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 | C | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 64 | 64 | 67 | 159 | 492 | 0 | 44 | 41 | 0 |
N.S. |
1 | 0.43 | 0.43 | 0.45 | 1.07 | 3.32 | 0.00 | 0.30 | 0.28 | 0.00 |
time (sec) |
N/A | 0.510 | 0.026 | 0.207 | 0.128 | 0.135 | 0.000 | 0.119 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 74 | 74 | 75 | 184 | 530 | 0 | 58 | 49 | 0 |
N.S. |
1 | 0.40 | 0.40 | 0.40 | 0.98 | 2.83 | 0.00 | 0.31 | 0.26 | 0.00 |
time (sec) |
N/A | 0.513 | 0.034 | 0.204 | 0.125 | 0.136 | 0.000 | 0.113 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 222 | 80 | 80 | 83 | 209 | 556 | 0 | 70 | 57 | 0 |
N.S. |
1 | 0.36 | 0.36 | 0.37 | 0.94 | 2.50 | 0.00 | 0.32 | 0.26 | 0.00 |
time (sec) |
N/A | 0.528 | 0.032 | 0.206 | 0.123 | 0.151 | 0.000 | 0.129 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 263 | 92 | 92 | 91 | 240 | 582 | 0 | 82 | 65 | 0 |
N.S. |
1 | 0.35 | 0.35 | 0.35 | 0.91 | 2.21 | 0.00 | 0.31 | 0.25 | 0.00 |
time (sec) |
N/A | 0.539 | 0.038 | 0.214 | 0.124 | 0.167 | 0.000 | 0.158 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 52 | 52 | 62 | 55 | 78 | 0 | 0 | 27 | 78 |
N.S. |
1 | 0.64 | 0.64 | 0.77 | 0.68 | 0.96 | 0.00 | 0.00 | 0.33 | 0.96 |
time (sec) |
N/A | 0.506 | 0.032 | 0.202 | 0.081 | 0.091 | 0.000 | 0.000 | 0.147 | 14.324 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 47 | 42 | 43 | 43 | 58 | 0 | 28 | 17 | 67 |
N.S. |
1 | 0.64 | 0.57 | 0.58 | 0.58 | 0.78 | 0.00 | 0.38 | 0.23 | 0.91 |
time (sec) |
N/A | 0.462 | 0.018 | 0.203 | 0.078 | 0.074 | 0.000 | 0.122 | 0.146 | 14.378 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 41 | 42 | 51 | 57 | 0 | 25 | 14 | 67 |
N.S. |
1 | 1.00 | 0.91 | 0.93 | 1.13 | 1.27 | 0.00 | 0.56 | 0.31 | 1.49 |
time (sec) |
N/A | 0.392 | 0.016 | 0.197 | 0.075 | 0.078 | 0.000 | 0.119 | 0.145 | 14.328 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 38 | 38 | 41 | 0 | 323 | 0 | 27 | 15 | 0 |
N.S. |
1 | 0.55 | 0.55 | 0.59 | 0.00 | 4.68 | 0.00 | 0.39 | 0.22 | 0.00 |
time (sec) |
N/A | 0.402 | 0.017 | 0.197 | 0.000 | 0.111 | 0.000 | 0.116 | 0.143 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 42 | 38 | 41 | 0 | 297 | 0 | 28 | 17 | 0 |
N.S. |
1 | 0.63 | 0.57 | 0.61 | 0.00 | 4.43 | 0.00 | 0.42 | 0.25 | 0.00 |
time (sec) |
N/A | 0.475 | 0.014 | 0.204 | 0.000 | 0.104 | 0.000 | 0.112 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 44 | 43 | 0 | 63 | 0 | 26 | 17 | 64 |
N.S. |
1 | 1.00 | 1.00 | 0.98 | 0.00 | 1.43 | 0.00 | 0.59 | 0.39 | 1.45 |
time (sec) |
N/A | 0.462 | 0.012 | 0.207 | 0.000 | 0.078 | 0.000 | 0.107 | 0.142 | 14.236 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 176 | 101 | 142 | 0 | 238 | 0 | 139 | 105 | 0 |
N.S. |
1 | 1.14 | 0.65 | 0.92 | 0.00 | 1.54 | 0.00 | 0.90 | 0.68 | 0.00 |
time (sec) |
N/A | 0.530 | 0.074 | 0.237 | 0.000 | 0.089 | 0.000 | 0.128 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 148 | 93 | 134 | 0 | 222 | 0 | 128 | 87 | 0 |
N.S. |
1 | 1.14 | 0.72 | 1.03 | 0.00 | 1.71 | 0.00 | 0.98 | 0.67 | 0.00 |
time (sec) |
N/A | 0.506 | 0.050 | 0.225 | 0.000 | 0.112 | 0.000 | 0.128 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 115 | 84 | 124 | 0 | 204 | 0 | 117 | 69 | 0 |
N.S. |
1 | 1.16 | 0.85 | 1.25 | 0.00 | 2.06 | 0.00 | 1.18 | 0.70 | 0.00 |
time (sec) |
N/A | 0.421 | 0.044 | 0.220 | 0.000 | 0.084 | 0.000 | 0.128 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 91 | 100 | 114 | 0 | 188 | 0 | 106 | 51 | 0 |
N.S. |
1 | 1.17 | 1.28 | 1.46 | 0.00 | 2.41 | 0.00 | 1.36 | 0.65 | 0.00 |
time (sec) |
N/A | 0.364 | 0.065 | 0.246 | 0.000 | 0.081 | 0.000 | 0.129 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 71 | 80 | 198 | 0 | 255 | 0 | 0 | 53 | 0 |
N.S. |
1 | 0.81 | 0.91 | 2.25 | 0.00 | 2.90 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.360 | 0.057 | 0.211 | 0.000 | 0.096 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 78 | 83 | 148 | 0 | 241 | 0 | 126 | 64 | 0 |
N.S. |
1 | 0.95 | 1.01 | 1.80 | 0.00 | 2.94 | 0.00 | 1.54 | 0.78 | 0.00 |
time (sec) |
N/A | 0.446 | 0.037 | 0.236 | 0.000 | 0.111 | 0.000 | 0.172 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 96 | 78 | 143 | 0 | 163 | 0 | 195 | 60 | 0 |
N.S. |
1 | 1.22 | 0.99 | 1.81 | 0.00 | 2.06 | 0.00 | 2.47 | 0.76 | 0.00 |
time (sec) |
N/A | 0.453 | 0.046 | 0.228 | 0.000 | 0.099 | 0.000 | 0.155 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 119 | 86 | 151 | 0 | 187 | 0 | 231 | 86 | 0 |
N.S. |
1 | 1.16 | 0.83 | 1.47 | 0.00 | 1.82 | 0.00 | 2.24 | 0.83 | 0.00 |
time (sec) |
N/A | 0.486 | 0.055 | 0.225 | 0.000 | 0.089 | 0.000 | 0.180 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 150 | 94 | 159 | 0 | 203 | 0 | 316 | 152 | 0 |
N.S. |
1 | 1.13 | 0.71 | 1.20 | 0.00 | 1.53 | 0.00 | 2.38 | 1.14 | 0.00 |
time (sec) |
N/A | 0.513 | 0.063 | 0.237 | 0.000 | 0.101 | 0.000 | 0.180 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 173 | 102 | 167 | 0 | 219 | 0 | 362 | 122 | 0 |
N.S. |
1 | 1.16 | 0.68 | 1.12 | 0.00 | 1.47 | 0.00 | 2.43 | 0.82 | 0.00 |
time (sec) |
N/A | 0.544 | 0.075 | 0.233 | 0.000 | 0.101 | 0.000 | 0.256 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 70 | 70 | 74 | 0 | 419 | 0 | 66 | 45 | 0 |
N.S. |
1 | 0.37 | 0.37 | 0.40 | 0.00 | 2.24 | 0.00 | 0.35 | 0.24 | 0.00 |
time (sec) |
N/A | 0.527 | 0.035 | 0.217 | 0.000 | 0.109 | 0.000 | 0.116 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 64 | 64 | 67 | 0 | 407 | 0 | 58 | 37 | 0 |
N.S. |
1 | 0.42 | 0.42 | 0.44 | 0.00 | 2.68 | 0.00 | 0.38 | 0.24 | 0.00 |
time (sec) |
N/A | 0.492 | 0.035 | 0.214 | 0.000 | 0.108 | 0.000 | 0.110 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 54 | 54 | 58 | 0 | 387 | 0 | 46 | 29 | 0 |
N.S. |
1 | 0.48 | 0.48 | 0.51 | 0.00 | 3.42 | 0.00 | 0.41 | 0.26 | 0.00 |
time (sec) |
N/A | 0.426 | 0.026 | 0.217 | 0.000 | 0.118 | 0.000 | 0.193 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 45 | 45 | 52 | 0 | 0 | 0 | 39 | 24 | 0 |
N.S. |
1 | 0.42 | 0.42 | 0.49 | 0.00 | 0.00 | 0.00 | 0.37 | 0.23 | 0.00 |
time (sec) |
N/A | 0.416 | 0.014 | 0.201 | 0.000 | 0.000 | 0.000 | 0.126 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 51 | 48 | 51 | 0 | 0 | 0 | 43 | 28 | 0 |
N.S. |
1 | 0.48 | 0.45 | 0.48 | 0.00 | 0.00 | 0.00 | 0.41 | 0.26 | 0.00 |
time (sec) |
N/A | 0.504 | 0.020 | 0.218 | 0.000 | 0.000 | 0.000 | 0.114 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 63 | 63 | 67 | 0 | 485 | 0 | 47 | 41 | 0 |
N.S. |
1 | 0.43 | 0.43 | 0.46 | 0.00 | 3.30 | 0.00 | 0.32 | 0.28 | 0.00 |
time (sec) |
N/A | 0.512 | 0.028 | 0.214 | 0.000 | 0.127 | 0.000 | 0.113 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 73 | 73 | 75 | 0 | 523 | 0 | 59 | 49 | 0 |
N.S. |
1 | 0.39 | 0.39 | 0.40 | 0.00 | 2.81 | 0.00 | 0.32 | 0.26 | 0.00 |
time (sec) |
N/A | 0.527 | 0.029 | 0.217 | 0.000 | 0.131 | 0.000 | 0.123 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 220 | 78 | 78 | 83 | 0 | 551 | 0 | 73 | 57 | 0 |
N.S. |
1 | 0.35 | 0.35 | 0.38 | 0.00 | 2.50 | 0.00 | 0.33 | 0.26 | 0.00 |
time (sec) |
N/A | 0.555 | 0.036 | 0.212 | 0.000 | 0.140 | 0.000 | 0.115 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 262 | 91 | 87 | 91 | 0 | 575 | 0 | 83 | 65 | 0 |
N.S. |
1 | 0.35 | 0.33 | 0.35 | 0.00 | 2.19 | 0.00 | 0.32 | 0.25 | 0.00 |
time (sec) |
N/A | 0.537 | 0.046 | 0.221 | 0.000 | 0.119 | 0.000 | 0.118 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | C | F | F(-1) | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 240 | 249 | 184 | 0 | 628 | 0 | 0 | 123 | 31 | 0 |
N.S. |
1 | 1.04 | 0.77 | 0.00 | 2.62 | 0.00 | 0.00 | 0.51 | 0.13 | 0.00 |
time (sec) |
N/A | 0.763 | 0.145 | 0.000 | 0.122 | 0.000 | 0.000 | 0.128 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | C | F | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 149 | 134 | 0 | 351 | 0 | 0 | 73 | 28 | 0 |
N.S. |
1 | 1.06 | 0.95 | 0.00 | 2.49 | 0.00 | 0.00 | 0.52 | 0.20 | 0.00 |
time (sec) |
N/A | 0.493 | 0.445 | 0.000 | 0.098 | 0.000 | 0.000 | 0.121 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | C | F | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 174 | 172 | 0 | 898 | 0 | 0 | 107 | 27 | 0 |
N.S. |
1 | 1.07 | 1.06 | 0.00 | 5.51 | 0.00 | 0.00 | 0.66 | 0.17 | 0.00 |
time (sec) |
N/A | 0.633 | 0.370 | 0.000 | 0.173 | 0.000 | 0.000 | 0.132 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | C | F | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 73 | 71 | 0 | 498 | 0 | 0 | 65 | 24 | 0 |
N.S. |
1 | 1.01 | 0.99 | 0.00 | 6.92 | 0.00 | 0.00 | 0.90 | 0.33 | 0.00 |
time (sec) |
N/A | 0.575 | 0.017 | 0.000 | 0.149 | 0.000 | 0.000 | 0.120 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | C | F | F(-1) | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 335 | 342 | 200 | 0 | 983 | 0 | 0 | 201 | 49 | 0 |
N.S. |
1 | 1.02 | 0.60 | 0.00 | 2.93 | 0.00 | 0.00 | 0.60 | 0.15 | 0.00 |
time (sec) |
N/A | 0.858 | 0.267 | 0.000 | 0.139 | 0.000 | 0.000 | 0.169 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | C | F | F(-1) | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 236 | 238 | 178 | 0 | 628 | 0 | 0 | 121 | 46 | 0 |
N.S. |
1 | 1.01 | 0.75 | 0.00 | 2.66 | 0.00 | 0.00 | 0.51 | 0.19 | 0.00 |
time (sec) |
N/A | 0.620 | 0.246 | 0.000 | 0.119 | 0.000 | 0.000 | 0.145 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | C | F | F(-1) | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 200 | 193 | 0 | 1457 | 0 | 0 | 121 | 29 | 0 |
N.S. |
1 | 1.04 | 1.00 | 0.00 | 7.55 | 0.00 | 0.00 | 0.63 | 0.15 | 0.00 |
time (sec) |
N/A | 0.732 | 0.211 | 0.000 | 0.213 | 0.000 | 0.000 | 0.131 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | C | F | F(-1) | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 166 | 176 | 0 | 905 | 0 | 0 | 85 | 28 | 0 |
N.S. |
1 | 1.06 | 1.12 | 0.00 | 5.76 | 0.00 | 0.00 | 0.54 | 0.18 | 0.00 |
time (sec) |
N/A | 0.560 | 0.355 | 0.000 | 0.156 | 0.000 | 0.000 | 0.134 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | C | F | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 153 | 162 | 0 | 347 | 0 | 0 | 73 | 14 | 0 |
N.S. |
1 | 1.09 | 1.16 | 0.00 | 2.48 | 0.00 | 0.00 | 0.52 | 0.10 | 0.00 |
time (sec) |
N/A | 0.492 | 0.210 | 0.000 | 0.094 | 0.000 | 0.000 | 0.144 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | C | F | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 70 | 0 | 168 | 0 | 0 | 47 | 13 | 0 |
N.S. |
1 | 1.00 | 1.13 | 0.00 | 2.71 | 0.00 | 0.00 | 0.76 | 0.21 | 0.00 |
time (sec) |
N/A | 0.495 | 0.030 | 0.000 | 0.079 | 0.000 | 0.000 | 0.112 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 166 | 149 | 163 | 540 | 144 | 818 | 148 | 325 | 0 |
N.S. |
1 | 0.91 | 0.82 | 0.90 | 2.97 | 0.79 | 4.49 | 0.81 | 1.79 | 0.00 |
time (sec) |
N/A | 0.369 | 0.241 | 0.524 | 0.109 | 0.080 | 2.160 | 0.159 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 142 | 159 | 129 | 355 | 116 | 563 | 106 | 196 | 0 |
N.S. |
1 | 1.09 | 1.22 | 0.99 | 2.73 | 0.89 | 4.33 | 0.82 | 1.51 | 0.00 |
time (sec) |
N/A | 0.357 | 0.169 | 0.424 | 0.110 | 0.113 | 1.852 | 0.152 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 96 | 130 | 104 | 209 | 92 | 352 | 68 | 96 | 0 |
N.S. |
1 | 1.14 | 1.55 | 1.24 | 2.49 | 1.10 | 4.19 | 0.81 | 1.14 | 0.00 |
time (sec) |
N/A | 0.289 | 0.121 | 0.349 | 0.117 | 0.079 | 1.239 | 0.133 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 53 | 28 | 87 | 65 | 76 | 42 | 45 | 34 | 101 |
N.S. |
1 | 1.36 | 0.72 | 2.23 | 1.67 | 1.95 | 1.08 | 1.15 | 0.87 | 2.59 |
time (sec) |
N/A | 0.235 | 0.019 | 0.339 | 0.107 | 0.103 | 1.150 | 0.160 | 0.146 | 14.325 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 79 | 106 | 109 | 0 | 306 | 0 | 88 | 54 | 132 |
N.S. |
1 | 1.23 | 1.66 | 1.70 | 0.00 | 4.78 | 0.00 | 1.38 | 0.84 | 2.06 |
time (sec) |
N/A | 0.299 | 0.079 | 0.326 | 0.000 | 0.117 | 0.000 | 0.151 | 0.155 | 14.222 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 88 | 117 | 0 | 282 | 0 | 226 | 101 | 241 |
N.S. |
1 | 1.00 | 0.90 | 1.19 | 0.00 | 2.88 | 0.00 | 2.31 | 1.03 | 2.46 |
time (sec) |
N/A | 0.272 | 0.049 | 0.376 | 0.000 | 0.095 | 0.000 | 0.152 | 0.145 | 14.511 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 157 | 123 | 153 | 0 | 359 | 0 | 748 | 334 | 0 |
N.S. |
1 | 0.97 | 0.76 | 0.94 | 0.00 | 2.22 | 0.00 | 4.62 | 2.06 | 0.00 |
time (sec) |
N/A | 0.328 | 0.164 | 0.441 | 0.000 | 0.108 | 0.000 | 0.133 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 220 | 183 | 207 | 0 | 488 | 0 | 1664 | 950 | 0 |
N.S. |
1 | 1.03 | 0.86 | 0.97 | 0.00 | 2.29 | 0.00 | 7.81 | 4.46 | 0.00 |
time (sec) |
N/A | 0.398 | 0.378 | 0.542 | 0.000 | 0.149 | 0.000 | 0.146 | 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 | 83 | 83 | 75 | 91 | 94 | 93 | 102 | 122 | 145 | 142 |
N.S. |
1 | 1.00 | 0.90 | 1.10 | 1.13 | 1.12 | 1.23 | 1.47 | 1.75 | 1.71 |
time (sec) |
N/A | 0.317 | 0.014 | 0.280 | 0.034 | 0.076 | 0.179 | 0.139 | 0.144 | 14.014 |
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 | 66 | 64 | 68 | 67 | 66 | 82 | 98 | 106 |
N.S. |
1 | 1.00 | 1.00 | 0.97 | 1.03 | 1.02 | 1.00 | 1.24 | 1.48 | 1.61 |
time (sec) |
N/A | 0.278 | 0.013 | 0.269 | 0.029 | 0.096 | 0.160 | 0.109 | 0.145 | 13.989 |
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 | 49 | 49 | 44 | 44 | 46 | 45 | 42 | 52 | 62 | 74 |
N.S. |
1 | 1.00 | 0.90 | 0.90 | 0.94 | 0.92 | 0.86 | 1.06 | 1.27 | 1.51 |
time (sec) |
N/A | 0.260 | 0.010 | 0.268 | 0.029 | 0.088 | 0.103 | 0.129 | 0.152 | 0.032 |
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 | 34 | 34 | 34 | 28 | 30 | 29 | 26 | 34 | 37 | 40 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.88 | 0.85 | 0.76 | 1.00 | 1.09 | 1.18 |
time (sec) |
N/A | 0.237 | 0.004 | 0.277 | 0.027 | 0.080 | 0.082 | 0.116 | 0.143 | 0.026 |
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 | 19 | 19 | 19 | 17 | 16 | 18 | 14 | 17 | 18 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.84 | 0.95 | 0.74 | 0.89 | 0.95 | 0.84 |
time (sec) |
N/A | 0.210 | 0.005 | 0.273 | 0.029 | 0.066 | 0.066 | 0.133 | 0.150 | 0.023 |
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 | 33 | 33 | 26 | 24 | 27 | 23 | 88 | 34 | 25 | 28 |
N.S. |
1 | 1.00 | 0.79 | 0.73 | 0.82 | 0.70 | 2.67 | 1.03 | 0.76 | 0.85 |
time (sec) |
N/A | 0.237 | 0.004 | 0.269 | 0.026 | 0.078 | 0.303 | 0.110 | 0.148 | 14.178 |
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 | 48 | 48 | 34 | 37 | 48 | 39 | 144 | 57 | 36 | 47 |
N.S. |
1 | 1.00 | 0.71 | 0.77 | 1.00 | 0.81 | 3.00 | 1.19 | 0.75 | 0.98 |
time (sec) |
N/A | 0.253 | 0.004 | 0.269 | 0.031 | 0.077 | 0.210 | 0.124 | 0.148 | 0.053 |
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 | 67 | 67 | 54 | 57 | 74 | 65 | 209 | 91 | 67 | 66 |
N.S. |
1 | 1.00 | 0.81 | 0.85 | 1.10 | 0.97 | 3.12 | 1.36 | 1.00 | 0.99 |
time (sec) |
N/A | 0.282 | 0.010 | 0.272 | 0.034 | 0.092 | 0.281 | 0.113 | 0.147 | 14.102 |
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 | 82 | 82 | 75 | 70 | 108 | 88 | 260 | 120 | 96 | 84 |
N.S. |
1 | 1.00 | 0.91 | 0.85 | 1.32 | 1.07 | 3.17 | 1.46 | 1.17 | 1.02 |
time (sec) |
N/A | 0.302 | 0.015 | 0.280 | 0.033 | 0.078 | 0.356 | 0.121 | 0.152 | 14.134 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 203 | 203 | 348 | 2349 | 192 | 0 | 211 | 700 | 0 |
N.S. |
1 | 0.95 | 0.95 | 1.63 | 11.03 | 0.90 | 0.00 | 0.99 | 3.29 | 0.00 |
time (sec) |
N/A | 0.437 | 0.297 | 0.774 | 0.134 | 0.109 | 0.000 | 0.161 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 173 | 170 | 268 | 1645 | 159 | 0 | 166 | 491 | 0 |
N.S. |
1 | 1.03 | 1.01 | 1.60 | 9.79 | 0.95 | 0.00 | 0.99 | 2.92 | 0.00 |
time (sec) |
N/A | 0.384 | 0.208 | 0.758 | 0.124 | 0.136 | 0.000 | 0.164 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 131 | 142 | 197 | 1137 | 131 | 0 | 127 | 321 | 0 |
N.S. |
1 | 1.08 | 1.17 | 1.63 | 9.40 | 1.08 | 0.00 | 1.05 | 2.65 | 0.00 |
time (sec) |
N/A | 0.317 | 0.170 | 0.598 | 0.121 | 0.098 | 0.000 | 0.137 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 84 | 43 | 136 | 753 | 100 | 0 | 93 | 183 | 0 |
N.S. |
1 | 1.24 | 0.63 | 2.00 | 11.07 | 1.47 | 0.00 | 1.37 | 2.69 | 0.00 |
time (sec) |
N/A | 0.261 | 0.036 | 0.602 | 0.114 | 0.097 | 0.000 | 0.158 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 126 | 153 | 722 | 0 | 439 | 0 | 157 | 295 | 0 |
N.S. |
1 | 1.18 | 1.43 | 6.75 | 0.00 | 4.10 | 0.00 | 1.47 | 2.76 | 0.00 |
time (sec) |
N/A | 0.356 | 0.665 | 0.510 | 0.000 | 0.147 | 0.000 | 0.146 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 143 | 106 | 174 | 0 | 370 | 0 | 606 | 788 | 0 |
N.S. |
1 | 1.07 | 0.79 | 1.30 | 0.00 | 2.76 | 0.00 | 4.52 | 5.88 | 0.00 |
time (sec) |
N/A | 0.308 | 0.078 | 0.589 | 0.000 | 0.110 | 0.000 | 0.159 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 202 | 141 | 189 | 0 | 523 | 0 | 826 | 1258 | 0 |
N.S. |
1 | 1.00 | 0.70 | 0.94 | 0.00 | 2.59 | 0.00 | 4.09 | 6.23 | 0.00 |
time (sec) |
N/A | 0.350 | 0.169 | 0.506 | 0.000 | 0.115 | 0.000 | 0.170 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 260 | 275 | 199 | 260 | 0 | 704 | 0 | 1836 | 27 | 0 |
N.S. |
1 | 1.06 | 0.77 | 1.00 | 0.00 | 2.71 | 0.00 | 7.06 | 0.10 | 0.00 |
time (sec) |
N/A | 0.490 | 0.340 | 0.773 | 0.000 | 0.144 | 0.000 | 0.164 | 200.016 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 165 | 160 | 163 | 338 | 143 | 0 | 148 | 325 | 0 |
N.S. |
1 | 0.92 | 0.89 | 0.91 | 1.89 | 0.80 | 0.00 | 0.83 | 1.82 | 0.00 |
time (sec) |
N/A | 0.376 | 0.323 | 0.481 | 0.123 | 0.096 | 0.000 | 0.149 | 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 | 130 | 141 | 126 | 129 | 174 | 117 | 0 | 106 | 196 | 0 |
N.S. |
1 | 1.08 | 0.97 | 0.99 | 1.34 | 0.90 | 0.00 | 0.82 | 1.51 | 0.00 |
time (sec) |
N/A | 0.372 | 0.149 | 0.427 | 0.109 | 0.082 | 0.000 | 0.128 | 0.142 | 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 | 84 | 95 | 99 | 104 | 107 | 91 | 0 | 68 | 98 | 0 |
N.S. |
1 | 1.13 | 1.18 | 1.24 | 1.27 | 1.08 | 0.00 | 0.81 | 1.17 | 0.00 |
time (sec) |
N/A | 0.288 | 0.108 | 0.379 | 0.111 | 0.097 | 0.000 | 0.130 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 52 | 26 | 88 | 37 | 77 | 0 | 44 | 33 | 0 |
N.S. |
1 | 1.37 | 0.68 | 2.32 | 0.97 | 2.03 | 0.00 | 1.16 | 0.87 | 0.00 |
time (sec) |
N/A | 0.241 | 0.014 | 0.382 | 0.107 | 0.086 | 0.000 | 0.132 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 79 | 106 | 235 | 0 | 303 | 0 | 89 | 55 | 0 |
N.S. |
1 | 1.16 | 1.56 | 3.46 | 0.00 | 4.46 | 0.00 | 1.31 | 0.81 | 0.00 |
time (sec) |
N/A | 0.301 | 0.040 | 0.418 | 0.000 | 0.121 | 0.000 | 0.141 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 89 | 116 | 0 | 277 | 0 | 223 | 98 | 0 |
N.S. |
1 | 1.00 | 0.95 | 1.23 | 0.00 | 2.95 | 0.00 | 2.37 | 1.04 | 0.00 |
time (sec) |
N/A | 0.276 | 0.058 | 0.477 | 0.000 | 0.116 | 0.000 | 0.171 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 153 | 122 | 153 | 0 | 356 | 0 | 750 | 533 | 0 |
N.S. |
1 | 0.94 | 0.75 | 0.94 | 0.00 | 2.20 | 0.00 | 4.63 | 3.29 | 0.00 |
time (sec) |
N/A | 0.322 | 0.151 | 0.546 | 0.000 | 0.138 | 0.000 | 0.134 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 218 | 185 | 207 | 0 | 483 | 0 | 1659 | 27 | 0 |
N.S. |
1 | 1.04 | 0.88 | 0.99 | 0.00 | 2.30 | 0.00 | 7.90 | 0.13 | 0.00 |
time (sec) |
N/A | 0.398 | 0.357 | 0.774 | 0.000 | 0.124 | 0.000 | 0.150 | 200.017 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 71 | 113 | 94 | 93 | 102 | 202 | 145 | 141 |
N.S. |
1 | 1.00 | 1.00 | 1.59 | 1.32 | 1.31 | 1.44 | 2.85 | 2.04 | 1.99 |
time (sec) |
N/A | 0.302 | 0.010 | 0.181 | 0.027 | 0.081 | 0.172 | 0.136 | 0.174 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 57 | 75 | 68 | 67 | 68 | 148 | 98 | 109 |
N.S. |
1 | 1.00 | 1.00 | 1.32 | 1.19 | 1.18 | 1.19 | 2.60 | 1.72 | 1.91 |
time (sec) |
N/A | 0.268 | 0.016 | 0.187 | 0.031 | 0.071 | 0.178 | 0.135 | 0.158 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 41 | 50 | 46 | 45 | 41 | 102 | 62 | 73 |
N.S. |
1 | 1.00 | 1.00 | 1.22 | 1.12 | 1.10 | 1.00 | 2.49 | 1.51 | 1.78 |
time (sec) |
N/A | 0.260 | 0.008 | 0.181 | 0.026 | 0.071 | 0.127 | 0.120 | 0.154 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 33 | 30 | 29 | 26 | 69 | 37 | 42 |
N.S. |
1 | 1.00 | 1.00 | 1.14 | 1.03 | 1.00 | 0.90 | 2.38 | 1.28 | 1.45 |
time (sec) |
N/A | 0.232 | 0.005 | 0.180 | 0.034 | 0.077 | 0.096 | 0.112 | 0.159 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 17 | 16 | 18 | 12 | 38 | 18 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.12 | 0.75 | 2.38 | 1.12 | 1.00 |
time (sec) |
N/A | 0.203 | 0.007 | 0.178 | 0.026 | 0.073 | 0.070 | 0.106 | 0.148 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 23 | 26 | 27 | 23 | 90 | 66 | 23 | 28 |
N.S. |
1 | 1.00 | 0.82 | 0.93 | 0.96 | 0.82 | 3.21 | 2.36 | 0.82 | 1.00 |
time (sec) |
N/A | 0.236 | 0.003 | 0.178 | 0.027 | 0.085 | 0.397 | 0.137 | 0.159 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 31 | 40 | 48 | 36 | 143 | 80 | 36 | 47 |
N.S. |
1 | 1.00 | 0.76 | 0.98 | 1.17 | 0.88 | 3.49 | 1.95 | 0.88 | 1.15 |
time (sec) |
N/A | 0.254 | 0.004 | 0.181 | 0.030 | 0.093 | 0.284 | 0.124 | 0.159 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 51 | 57 | 74 | 65 | 209 | 121 | 65 | 66 |
N.S. |
1 | 1.00 | 0.88 | 0.98 | 1.28 | 1.12 | 3.60 | 2.09 | 1.12 | 1.14 |
time (sec) |
N/A | 0.273 | 0.010 | 0.184 | 0.026 | 0.078 | 0.356 | 0.134 | 0.158 | 14.184 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 70 | 69 | 108 | 86 | 262 | 159 | 96 | 83 |
N.S. |
1 | 1.00 | 1.00 | 0.99 | 1.54 | 1.23 | 3.74 | 2.27 | 1.37 | 1.19 |
time (sec) |
N/A | 0.289 | 0.015 | 0.184 | 0.032 | 0.075 | 0.422 | 0.141 | 0.160 | 0.058 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 202 | 231 | 349 | 985 | 191 | 0 | 211 | 703 | 0 |
N.S. |
1 | 0.95 | 1.08 | 1.64 | 4.62 | 0.90 | 0.00 | 0.99 | 3.30 | 0.00 |
time (sec) |
N/A | 0.441 | 0.196 | 0.579 | 0.126 | 0.106 | 0.000 | 0.144 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 171 | 190 | 269 | 622 | 159 | 0 | 166 | 494 | 0 |
N.S. |
1 | 1.02 | 1.14 | 1.61 | 3.72 | 0.95 | 0.00 | 0.99 | 2.96 | 0.00 |
time (sec) |
N/A | 0.402 | 0.165 | 0.596 | 0.125 | 0.137 | 0.000 | 0.140 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 127 | 157 | 198 | 299 | 130 | 0 | 127 | 325 | 0 |
N.S. |
1 | 1.07 | 1.32 | 1.66 | 2.51 | 1.09 | 0.00 | 1.07 | 2.73 | 0.00 |
time (sec) |
N/A | 0.333 | 0.161 | 0.543 | 0.113 | 0.090 | 0.000 | 0.142 | 0.157 | 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 | 68 | 83 | 43 | 135 | 104 | 101 | 0 | 94 | 183 | 0 |
N.S. |
1 | 1.22 | 0.63 | 1.99 | 1.53 | 1.49 | 0.00 | 1.38 | 2.69 | 0.00 |
time (sec) |
N/A | 0.252 | 0.036 | 0.592 | 0.110 | 0.112 | 0.000 | 0.151 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 123 | 137 | 908 | 0 | 438 | 0 | 154 | 291 | 0 |
N.S. |
1 | 1.19 | 1.33 | 8.82 | 0.00 | 4.25 | 0.00 | 1.50 | 2.83 | 0.00 |
time (sec) |
N/A | 0.351 | 0.473 | 0.648 | 0.000 | 0.122 | 0.000 | 0.148 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 137 | 106 | 175 | 0 | 369 | 0 | 604 | 700 | 0 |
N.S. |
1 | 1.05 | 0.82 | 1.35 | 0.00 | 2.84 | 0.00 | 4.65 | 5.38 | 0.00 |
time (sec) |
N/A | 0.299 | 0.106 | 0.910 | 0.000 | 0.125 | 0.000 | 0.146 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 196 | 139 | 189 | 0 | 520 | 0 | 822 | 1257 | 0 |
N.S. |
1 | 0.98 | 0.70 | 0.94 | 0.00 | 2.60 | 0.00 | 4.11 | 6.28 | 0.00 |
time (sec) |
N/A | 0.343 | 0.161 | 0.990 | 0.000 | 0.114 | 0.000 | 0.152 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 270 | 194 | 260 | 0 | 697 | 0 | 1839 | 4014 | 0 |
N.S. |
1 | 1.05 | 0.75 | 1.01 | 0.00 | 2.71 | 0.00 | 7.16 | 15.62 | 0.00 |
time (sec) |
N/A | 0.441 | 0.334 | 1.228 | 0.000 | 0.151 | 0.000 | 0.169 | 0.352 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 114 | 0 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.307 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.151 | 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 | 245 | 212 | 220 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.87 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.400 | 0.112 | 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 | 170 | 176 | 127 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.04 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.366 | 0.090 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.151 | 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 | 114 | 114 | 96 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.280 | 0.038 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.154 | 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 | 71 | 71 | 50 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.00 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.223 | 0.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 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 | 135 | 135 | 111 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.306 | 0.036 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.152 | 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 | 92 | 92 | 83 | 0 | 0 | 0 | 0 | 0 | 153 | 0 |
N.S. |
1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.66 | 0.00 |
time (sec) |
N/A | 0.258 | 0.020 | 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 | 152 | 156 | 123 | 0 | 0 | 0 | 0 | 0 | 600 | 0 |
N.S. |
1 | 1.03 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.95 | 0.00 |
time (sec) |
N/A | 0.327 | 0.059 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 23 | 37 | 25 | 18 | 29 | 66 | 38 | 26 | 10 |
N.S. |
1 | 2.30 | 3.70 | 2.50 | 1.80 | 2.90 | 6.60 | 3.80 | 2.60 | 1.00 |
time (sec) |
N/A | 0.229 | 0.011 | 0.198 | 0.104 | 0.071 | 0.462 | 0.143 | 0.151 | 14.254 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 128 | 90 | 255 | 576 | 150 | 0 | 143 | 428 | 0 |
N.S. |
1 | 0.96 | 0.67 | 1.90 | 4.30 | 1.12 | 0.00 | 1.07 | 3.19 | 0.00 |
time (sec) |
N/A | 0.418 | 0.089 | 0.727 | 0.233 | 0.096 | 0.000 | 0.152 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 98 | 64 | 194 | 329 | 120 | 0 | 112 | 260 | 0 |
N.S. |
1 | 1.26 | 0.82 | 2.49 | 4.22 | 1.54 | 0.00 | 1.44 | 3.33 | 0.00 |
time (sec) |
N/A | 0.376 | 0.065 | 0.635 | 0.185 | 0.117 | 0.000 | 0.138 | 0.153 | 0.000 |