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 | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 124 | 82 | 119 | 232 | 85 | 151 | 152 | 121 | 122 |
N.S. |
1 | 1.00 | 0.66 | 0.96 | 1.87 | 0.69 | 1.22 | 1.23 | 0.98 | 0.98 |
time (sec) |
N/A | 0.545 | 0.126 | 0.625 | 0.041 | 0.077 | 0.320 | 0.117 | 0.152 | 2.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 65 | 94 | 196 | 67 | 117 | 116 | 91 | 92 |
N.S. |
1 | 1.00 | 0.69 | 1.00 | 2.09 | 0.71 | 1.24 | 1.23 | 0.97 | 0.98 |
time (sec) |
N/A | 0.438 | 0.111 | 0.577 | 0.041 | 0.082 | 0.240 | 0.112 | 0.151 | 2.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 45 | 73 | 160 | 48 | 82 | 79 | 61 | 62 |
N.S. |
1 | 1.00 | 0.70 | 1.14 | 2.50 | 0.75 | 1.28 | 1.23 | 0.95 | 0.97 |
time (sec) |
N/A | 0.313 | 0.094 | 0.563 | 0.049 | 0.081 | 0.196 | 0.124 | 0.148 | 1.978 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 27 | 30 | 68 | 30 | 46 | 46 | 33 | 35 |
N.S. |
1 | 1.00 | 0.96 | 1.07 | 2.43 | 1.07 | 1.64 | 1.64 | 1.18 | 1.25 |
time (sec) |
N/A | 0.255 | 0.049 | 0.375 | 0.043 | 0.079 | 0.154 | 0.110 | 0.149 | 0.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 39 | 52 | 97 | 54 | 39 | 47 | 28 | 0 |
N.S. |
1 | 1.00 | 1.39 | 1.86 | 3.46 | 1.93 | 1.39 | 1.68 | 1.00 | 0.00 |
time (sec) |
N/A | 0.332 | 0.052 | 0.496 | 0.103 | 0.085 | 1.462 | 0.111 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 59 | 75 | 82 | 76 | 0 | 72 | 92 | 0 |
N.S. |
1 | 1.00 | 1.26 | 1.60 | 1.74 | 1.62 | 0.00 | 1.53 | 1.96 | 0.00 |
time (sec) |
N/A | 0.414 | 0.118 | 0.542 | 0.128 | 0.075 | 0.000 | 0.112 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 78 | 137 | 66 | 116 | 0 | 134 | 144 | 0 |
N.S. |
1 | 1.00 | 0.89 | 1.56 | 0.75 | 1.32 | 0.00 | 1.52 | 1.64 | 0.00 |
time (sec) |
N/A | 0.501 | 0.137 | 0.561 | 0.126 | 0.086 | 0.000 | 0.121 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 132 | 110 | 204 | 78 | 143 | 0 | 199 | 201 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.55 | 0.59 | 1.08 | 0.00 | 1.51 | 1.52 | 0.00 |
time (sec) |
N/A | 0.556 | 0.211 | 0.584 | 0.135 | 0.076 | 0.000 | 0.136 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 166 | 140 | 273 | 82 | 161 | 0 | 266 | 256 | 0 |
N.S. |
1 | 1.00 | 0.84 | 1.64 | 0.49 | 0.97 | 0.00 | 1.60 | 1.54 | 0.00 |
time (sec) |
N/A | 0.659 | 0.240 | 0.607 | 0.135 | 0.077 | 0.000 | 0.136 | 0.151 | 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 | 184 | 184 | 100 | 134 | 329 | 127 | 228 | 236 | 181 | 168 |
N.S. |
1 | 1.00 | 0.54 | 0.73 | 1.79 | 0.69 | 1.24 | 1.28 | 0.98 | 0.91 |
time (sec) |
N/A | 0.630 | 0.138 | 0.677 | 0.047 | 0.084 | 0.396 | 0.130 | 0.150 | 0.174 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 134 | 87 | 108 | 275 | 95 | 172 | 171 | 131 | 125 |
N.S. |
1 | 1.00 | 0.65 | 0.81 | 2.05 | 0.71 | 1.28 | 1.28 | 0.98 | 0.93 |
time (sec) |
N/A | 0.509 | 0.114 | 0.564 | 0.057 | 0.084 | 0.308 | 0.131 | 0.148 | 1.982 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 59 | 56 | 77 | 135 | 64 | 112 | 112 | 83 | 82 |
N.S. |
1 | 1.20 | 1.14 | 1.57 | 2.76 | 1.31 | 2.29 | 2.29 | 1.69 | 1.67 |
time (sec) |
N/A | 0.395 | 0.089 | 0.546 | 0.057 | 0.089 | 0.232 | 0.134 | 0.150 | 1.943 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 51 | 121 | 175 | 94 | 73 | 113 | 58 | 0 |
N.S. |
1 | 1.00 | 0.82 | 1.95 | 2.82 | 1.52 | 1.18 | 1.82 | 0.94 | 0.00 |
time (sec) |
N/A | 0.437 | 0.151 | 0.515 | 0.116 | 0.097 | 1.826 | 0.139 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 62 | 124 | 136 | 122 | 0 | 119 | 136 | 0 |
N.S. |
1 | 1.00 | 0.89 | 1.77 | 1.94 | 1.74 | 0.00 | 1.70 | 1.94 | 0.00 |
time (sec) |
N/A | 0.525 | 0.148 | 0.566 | 0.129 | 0.089 | 0.000 | 0.127 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 93 | 186 | 126 | 153 | 0 | 181 | 199 | 0 |
N.S. |
1 | 1.00 | 0.77 | 1.54 | 1.04 | 1.26 | 0.00 | 1.50 | 1.64 | 0.00 |
time (sec) |
N/A | 0.625 | 0.225 | 0.536 | 0.161 | 0.082 | 0.000 | 0.121 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 172 | 154 | 292 | 117 | 194 | 0 | 285 | 290 | 0 |
N.S. |
1 | 1.00 | 0.90 | 1.70 | 0.68 | 1.13 | 0.00 | 1.66 | 1.69 | 0.00 |
time (sec) |
N/A | 0.733 | 0.267 | 0.582 | 0.127 | 0.082 | 0.000 | 0.122 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 248 | 206 | 400 | 128 | 231 | 0 | 395 | 383 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.61 | 0.52 | 0.93 | 0.00 | 1.59 | 1.54 | 0.00 |
time (sec) |
N/A | 0.777 | 0.315 | 0.623 | 0.139 | 0.080 | 0.000 | 0.134 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 219 | 159 | 442 | 437 | 236 | 0 | 407 | 179 | 0 |
N.S. |
1 | 1.00 | 0.73 | 2.02 | 2.00 | 1.08 | 0.00 | 1.86 | 0.82 | 0.00 |
time (sec) |
N/A | 0.749 | 0.370 | 0.622 | 0.138 | 0.103 | 0.000 | 0.133 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 150 | 118 | 292 | 328 | 190 | 0 | 256 | 109 | 0 |
N.S. |
1 | 1.00 | 0.79 | 1.95 | 2.19 | 1.27 | 0.00 | 1.71 | 0.73 | 0.00 |
time (sec) |
N/A | 0.558 | 0.263 | 0.499 | 0.113 | 0.089 | 0.000 | 0.130 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 100 | 89 | 184 | 233 | 156 | 0 | 148 | 60 | 0 |
N.S. |
1 | 1.10 | 0.98 | 2.02 | 2.56 | 1.71 | 0.00 | 1.63 | 0.66 | 0.00 |
time (sec) |
N/A | 0.491 | 0.180 | 0.465 | 0.119 | 0.087 | 0.000 | 0.134 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 64 | 114 | 156 | 118 | 0 | 83 | 34 | 0 |
N.S. |
1 | 1.00 | 0.94 | 1.68 | 2.29 | 1.74 | 0.00 | 1.22 | 0.50 | 0.00 |
time (sec) |
N/A | 0.374 | 0.086 | 0.425 | 0.090 | 0.090 | 0.000 | 0.129 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 49 | 81 | 57 | 95 | 0 | 56 | 16 | 0 |
N.S. |
1 | 1.00 | 0.96 | 1.59 | 1.12 | 1.86 | 0.00 | 1.10 | 0.31 | 0.00 |
time (sec) |
N/A | 0.412 | 0.055 | 0.378 | 0.085 | 0.073 | 0.000 | 0.127 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 63 | 108 | 155 | 123 | 0 | 75 | 20 | 0 |
N.S. |
1 | 1.00 | 0.86 | 1.48 | 2.12 | 1.68 | 0.00 | 1.03 | 0.27 | 0.00 |
time (sec) |
N/A | 0.452 | 0.091 | 0.442 | 0.116 | 0.094 | 0.000 | 0.117 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 101 | 155 | 192 | 179 | 0 | 129 | 22 | 0 |
N.S. |
1 | 1.00 | 0.89 | 1.37 | 1.70 | 1.58 | 0.00 | 1.14 | 0.19 | 0.00 |
time (sec) |
N/A | 0.572 | 0.238 | 0.468 | 0.154 | 0.096 | 0.000 | 0.114 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 190 | 178 | 281 | 242 | 275 | 0 | 248 | 22 | 0 |
N.S. |
1 | 1.00 | 0.94 | 1.48 | 1.27 | 1.45 | 0.00 | 1.31 | 0.12 | 0.00 |
time (sec) |
N/A | 0.760 | 0.277 | 0.517 | 0.208 | 0.081 | 0.000 | 0.117 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 231 | 173 | 669 | 406 | 371 | 0 | 2979 | 0 | 0 |
N.S. |
1 | 1.00 | 0.75 | 2.90 | 1.76 | 1.61 | 0.00 | 12.90 | 0.00 | 0.00 |
time (sec) |
N/A | 0.823 | 0.687 | 0.684 | 0.138 | 0.091 | 0.000 | 0.173 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 182 | 156 | 549 | 312 | 333 | 0 | 1991 | 0 | 0 |
N.S. |
1 | 1.04 | 0.89 | 3.14 | 1.78 | 1.90 | 0.00 | 11.38 | 0.00 | 0.00 |
time (sec) |
N/A | 0.767 | 0.553 | 0.588 | 0.123 | 0.094 | 0.000 | 0.165 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 147 | 115 | 436 | 236 | 274 | 0 | 1308 | 0 | 0 |
N.S. |
1 | 1.00 | 0.78 | 2.97 | 1.61 | 1.86 | 0.00 | 8.90 | 0.00 | 0.00 |
time (sec) |
N/A | 0.707 | 0.435 | 0.536 | 0.134 | 0.083 | 0.000 | 0.149 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 125 | 97 | 294 | 178 | 200 | 0 | 994 | 79 | 0 |
N.S. |
1 | 1.00 | 0.78 | 2.35 | 1.42 | 1.60 | 0.00 | 7.95 | 0.63 | 0.00 |
time (sec) |
N/A | 0.571 | 0.288 | 0.505 | 0.108 | 0.082 | 0.000 | 0.143 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | B | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 84 | 65 | 132 | 81 | 149 | 0 | 615 | 76 | 0 |
N.S. |
1 | 1.18 | 0.92 | 1.86 | 1.14 | 2.10 | 0.00 | 8.66 | 1.07 | 0.00 |
time (sec) |
N/A | 0.573 | 0.136 | 0.461 | 0.074 | 0.073 | 0.000 | 0.129 | 0.152 | 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 | 150 | 150 | 139 | 254 | 227 | 270 | 0 | 1329 | 31 | 0 |
N.S. |
1 | 1.00 | 0.93 | 1.69 | 1.51 | 1.80 | 0.00 | 8.86 | 0.21 | 0.00 |
time (sec) |
N/A | 0.742 | 0.718 | 0.531 | 0.143 | 0.083 | 0.000 | 0.147 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 186 | 183 | 312 | 0 | 377 | 0 | 3353 | 604 | 0 |
N.S. |
1 | 1.00 | 0.98 | 1.68 | 0.00 | 2.03 | 0.00 | 18.03 | 3.25 | 0.00 |
time (sec) |
N/A | 0.903 | 0.811 | 0.599 | 0.000 | 0.092 | 0.000 | 0.169 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 264 | 264 | 236 | 1055 | 0 | 566 | 0 | 879 | 0 | 0 |
N.S. |
1 | 1.00 | 0.89 | 4.00 | 0.00 | 2.14 | 0.00 | 3.33 | 0.00 | 0.00 |
time (sec) |
N/A | 0.895 | 0.552 | 0.759 | 0.000 | 0.144 | 0.000 | 0.118 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 241 | 241 | 153 | 917 | 0 | 475 | 0 | 741 | 0 | 0 |
N.S. |
1 | 1.00 | 0.63 | 3.80 | 0.00 | 1.97 | 0.00 | 3.07 | 0.00 | 0.00 |
time (sec) |
N/A | 0.850 | 0.595 | 0.670 | 0.000 | 0.138 | 0.000 | 0.115 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 178 | 158 | 435 | 0 | 373 | 0 | 529 | 106 | 0 |
N.S. |
1 | 1.00 | 0.89 | 2.44 | 0.00 | 2.10 | 0.00 | 2.97 | 0.60 | 0.00 |
time (sec) |
N/A | 0.614 | 0.362 | 0.624 | 0.000 | 0.122 | 0.000 | 0.115 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | A | B | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 111 | 88 | 276 | 95 | 253 | 0 | 298 | 103 | 0 |
N.S. |
1 | 1.07 | 0.85 | 2.65 | 0.91 | 2.43 | 0.00 | 2.87 | 0.99 | 0.00 |
time (sec) |
N/A | 0.689 | 0.305 | 0.562 | 0.080 | 0.120 | 0.000 | 0.118 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 262 | 262 | 451 | 488 | 0 | 601 | 0 | 837 | 42 | 0 |
N.S. |
1 | 1.00 | 1.72 | 1.86 | 0.00 | 2.29 | 0.00 | 3.19 | 0.16 | 0.00 |
time (sec) |
N/A | 0.959 | 0.812 | 0.651 | 0.000 | 0.151 | 0.000 | 0.109 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 298 | 298 | 541 | 643 | 0 | 762 | 0 | 1006 | 1170 | 0 |
N.S. |
1 | 1.00 | 1.82 | 2.16 | 0.00 | 2.56 | 0.00 | 3.38 | 3.93 | 0.00 |
time (sec) |
N/A | 1.049 | 0.870 | 0.734 | 0.000 | 0.133 | 0.000 | 0.118 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 377 | 377 | 627 | 760 | 0 | 892 | 0 | 1169 | 0 | 0 |
N.S. |
1 | 1.00 | 1.66 | 2.02 | 0.00 | 2.37 | 0.00 | 3.10 | 0.00 | 0.00 |
time (sec) |
N/A | 1.176 | 1.042 | 0.814 | 0.000 | 0.106 | 0.000 | 0.120 | 0.167 | 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 | 139 | 139 | 92 | 135 | 250 | 95 | 168 | 174 | 138 | 116 |
N.S. |
1 | 1.00 | 0.66 | 0.97 | 1.80 | 0.68 | 1.21 | 1.25 | 0.99 | 0.83 |
time (sec) |
N/A | 0.529 | 0.108 | 0.668 | 0.041 | 0.117 | 0.564 | 0.113 | 0.150 | 1.948 |
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 | 109 | 109 | 74 | 70 | 214 | 78 | 134 | 138 | 108 | 93 |
N.S. |
1 | 1.00 | 0.68 | 0.64 | 1.96 | 0.72 | 1.23 | 1.27 | 0.99 | 0.85 |
time (sec) |
N/A | 0.448 | 0.071 | 0.606 | 0.044 | 0.113 | 0.426 | 0.106 | 0.150 | 1.905 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 57 | 86 | 213 | 60 | 99 | 101 | 78 | 70 |
N.S. |
1 | 1.00 | 0.72 | 1.09 | 2.70 | 0.76 | 1.25 | 1.28 | 0.99 | 0.89 |
time (sec) |
N/A | 0.376 | 0.059 | 0.530 | 0.047 | 0.118 | 0.318 | 0.111 | 0.151 | 1.932 |
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 | 51 | 40 | 39 | 86 | 42 | 65 | 70 | 50 | 47 |
N.S. |
1 | 1.00 | 0.78 | 0.76 | 1.69 | 0.82 | 1.27 | 1.37 | 0.98 | 0.92 |
time (sec) |
N/A | 0.292 | 0.036 | 0.494 | 0.052 | 0.094 | 0.256 | 0.112 | 0.148 | 1.969 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 55 | 81 | 122 | 73 | 49 | 76 | 41 | 0 |
N.S. |
1 | 1.00 | 1.34 | 1.98 | 2.98 | 1.78 | 1.20 | 1.85 | 1.00 | 0.00 |
time (sec) |
N/A | 0.342 | 0.064 | 0.485 | 0.103 | 0.087 | 2.009 | 0.110 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 42 | 83 | 80 | 82 | 0 | 80 | 89 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.98 | 1.90 | 1.95 | 0.00 | 1.90 | 2.12 | 0.00 |
time (sec) |
N/A | 0.347 | 0.049 | 0.515 | 0.096 | 0.168 | 0.000 | 0.114 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 80 | 112 | 90 | 107 | 0 | 109 | 124 | 0 |
N.S. |
1 | 1.00 | 1.08 | 1.51 | 1.22 | 1.45 | 0.00 | 1.47 | 1.68 | 0.00 |
time (sec) |
N/A | 0.398 | 0.087 | 0.528 | 0.121 | 0.196 | 0.000 | 0.114 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 95 | 175 | 73 | 127 | 0 | 170 | 177 | 0 |
N.S. |
1 | 1.00 | 0.90 | 1.67 | 0.70 | 1.21 | 0.00 | 1.62 | 1.69 | 0.00 |
time (sec) |
N/A | 0.500 | 0.129 | 0.542 | 0.123 | 0.142 | 0.000 | 0.110 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 149 | 127 | 244 | 76 | 152 | 0 | 237 | 232 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.64 | 0.51 | 1.02 | 0.00 | 1.59 | 1.56 | 0.00 |
time (sec) |
N/A | 0.607 | 0.155 | 0.595 | 0.126 | 0.178 | 0.000 | 0.113 | 0.153 | 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 | 234 | 234 | 138 | 129 | 383 | 155 | 286 | 304 | 233 | 182 |
N.S. |
1 | 1.00 | 0.59 | 0.55 | 1.64 | 0.66 | 1.22 | 1.30 | 1.00 | 0.78 |
time (sec) |
N/A | 0.701 | 0.185 | 0.795 | 0.054 | 0.091 | 0.695 | 0.115 | 0.153 | 2.150 |
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 | 184 | 184 | 113 | 155 | 353 | 126 | 226 | 239 | 183 | 148 |
N.S. |
1 | 1.00 | 0.61 | 0.84 | 1.92 | 0.68 | 1.23 | 1.30 | 0.99 | 0.80 |
time (sec) |
N/A | 0.562 | 0.137 | 0.720 | 0.066 | 0.090 | 0.688 | 0.114 | 0.150 | 2.018 |
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 | 136 | 136 | 85 | 72 | 189 | 98 | 172 | 180 | 135 | 114 |
N.S. |
1 | 1.00 | 0.62 | 0.53 | 1.39 | 0.72 | 1.26 | 1.32 | 0.99 | 0.84 |
time (sec) |
N/A | 0.423 | 0.106 | 0.625 | 0.051 | 0.083 | 0.372 | 0.108 | 0.150 | 0.126 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 82 | 226 | 235 | 130 | 121 | 222 | 108 | 0 |
N.S. |
1 | 1.00 | 0.75 | 2.05 | 2.14 | 1.18 | 1.10 | 2.02 | 0.98 | 0.00 |
time (sec) |
N/A | 0.407 | 0.239 | 0.603 | 0.128 | 0.094 | 2.205 | 0.114 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 95 | 95 | 200 | 179 | 127 | 0 | 197 | 191 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.11 | 1.88 | 1.34 | 0.00 | 2.07 | 2.01 | 0.00 |
time (sec) |
N/A | 0.393 | 0.163 | 0.645 | 0.120 | 0.084 | 0.000 | 0.116 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 114 | 97 | 209 | 165 | 164 | 0 | 206 | 211 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.83 | 1.45 | 1.44 | 0.00 | 1.81 | 1.85 | 0.00 |
time (sec) |
N/A | 0.435 | 0.233 | 0.701 | 0.119 | 0.087 | 0.000 | 0.123 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 133 | 114 | 241 | 135 | 171 | 0 | 236 | 238 | 0 |
N.S. |
1 | 1.00 | 0.86 | 1.81 | 1.02 | 1.29 | 0.00 | 1.77 | 1.79 | 0.00 |
time (sec) |
N/A | 0.476 | 0.240 | 0.685 | 0.111 | 0.110 | 0.000 | 0.113 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 175 | 124 | 299 | 139 | 194 | 0 | 294 | 297 | 0 |
N.S. |
1 | 1.00 | 0.71 | 1.71 | 0.79 | 1.11 | 0.00 | 1.68 | 1.70 | 0.00 |
time (sec) |
N/A | 0.602 | 0.286 | 0.747 | 0.165 | 0.108 | 0.000 | 0.121 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 273 | 273 | 276 | 369 | 0 | 605 | 0 | 0 | 79 | 0 |
N.S. |
1 | 1.00 | 1.01 | 1.35 | 0.00 | 2.22 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 1.010 | 0.979 | 0.809 | 0.000 | 0.103 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 209 | 209 | 209 | 268 | 0 | 502 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.28 | 0.00 | 2.40 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.642 | 1.182 | 0.619 | 0.000 | 0.098 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 226 | 226 | 221 | 259 | 0 | 496 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 0.98 | 1.15 | 0.00 | 2.19 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.645 | 0.307 | 0.573 | 0.000 | 0.093 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 177 | 155 | 200 | 0 | 219 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 0.88 | 1.13 | 0.00 | 1.24 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.570 | 0.175 | 0.509 | 0.000 | 0.098 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 213 | 166 | 212 | 0 | 316 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.00 | 0.78 | 1.00 | 0.00 | 1.48 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.554 | 0.285 | 0.460 | 0.000 | 0.091 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 197 | 173 | 227 | 0 | 249 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 0.88 | 1.15 | 0.00 | 1.26 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.715 | 0.264 | 0.492 | 0.000 | 0.100 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 249 | 243 | 288 | 0 | 599 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 0.98 | 1.16 | 0.00 | 2.41 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.842 | 0.591 | 0.533 | 0.000 | 0.108 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 270 | 232 | 330 | 0 | 583 | 0 | 0 | 260 | 0 |
N.S. |
1 | 1.00 | 0.86 | 1.22 | 0.00 | 2.16 | 0.00 | 0.00 | 0.96 | 0.00 |
time (sec) |
N/A | 0.847 | 0.706 | 0.566 | 0.000 | 0.109 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 449 | 476 | 307 | 1038 | 0 | 1179 | 0 | 0 | 463 | 0 |
N.S. |
1 | 1.06 | 0.68 | 2.31 | 0.00 | 2.63 | 0.00 | 0.00 | 1.03 | 0.00 |
time (sec) |
N/A | 1.630 | 2.473 | 0.974 | 0.000 | 0.134 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 431 | 441 | 290 | 903 | 0 | 931 | 0 | 0 | 772 | 0 |
N.S. |
1 | 1.02 | 0.67 | 2.10 | 0.00 | 2.16 | 0.00 | 0.00 | 1.79 | 0.00 |
time (sec) |
N/A | 1.329 | 1.380 | 0.821 | 0.000 | 0.104 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 416 | 429 | 287 | 901 | 0 | 1162 | 0 | 0 | 87 | 0 |
N.S. |
1 | 1.03 | 0.69 | 2.17 | 0.00 | 2.79 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 1.202 | 2.244 | 0.745 | 0.000 | 0.099 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 244 | 236 | 449 | 0 | 641 | 0 | 0 | 163 | 0 |
N.S. |
1 | 1.02 | 0.99 | 1.88 | 0.00 | 2.68 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.639 | 0.746 | 0.652 | 0.000 | 0.125 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 476 | 476 | 293 | 503 | 0 | 1162 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 0.62 | 1.06 | 0.00 | 2.44 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.278 | 1.838 | 0.601 | 0.000 | 0.108 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 435 | 435 | 415 | 546 | 0 | 992 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 0.95 | 1.26 | 0.00 | 2.28 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 1.256 | 0.788 | 0.663 | 0.000 | 0.142 | 0.000 | 0.000 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 500 | 500 | 334 | 595 | 0 | 1310 | 0 | 0 | 731 | 0 |
N.S. |
1 | 1.00 | 0.67 | 1.19 | 0.00 | 2.62 | 0.00 | 0.00 | 1.46 | 0.00 |
time (sec) |
N/A | 1.892 | 2.222 | 0.787 | 0.000 | 0.133 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 476 | 714 | 332 | 1555 | 0 | 1620 | 0 | 0 | 1439 | 0 |
N.S. |
1 | 1.50 | 0.70 | 3.27 | 0.00 | 3.40 | 0.00 | 0.00 | 3.02 | 0.00 |
time (sec) |
N/A | 2.610 | 0.930 | 1.310 | 0.000 | 0.149 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 746 | 759 | 380 | 2172 | 0 | 2047 | 0 | 0 | 114 | 0 |
N.S. |
1 | 1.02 | 0.51 | 2.91 | 0.00 | 2.74 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 2.323 | 2.772 | 1.103 | 0.000 | 0.120 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 512 | 507 | 325 | 1503 | 0 | 1607 | 0 | 0 | 514 | 0 |
N.S. |
1 | 0.99 | 0.63 | 2.94 | 0.00 | 3.14 | 0.00 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 1.293 | 0.879 | 0.974 | 0.000 | 0.144 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 856 | 856 | 392 | 1064 | 0 | 2116 | 0 | 0 | 586 | 0 |
N.S. |
1 | 1.00 | 0.46 | 1.24 | 0.00 | 2.47 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 1.886 | 2.888 | 0.853 | 0.000 | 0.139 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 730 | 730 | 674 | 1090 | 0 | 2076 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.49 | 0.00 | 2.84 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 2.513 | 1.445 | 0.959 | 0.000 | 0.152 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 874 | 874 | 613 | 1178 | 0 | 2346 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.70 | 1.35 | 0.00 | 2.68 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.436 | 3.884 | 1.114 | 0.000 | 0.168 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 791 | 791 | 438 | 1294 | 0 | 2363 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.55 | 1.64 | 0.00 | 2.99 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.446 | 1.660 | 1.300 | 0.000 | 0.149 | 0.000 | 0.000 | 0.174 | 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 | 154 | 154 | 100 | 153 | 268 | 105 | 185 | 192 | 153 | 152 |
N.S. |
1 | 1.00 | 0.65 | 0.99 | 1.74 | 0.68 | 1.20 | 1.25 | 0.99 | 0.99 |
time (sec) |
N/A | 0.513 | 0.121 | 0.653 | 0.046 | 0.092 | 0.630 | 0.132 | 0.152 | 2.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 124 | 84 | 129 | 267 | 87 | 151 | 156 | 123 | 122 |
N.S. |
1 | 1.00 | 0.68 | 1.04 | 2.15 | 0.70 | 1.22 | 1.26 | 0.99 | 0.98 |
time (sec) |
N/A | 0.451 | 0.078 | 0.610 | 0.042 | 0.090 | 0.465 | 0.127 | 0.152 | 1.945 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 66 | 104 | 196 | 68 | 116 | 119 | 93 | 92 |
N.S. |
1 | 1.00 | 0.70 | 1.11 | 2.09 | 0.72 | 1.23 | 1.27 | 0.99 | 0.98 |
time (sec) |
N/A | 0.371 | 0.066 | 0.584 | 0.052 | 0.092 | 0.367 | 0.124 | 0.153 | 1.899 |
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 | 66 | 66 | 49 | 81 | 104 | 53 | 82 | 88 | 65 | 65 |
N.S. |
1 | 1.00 | 0.74 | 1.23 | 1.58 | 0.80 | 1.24 | 1.33 | 0.98 | 0.98 |
time (sec) |
N/A | 0.307 | 0.054 | 0.497 | 0.034 | 0.085 | 0.299 | 0.125 | 0.149 | 0.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 49 | 113 | 140 | 86 | 66 | 109 | 56 | 0 |
N.S. |
1 | 1.00 | 0.88 | 2.02 | 2.50 | 1.54 | 1.18 | 1.95 | 1.00 | 0.00 |
time (sec) |
N/A | 0.326 | 0.106 | 0.528 | 0.130 | 0.089 | 1.854 | 0.132 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 55 | 114 | 102 | 90 | 0 | 111 | 117 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.07 | 1.85 | 1.64 | 0.00 | 2.02 | 2.13 | 0.00 |
time (sec) |
N/A | 0.345 | 0.069 | 0.552 | 0.098 | 0.091 | 0.000 | 0.120 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 86 | 119 | 87 | 101 | 0 | 118 | 64 | 0 |
N.S. |
1 | 1.00 | 1.25 | 1.72 | 1.26 | 1.46 | 0.00 | 1.71 | 0.93 | 0.00 |
time (sec) |
N/A | 0.372 | 0.075 | 0.582 | 0.097 | 0.093 | 0.000 | 0.138 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 73 | 146 | 95 | 118 | 0 | 141 | 153 | 0 |
N.S. |
1 | 1.00 | 0.80 | 1.60 | 1.04 | 1.30 | 0.00 | 1.55 | 1.68 | 0.00 |
time (sec) |
N/A | 0.455 | 0.133 | 0.604 | 0.128 | 0.097 | 0.000 | 0.128 | 0.151 | 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 | 234 | 234 | 139 | 206 | 383 | 161 | 284 | 303 | 233 | 301 |
N.S. |
1 | 1.00 | 0.59 | 0.88 | 1.64 | 0.69 | 1.21 | 1.29 | 1.00 | 1.29 |
time (sec) |
N/A | 0.695 | 0.185 | 0.804 | 0.043 | 0.100 | 0.939 | 0.131 | 0.146 | 0.373 |
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 | 186 | 186 | 111 | 159 | 243 | 130 | 226 | 244 | 185 | 182 |
N.S. |
1 | 1.00 | 0.60 | 0.85 | 1.31 | 0.70 | 1.22 | 1.31 | 0.99 | 0.98 |
time (sec) |
N/A | 0.596 | 0.130 | 0.712 | 0.046 | 0.096 | 0.841 | 0.126 | 0.149 | 0.249 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 160 | 108 | 303 | 289 | 161 | 168 | 331 | 158 | 0 |
N.S. |
1 | 1.00 | 0.68 | 1.89 | 1.81 | 1.01 | 1.05 | 2.07 | 0.99 | 0.00 |
time (sec) |
N/A | 0.565 | 0.287 | 0.762 | 0.116 | 0.086 | 2.766 | 0.128 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 143 | 143 | 306 | 235 | 160 | 0 | 308 | 285 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.14 | 1.64 | 1.12 | 0.00 | 2.15 | 1.99 | 0.00 |
time (sec) |
N/A | 0.523 | 0.228 | 0.751 | 0.105 | 0.078 | 0.000 | 0.128 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 141 | 136 | 281 | 203 | 161 | 0 | 280 | 139 | 0 |
N.S. |
1 | 1.00 | 0.96 | 1.99 | 1.44 | 1.14 | 0.00 | 1.99 | 0.99 | 0.00 |
time (sec) |
N/A | 0.537 | 0.219 | 0.776 | 0.129 | 0.100 | 0.000 | 0.139 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 150 | 135 | 284 | 188 | 187 | 0 | 279 | 276 | 0 |
N.S. |
1 | 1.00 | 0.90 | 1.89 | 1.25 | 1.25 | 0.00 | 1.86 | 1.84 | 0.00 |
time (sec) |
N/A | 0.520 | 0.347 | 0.827 | 0.144 | 0.090 | 0.000 | 0.133 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 167 | 150 | 322 | 154 | 196 | 0 | 315 | 305 | 0 |
N.S. |
1 | 1.00 | 0.90 | 1.93 | 0.92 | 1.17 | 0.00 | 1.89 | 1.83 | 0.00 |
time (sec) |
N/A | 0.568 | 0.341 | 0.867 | 0.120 | 0.102 | 0.000 | 0.111 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F(-1) | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 373 | 373 | 213 | 925 | 0 | 989 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.00 | 0.57 | 2.48 | 0.00 | 2.65 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 1.162 | 0.140 | 0.687 | 0.000 | 0.137 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F(-1) | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 358 | 358 | 198 | 671 | 0 | 977 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 0.55 | 1.87 | 0.00 | 2.73 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.953 | 0.103 | 0.599 | 0.000 | 0.118 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 283 | 283 | 170 | 423 | 0 | 500 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 0.60 | 1.49 | 0.00 | 1.77 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.743 | 5.039 | 0.582 | 0.000 | 0.102 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F(-1) | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 345 | 345 | 180 | 280 | 0 | 671 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 0.52 | 0.81 | 0.00 | 1.94 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.695 | 5.046 | 0.541 | 0.000 | 0.121 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F(-1) | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 345 | 345 | 180 | 143 | 0 | 673 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.00 | 0.52 | 0.41 | 0.00 | 1.95 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.867 | 5.045 | 0.516 | 0.000 | 0.108 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 303 | 303 | 186 | 138 | 0 | 530 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 0.61 | 0.46 | 0.00 | 1.75 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.917 | 0.127 | 0.554 | 0.000 | 0.118 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F(-1) | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 381 | 381 | 215 | 175 | 0 | 1154 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 0.56 | 0.46 | 0.00 | 3.03 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.964 | 0.178 | 0.648 | 0.000 | 0.128 | 0.000 | 0.000 | 0.158 | 0.000 |