | 0 | 0 | 0 | 100 | 0 |
N.S. |
1 | 1.27 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.05 | 0.00 |
time (sec) |
N/A | 0.290 | 0.113 | 0.000 | 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 | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 119 | 92 | 0 | 0 | 0 | 0 | 0 | 55 | 0 |
N.S. |
1 | 1.28 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.268 | 0.596 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 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 | 95 | 121 | 94 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.27 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.305 | 0.169 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.187 | 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 | 93 | 121 | 94 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.30 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.302 | 0.179 | 0.000 | 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 | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 121 | 94 | 0 | 0 | 0 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.30 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.301 | 0.169 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 144 | 102 | 0 | 0 | 0 | 0 | 0 | 86 | 0 |
N.S. |
1 | 1.38 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.356 | 0.242 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.227 | 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 | 104 | 144 | 101 | 0 | 0 | 0 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.38 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.326 | 0.215 | 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 | 100 | 149 | 98 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.49 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.325 | 0.397 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.284 | 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 | 98 | 139 | 97 | 0 | 0 | 0 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.42 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.343 | 0.109 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 144 | 101 | 0 | 0 | 0 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.38 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.341 | 0.183 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 144 | 102 | 0 | 0 | 0 | 0 | 0 | 59 | 0 |
N.S. |
1 | 1.38 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.340 | 0.158 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 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 | 111 | 162 | 112 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.46 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.330 | 0.212 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 99 | 89 | 212 | 520 | 153 | 0 | 517 | 23 | 555 |
N.S. |
1 | 0.91 | 0.82 | 1.94 | 4.77 | 1.40 | 0.00 | 4.74 | 0.21 | 5.09 |
time (sec) |
N/A | 0.282 | 0.717 | 7.120 | 0.044 | 0.114 | 0.000 | 0.132 | 200.022 | 19.486 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 74 | 68 | 136 | 266 | 102 | 5534 | 294 | 23 | 195 |
N.S. |
1 | 0.91 | 0.84 | 1.68 | 3.28 | 1.26 | 68.32 | 3.63 | 0.28 | 2.41 |
time (sec) |
N/A | 0.261 | 0.344 | 2.056 | 0.039 | 0.109 | 38.103 | 0.148 | 0.335 | 1.215 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 51 | 52 | 68 | 111 | 61 | 1114 | 137 | 23 | 85 |
N.S. |
1 | 0.93 | 0.95 | 1.24 | 2.02 | 1.11 | 20.25 | 2.49 | 0.42 | 1.55 |
time (sec) |
N/A | 0.253 | 0.124 | 0.766 | 0.038 | 0.101 | 3.684 | 0.140 | 0.189 | 0.437 |
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 | 26 | 26 | 26 | 27 | 26 | 28 | 80 | 26 | 29 | 29 |
N.S. |
1 | 1.00 | 1.00 | 1.04 | 1.00 | 1.08 | 3.08 | 1.00 | 1.12 | 1.12 |
time (sec) |
N/A | 0.209 | 0.075 | 2.485 | 0.031 | 0.090 | 0.549 | 0.120 | 0.159 | 0.126 |
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 | 40 | 45 | 63 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.12 | 1.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.226 | 0.121 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 52 | 111 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.11 | 2.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.241 | 0.363 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 56 | 163 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.10 | 3.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.237 | 0.729 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 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 | 78 | 83 | 78 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.06 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.291 | 0.149 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 2.125 | 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 | 78 | 81 | 78 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.04 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.279 | 0.115 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 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 | 73 | 73 | 73 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.291 | 0.225 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 83 | 78 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.06 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.289 | 0.179 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 88 | 85 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.04 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.285 | 0.211 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 88 | 85 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.04 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.297 | 0.159 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 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 | 85 | 88 | 85 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.04 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.292 | 0.105 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 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 | 83 | 86 | 83 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.04 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.305 | 0.102 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 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 | 82 | 82 | 82 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.309 | 0.128 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 85 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.309 | 0.143 | 0.000 | 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 | F | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 200 | 101 | 0 | 0 | 104 | 0 | 0 | 42 | 137 |
N.S. |
1 | 1.00 | 0.50 | 0.00 | 0.00 | 0.52 | 0.00 | 0.00 | 0.21 | 0.68 |
time (sec) |
N/A | 0.855 | 0.214 | 0.000 | 0.000 | 0.161 | 0.000 | 0.000 | 0.175 | 16.736 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 140 | 76 | 0 | 0 | 75 | 0 | 0 | 42 | 103 |
N.S. |
1 | 0.99 | 0.54 | 0.00 | 0.00 | 0.53 | 0.00 | 0.00 | 0.30 | 0.73 |
time (sec) |
N/A | 0.607 | 0.145 | 0.000 | 0.000 | 0.134 | 0.000 | 0.000 | 0.176 | 16.249 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 92 | 53 | 0 | 0 | 61 | 0 | 0 | 42 | 71 |
N.S. |
1 | 1.03 | 0.60 | 0.00 | 0.00 | 0.69 | 0.00 | 0.00 | 0.47 | 0.80 |
time (sec) |
N/A | 0.422 | 0.132 | 0.000 | 0.000 | 0.131 | 0.000 | 0.000 | 0.168 | 16.140 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 34 | 0 | 65 | 39 | 0 | 0 | 42 | 34 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 1.91 | 1.15 | 0.00 | 0.00 | 1.24 | 1.00 |
time (sec) |
N/A | 0.235 | 0.064 | 0.000 | 0.125 | 0.106 | 0.000 | 0.000 | 0.172 | 0.170 |
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 | 112 | 145 | 108 | 0 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.29 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.344 | 0.147 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.163 | 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 | 106 | 135 | 97 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.27 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.338 | 0.295 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 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 | 112 | 145 | 113 | 0 | 0 | 0 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.29 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.369 | 0.280 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | B | F | B | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 153 | 105 | 0 | 624 | 314 | 0 | 37234 | 46 | 601 |
N.S. |
1 | 1.02 | 0.70 | 0.00 | 4.16 | 2.09 | 0.00 | 248.23 | 0.31 | 4.01 |
time (sec) |
N/A | 0.649 | 0.437 | 0.000 | 0.156 | 0.103 | 0.000 | 24.331 | 0.172 | 23.337 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | A | F | B | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 98 | 72 | 0 | 351 | 170 | 0 | 16008 | 46 | 241 |
N.S. |
1 | 1.04 | 0.77 | 0.00 | 3.73 | 1.81 | 0.00 | 170.30 | 0.49 | 2.56 |
time (sec) |
N/A | 0.441 | 0.237 | 0.000 | 0.143 | 0.112 | 0.000 | 10.114 | 0.177 | 18.341 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 43 | 44 | 144 | 80 | 0 | 3600 | 42 | 58 |
N.S. |
1 | 1.00 | 0.98 | 1.00 | 3.27 | 1.82 | 0.00 | 81.82 | 0.95 | 1.32 |
time (sec) |
N/A | 0.254 | 1.227 | 1.723 | 0.133 | 0.092 | 0.000 | 2.787 | 0.166 | 16.204 |
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 | 61 | 61 | 61 | 0 | 0 | 0 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 0.294 | 0.087 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 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 | 70 | 70 | 76 | 0 | 0 | 0 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.00 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.327 | 0.160 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.178 | 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 | 94 | 132 | 96 | 0 | 0 | 0 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.40 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.357 | 0.247 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 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 | 94 | 130 | 96 | 0 | 0 | 0 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.38 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.357 | 0.197 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 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 | 94 | 127 | 90 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.35 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.352 | 0.099 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 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 | 93 | 127 | 87 | 0 | 0 | 0 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.37 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.356 | 0.259 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 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 | 60 | 74 | 60 | 69 | 70 | 51 | 83 | 70 | 68 | 68 |
N.S. |
1 | 1.23 | 1.00 | 1.15 | 1.17 | 0.85 | 1.38 | 1.17 | 1.13 | 1.13 |
time (sec) |
N/A | 0.258 | 0.010 | 4.700 | 0.028 | 0.098 | 0.372 | 0.143 | 0.171 | 15.295 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 59 | 44 | 49 | 48 | 39 | 60 | 48 | 46 | 46 |
N.S. |
1 | 1.34 | 1.00 | 1.11 | 1.09 | 0.89 | 1.36 | 1.09 | 1.05 | 1.05 |
time (sec) |
N/A | 0.243 | 0.008 | 1.226 | 0.026 | 0.105 | 0.187 | 0.130 | 0.161 | 0.034 |
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 | 22 | 22 | 39 | 25 | 20 | 25 | 34 | 25 | 26 | 23 |
N.S. |
1 | 1.00 | 1.77 | 1.14 | 0.91 | 1.14 | 1.55 | 1.14 | 1.18 | 1.05 |
time (sec) |
N/A | 0.188 | 0.009 | 0.294 | 0.030 | 0.087 | 0.096 | 0.126 | 0.155 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 40 | 26 | 32 | 35 | 37 | 0 | 39 | 80 | 54 |
N.S. |
1 | 0.93 | 0.60 | 0.74 | 0.81 | 0.86 | 0.00 | 0.91 | 1.86 | 1.26 |
time (sec) |
N/A | 0.214 | 0.014 | 0.156 | 0.027 | 0.097 | 0.000 | 0.131 | 0.165 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 62 | 52 | 50 | 53 | 67 | 0 | 60 | 112 | 44 |
N.S. |
1 | 1.51 | 1.27 | 1.22 | 1.29 | 1.63 | 0.00 | 1.46 | 2.73 | 1.07 |
time (sec) |
N/A | 0.224 | 0.015 | 0.340 | 0.026 | 0.090 | 0.000 | 0.143 | 0.160 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 102 | 74 | 63 | 78 | 82 | 0 | 74 | 192 | 64 |
N.S. |
1 | 1.67 | 1.21 | 1.03 | 1.28 | 1.34 | 0.00 | 1.21 | 3.15 | 1.05 |
time (sec) |
N/A | 0.257 | 0.015 | 0.500 | 0.033 | 0.121 | 0.000 | 0.137 | 0.162 | 15.491 |
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 | 65 | 70 | 62 | 52 | 48 | 51 | 124 | 77 | 89 | 111 |
N.S. |
1 | 1.08 | 0.95 | 0.80 | 0.74 | 0.78 | 1.91 | 1.18 | 1.37 | 1.71 |
time (sec) |
N/A | 0.337 | 0.110 | 2.544 | 0.033 | 0.086 | 0.252 | 0.137 | 0.175 | 18.305 |
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 | 43 | 44 | 46 | 41 | 37 | 37 | 71 | 47 | 55 | 68 |
N.S. |
1 | 1.02 | 1.07 | 0.95 | 0.86 | 0.86 | 1.65 | 1.09 | 1.28 | 1.58 |
time (sec) |
N/A | 0.255 | 0.057 | 0.732 | 0.030 | 0.101 | 0.128 | 0.135 | 0.161 | 17.616 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 24 | 23 | 22 | 0 | 33 | 31 | 22 |
N.S. |
1 | 1.00 | 1.00 | 1.04 | 1.00 | 0.96 | 0.00 | 1.43 | 1.35 | 0.96 |
time (sec) |
N/A | 0.255 | 0.012 | 0.241 | 0.032 | 0.084 | 0.000 | 0.151 | 0.164 | 16.429 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 41 | 38 | 35 | 35 | 0 | 76 | 74 | 42 |
N.S. |
1 | 1.00 | 0.93 | 0.86 | 0.80 | 0.80 | 0.00 | 1.73 | 1.68 | 0.95 |
time (sec) |
N/A | 0.278 | 0.089 | 0.315 | 0.030 | 0.072 | 0.000 | 0.153 | 0.156 | 16.525 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 56 | 53 | 48 | 48 | 50 | 0 | 120 | 113 | 75 |
N.S. |
1 | 0.93 | 0.88 | 0.80 | 0.80 | 0.83 | 0.00 | 2.00 | 1.88 | 1.25 |
time (sec) |
N/A | 0.278 | 0.192 | 0.418 | 0.039 | 0.091 | 0.000 | 0.153 | 0.159 | 16.428 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 110 | 104 | 102 | 106 | 87 | 158 | 118 | 116 | 104 |
N.S. |
1 | 1.11 | 1.05 | 1.03 | 1.07 | 0.88 | 1.60 | 1.19 | 1.17 | 1.05 |
time (sec) |
N/A | 0.291 | 0.237 | 30.387 | 0.031 | 0.098 | 0.578 | 0.145 | 0.173 | 15.797 |
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 | 77 | 66 | 56 | 74 | 73 | 69 | 107 | 80 | 78 | 74 |
N.S. |
1 | 0.86 | 0.73 | 0.96 | 0.95 | 0.90 | 1.39 | 1.04 | 1.01 | 0.96 |
time (sec) |
N/A | 0.273 | 0.130 | 6.348 | 0.034 | 0.083 | 0.273 | 0.136 | 0.166 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 46 | 21 | 20 | 48 | 53 | 41 | 41 | 39 |
N.S. |
1 | 1.00 | 2.09 | 0.95 | 0.91 | 2.18 | 2.41 | 1.86 | 1.86 | 1.77 |
time (sec) |
N/A | 0.202 | 0.017 | 1.024 | 0.025 | 0.105 | 0.126 | 0.139 | 0.158 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 64 | 54 | 62 | 60 | 62 | 0 | 67 | 132 | 50 |
N.S. |
1 | 1.05 | 0.89 | 1.02 | 0.98 | 1.02 | 0.00 | 1.10 | 2.16 | 0.82 |
time (sec) |
N/A | 0.277 | 0.069 | 0.205 | 0.033 | 0.106 | 0.000 | 0.135 | 0.163 | 0.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 80 | 113 | 99 | 78 | 90 | 0 | 91 | 216 | 62 |
N.S. |
1 | 1.36 | 1.92 | 1.68 | 1.32 | 1.53 | 0.00 | 1.54 | 3.66 | 1.05 |
time (sec) |
N/A | 0.310 | 1.042 | 0.400 | 0.028 | 0.089 | 0.000 | 0.138 | 0.159 | 0.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 141 | 166 | 131 | 115 | 118 | 0 | 123 | 364 | 93 |
N.S. |
1 | 1.23 | 1.44 | 1.14 | 1.00 | 1.03 | 0.00 | 1.07 | 3.17 | 0.81 |
time (sec) |
N/A | 0.385 | 0.834 | 0.599 | 0.033 | 0.100 | 0.000 | 0.147 | 0.165 | 15.737 |
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 | 146 | 136 | 141 | 128 | 114 | 108 | 398 | 162 | 217 | 178 |
N.S. |
1 | 0.93 | 0.97 | 0.88 | 0.78 | 0.74 | 2.73 | 1.11 | 1.49 | 1.22 |
time (sec) |
N/A | 0.616 | 0.671 | 59.512 | 0.034 | 0.108 | 0.836 | 0.195 | 0.181 | 15.724 |
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 | 116 | 110 | 133 | 108 | 88 | 89 | 287 | 123 | 161 | 134 |
N.S. |
1 | 0.95 | 1.15 | 0.93 | 0.76 | 0.77 | 2.47 | 1.06 | 1.39 | 1.16 |
time (sec) |
N/A | 0.493 | 0.439 | 14.992 | 0.033 | 0.101 | 0.395 | 0.164 | 0.160 | 15.424 |
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 | 86 | 84 | 85 | 76 | 64 | 70 | 180 | 76 | 105 | 71 |
N.S. |
1 | 0.98 | 0.99 | 0.88 | 0.74 | 0.81 | 2.09 | 0.88 | 1.22 | 0.83 |
time (sec) |
N/A | 0.399 | 0.674 | 2.498 | 0.032 | 0.086 | 0.231 | 0.130 | 0.165 | 15.448 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 55 | 46 | 46 | 45 | 0 | 63 | 60 | 53 |
N.S. |
1 | 1.00 | 1.12 | 0.94 | 0.94 | 0.92 | 0.00 | 1.29 | 1.22 | 1.08 |
time (sec) |
N/A | 0.251 | 0.071 | 0.254 | 0.108 | 0.083 | 0.000 | 0.140 | 0.159 | 15.513 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 74 | 105 | 62 | 51 | 52 | 0 | 102 | 95 | 71 |
N.S. |
1 | 0.99 | 1.40 | 0.83 | 0.68 | 0.69 | 0.00 | 1.36 | 1.27 | 0.95 |
time (sec) |
N/A | 0.429 | 0.373 | 0.363 | 0.033 | 0.085 | 0.000 | 0.144 | 0.178 | 15.966 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 92 | 84 | 92 | 76 | 77 | 0 | 181 | 149 | 103 |
N.S. |
1 | 0.89 | 0.82 | 0.89 | 0.74 | 0.75 | 0.00 | 1.76 | 1.45 | 1.00 |
time (sec) |
N/A | 0.468 | 0.485 | 0.495 | 0.033 | 0.086 | 0.000 | 0.145 | 0.174 | 16.070 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 104 | 110 | 120 | 97 | 99 | 0 | 260 | 203 | 135 |
N.S. |
1 | 0.81 | 0.85 | 0.93 | 0.75 | 0.77 | 0.00 | 2.02 | 1.57 | 1.05 |
time (sec) |
N/A | 0.484 | 0.871 | 0.612 | 0.034 | 0.107 | 0.000 | 0.158 | 0.167 | 16.224 |
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 | 144 | 121 | 120 | 141 | 144 | 117 | 226 | 166 | 164 | 141 |
N.S. |
1 | 0.84 | 0.83 | 0.98 | 1.00 | 0.81 | 1.57 | 1.15 | 1.14 | 0.98 |
time (sec) |
N/A | 0.335 | 0.571 | 333.530 | 0.027 | 0.109 | 0.824 | 0.141 | 0.164 | 15.710 |
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 | 77 | 66 | 56 | 101 | 100 | 95 | 151 | 112 | 110 | 98 |
N.S. |
1 | 0.86 | 0.73 | 1.31 | 1.30 | 1.23 | 1.96 | 1.45 | 1.43 | 1.27 |
time (sec) |
N/A | 0.272 | 0.159 | 47.245 | 0.040 | 0.124 | 0.436 | 0.131 | 0.163 | 15.477 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 57 | 21 | 20 | 71 | 73 | 57 | 57 | 55 |
N.S. |
1 | 1.00 | 2.59 | 0.95 | 0.91 | 3.23 | 3.32 | 2.59 | 2.59 | 2.50 |
time (sec) |
N/A | 0.202 | 0.076 | 5.208 | 0.030 | 0.111 | 0.180 | 0.137 | 0.159 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 67 | 90 | 91 | 93 | 0 | 103 | 210 | 65 |
N.S. |
1 | 1.00 | 0.84 | 1.12 | 1.14 | 1.16 | 0.00 | 1.29 | 2.62 | 0.81 |
time (sec) |
N/A | 0.279 | 0.127 | 0.325 | 0.030 | 0.100 | 0.000 | 0.133 | 0.164 | 0.064 |