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 | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 99 | 97 | 92 | 121 | 114 | 124 | 491 | 103 | 103 |
N.S. |
1 | 0.92 | 0.90 | 0.85 | 1.12 | 1.06 | 1.15 | 4.55 | 0.95 | 0.95 |
time (sec) |
N/A | 0.307 | 0.042 | 0.232 | 0.026 | 0.085 | 0.419 | 0.124 | 0.171 | 3.429 |
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 | 96 | 89 | 87 | 84 | 110 | 102 | 112 | 394 | 92 | 92 |
N.S. |
1 | 0.93 | 0.91 | 0.88 | 1.15 | 1.06 | 1.17 | 4.10 | 0.96 | 0.96 |
time (sec) |
N/A | 0.317 | 0.040 | 0.222 | 0.031 | 0.092 | 0.473 | 0.124 | 0.163 | 3.504 |
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 | 84 | 81 | 79 | 76 | 99 | 93 | 100 | 305 | 84 | 83 |
N.S. |
1 | 0.96 | 0.94 | 0.90 | 1.18 | 1.11 | 1.19 | 3.63 | 1.00 | 0.99 |
time (sec) |
N/A | 0.289 | 0.033 | 0.162 | 0.031 | 0.081 | 0.327 | 0.120 | 0.160 | 3.453 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 46 | 95 | 59 | 85 | 77 | 75 | 211 | 64 | 65 |
N.S. |
1 | 1.05 | 2.16 | 1.34 | 1.93 | 1.75 | 1.70 | 4.80 | 1.45 | 1.48 |
time (sec) |
N/A | 0.231 | 0.013 | 0.155 | 0.028 | 0.076 | 0.188 | 0.119 | 0.159 | 3.312 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 57 | 73 | 0 | 0 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.00 | 0.95 | 1.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.82 | 0.00 |
time (sec) |
N/A | 0.264 | 0.023 | 0.173 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 71 | 87 | 0 | 0 | 0 | 0 | 66 | 0 |
N.S. |
1 | 1.00 | 1.01 | 1.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 0.289 | 0.053 | 0.227 | 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 | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 52 | 76 | 76 | 89 | 89 | 95 | 192 | 79 | 75 |
N.S. |
1 | 0.93 | 1.36 | 1.36 | 1.59 | 1.59 | 1.70 | 3.43 | 1.41 | 1.34 |
time (sec) |
N/A | 0.262 | 0.050 | 0.214 | 0.025 | 0.090 | 0.374 | 0.124 | 0.174 | 3.455 |
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 | 98 | 87 | 86 | 86 | 99 | 101 | 117 | 306 | 87 | 110 |
N.S. |
1 | 0.89 | 0.88 | 0.88 | 1.01 | 1.03 | 1.19 | 3.12 | 0.89 | 1.12 |
time (sec) |
N/A | 0.309 | 0.052 | 0.214 | 0.029 | 0.094 | 0.462 | 0.120 | 0.171 | 3.437 |
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 | 110 | 95 | 94 | 94 | 114 | 110 | 129 | 401 | 97 | 120 |
N.S. |
1 | 0.86 | 0.85 | 0.85 | 1.04 | 1.00 | 1.17 | 3.65 | 0.88 | 1.09 |
time (sec) |
N/A | 0.322 | 0.052 | 0.218 | 0.026 | 0.089 | 0.632 | 0.122 | 0.172 | 3.462 |
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 | 157 | 131 | 125 | 124 | 210 | 162 | 196 | 620 | 136 | 146 |
N.S. |
1 | 0.83 | 0.80 | 0.79 | 1.34 | 1.03 | 1.25 | 3.95 | 0.87 | 0.93 |
time (sec) |
N/A | 0.450 | 0.055 | 0.414 | 0.031 | 0.105 | 0.556 | 0.127 | 0.170 | 3.636 |
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 | 143 | 123 | 115 | 116 | 184 | 146 | 177 | 525 | 127 | 134 |
N.S. |
1 | 0.86 | 0.80 | 0.81 | 1.29 | 1.02 | 1.24 | 3.67 | 0.89 | 0.94 |
time (sec) |
N/A | 0.416 | 0.050 | 0.287 | 0.034 | 0.086 | 0.450 | 0.135 | 0.167 | 3.465 |
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 | 129 | 113 | 107 | 108 | 179 | 137 | 167 | 425 | 117 | 122 |
N.S. |
1 | 0.88 | 0.83 | 0.84 | 1.39 | 1.06 | 1.29 | 3.29 | 0.91 | 0.95 |
time (sec) |
N/A | 0.403 | 0.045 | 0.320 | 0.031 | 0.090 | 0.398 | 0.124 | 0.165 | 3.414 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 58 | 92 | 80 | 147 | 114 | 131 | 330 | 100 | 105 |
N.S. |
1 | 0.82 | 1.30 | 1.13 | 2.07 | 1.61 | 1.85 | 4.65 | 1.41 | 1.48 |
time (sec) |
N/A | 0.246 | 0.051 | 0.179 | 0.030 | 0.084 | 0.329 | 0.122 | 0.169 | 3.380 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 114 | 103 | 103 | 173 | 0 | 0 | 0 | 82 | 0 |
N.S. |
1 | 1.00 | 0.90 | 0.90 | 1.52 | 0.00 | 0.00 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.330 | 0.067 | 0.236 | 0.138 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 80 | 73 | 89 | 0 | 0 | 0 | 410 | 66 | 0 |
N.S. |
1 | 1.31 | 1.20 | 1.46 | 0.00 | 0.00 | 0.00 | 6.72 | 1.08 | 0.00 |
time (sec) |
N/A | 0.331 | 0.067 | 0.290 | 0.000 | 0.000 | 0.000 | 0.970 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 137 | 143 | 123 | 0 | 0 | 0 | 0 | 111 | 0 |
N.S. |
1 | 1.00 | 1.04 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.372 | 0.078 | 0.361 | 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 | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 68 | 103 | 110 | 157 | 128 | 158 | 330 | 112 | 116 |
N.S. |
1 | 0.84 | 1.27 | 1.36 | 1.94 | 1.58 | 1.95 | 4.07 | 1.38 | 1.43 |
time (sec) |
N/A | 0.293 | 0.067 | 0.296 | 0.034 | 0.096 | 0.477 | 0.119 | 0.165 | 3.348 |
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 | 147 | 122 | 114 | 118 | 178 | 147 | 189 | 431 | 120 | 168 |
N.S. |
1 | 0.83 | 0.78 | 0.80 | 1.21 | 1.00 | 1.29 | 2.93 | 0.82 | 1.14 |
time (sec) |
N/A | 0.427 | 0.072 | 0.289 | 0.033 | 0.102 | 0.520 | 0.126 | 0.160 | 3.517 |
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 | 161 | 132 | 122 | 126 | 194 | 156 | 199 | 532 | 130 | 182 |
N.S. |
1 | 0.82 | 0.76 | 0.78 | 1.20 | 0.97 | 1.24 | 3.30 | 0.81 | 1.13 |
time (sec) |
N/A | 0.461 | 0.071 | 0.301 | 0.031 | 0.102 | 0.637 | 0.130 | 0.158 | 3.501 |
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 | 192 | 158 | 151 | 152 | 285 | 190 | 243 | 722 | 167 | 177 |
N.S. |
1 | 0.82 | 0.79 | 0.79 | 1.48 | 0.99 | 1.27 | 3.76 | 0.87 | 0.92 |
time (sec) |
N/A | 0.476 | 0.067 | 0.589 | 0.032 | 0.099 | 0.568 | 0.131 | 0.168 | 3.805 |
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 | 178 | 150 | 142 | 144 | 265 | 178 | 235 | 621 | 158 | 165 |
N.S. |
1 | 0.84 | 0.80 | 0.81 | 1.49 | 1.00 | 1.32 | 3.49 | 0.89 | 0.93 |
time (sec) |
N/A | 0.547 | 0.062 | 0.510 | 0.031 | 0.103 | 0.488 | 0.138 | 0.160 | 4.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 112 | 133 | 134 | 244 | 165 | 211 | 527 | 148 | 153 |
N.S. |
1 | 0.83 | 0.99 | 0.99 | 1.81 | 1.22 | 1.56 | 3.90 | 1.10 | 1.13 |
time (sec) |
N/A | 0.529 | 0.052 | 0.410 | 0.033 | 0.092 | 0.612 | 0.127 | 0.166 | 3.950 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 76 | 115 | 101 | 219 | 149 | 182 | 425 | 131 | 136 |
N.S. |
1 | 0.90 | 1.37 | 1.20 | 2.61 | 1.77 | 2.17 | 5.06 | 1.56 | 1.62 |
time (sec) |
N/A | 0.447 | 0.059 | 0.266 | 0.031 | 0.083 | 0.336 | 0.130 | 0.162 | 3.698 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 152 | 148 | 131 | 228 | 0 | 0 | 0 | 115 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.86 | 1.50 | 0.00 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.488 | 0.079 | 0.306 | 0.140 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 150 | 149 | 131 | 229 | 0 | 0 | 0 | 122 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.87 | 1.53 | 0.00 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.648 | 0.086 | 0.416 | 0.133 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 160 | 165 | 137 | 0 | 0 | 0 | 0 | 133 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.604 | 0.086 | 0.495 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 176 | 175 | 151 | 0 | 0 | 0 | 0 | 142 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.520 | 0.091 | 0.531 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 76 | 131 | 138 | 228 | 163 | 207 | 431 | 143 | 147 |
N.S. |
1 | 0.82 | 1.41 | 1.48 | 2.45 | 1.75 | 2.23 | 4.63 | 1.54 | 1.58 |
time (sec) |
N/A | 0.307 | 0.080 | 0.391 | 0.035 | 0.096 | 0.540 | 0.129 | 0.170 | 3.671 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 108 | 140 | 146 | 250 | 175 | 233 | 533 | 151 | 233 |
N.S. |
1 | 0.79 | 1.02 | 1.07 | 1.82 | 1.28 | 1.70 | 3.89 | 1.10 | 1.70 |
time (sec) |
N/A | 0.345 | 0.076 | 0.407 | 0.033 | 0.093 | 0.686 | 0.118 | 0.158 | 3.721 |
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 | 196 | 161 | 149 | 154 | 273 | 188 | 257 | 634 | 161 | 220 |
N.S. |
1 | 0.82 | 0.76 | 0.79 | 1.39 | 0.96 | 1.31 | 3.23 | 0.82 | 1.12 |
time (sec) |
N/A | 0.474 | 0.081 | 0.410 | 0.036 | 0.094 | 0.987 | 0.129 | 0.165 | 3.657 |
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 | 224 | 186 | 177 | 178 | 373 | 222 | 294 | 817 | 198 | 337 |
N.S. |
1 | 0.83 | 0.79 | 0.79 | 1.67 | 0.99 | 1.31 | 3.65 | 0.88 | 1.50 |
time (sec) |
N/A | 0.510 | 0.071 | 0.842 | 0.037 | 0.094 | 0.720 | 0.129 | 0.164 | 4.336 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 147 | 168 | 170 | 339 | 208 | 279 | 723 | 189 | 196 |
N.S. |
1 | 0.86 | 0.98 | 0.99 | 1.98 | 1.22 | 1.63 | 4.23 | 1.11 | 1.15 |
time (sec) |
N/A | 0.413 | 0.069 | 0.722 | 0.038 | 0.096 | 0.738 | 0.134 | 0.162 | 3.578 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 126 | 159 | 164 | 326 | 198 | 269 | 621 | 180 | 185 |
N.S. |
1 | 0.82 | 1.04 | 1.07 | 2.13 | 1.29 | 1.76 | 4.06 | 1.18 | 1.21 |
time (sec) |
N/A | 0.344 | 0.062 | 0.639 | 0.034 | 0.092 | 0.535 | 0.130 | 0.161 | 3.496 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 90 | 146 | 121 | 283 | 177 | 226 | 526 | 163 | 168 |
N.S. |
1 | 0.84 | 1.36 | 1.13 | 2.64 | 1.65 | 2.11 | 4.92 | 1.52 | 1.57 |
time (sec) |
N/A | 0.272 | 0.064 | 0.388 | 0.036 | 0.089 | 0.399 | 0.120 | 0.159 | 3.495 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 185 | 179 | 159 | 276 | 0 | 0 | 0 | 146 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.86 | 1.49 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.437 | 0.101 | 0.426 | 0.132 | 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 | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 178 | 194 | 159 | 281 | 0 | 0 | 0 | 155 | 0 |
N.S. |
1 | 1.00 | 1.09 | 0.89 | 1.58 | 0.00 | 0.00 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.440 | 0.102 | 0.576 | 0.133 | 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 | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 156 | 143 | 147 | 293 | 0 | 0 | 0 | 129 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.94 | 1.88 | 0.00 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.424 | 0.098 | 0.717 | 0.130 | 0.000 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 189 | 197 | 165 | 0 | 0 | 0 | 0 | 164 | 0 |
N.S. |
1 | 1.00 | 1.04 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.468 | 0.105 | 0.780 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 209 | 209 | 206 | 179 | 0 | 0 | 0 | 0 | 173 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.487 | 0.108 | 0.797 | 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 | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 88 | 157 | 166 | 299 | 191 | 253 | 532 | 174 | 179 |
N.S. |
1 | 0.81 | 1.44 | 1.52 | 2.74 | 1.75 | 2.32 | 4.88 | 1.60 | 1.64 |
time (sec) |
N/A | 0.313 | 0.095 | 0.567 | 0.033 | 0.102 | 0.654 | 0.134 | 0.169 | 4.242 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 118 | 166 | 174 | 329 | 208 | 291 | 634 | 183 | 248 |
N.S. |
1 | 0.78 | 1.10 | 1.15 | 2.18 | 1.38 | 1.93 | 4.20 | 1.21 | 1.64 |
time (sec) |
N/A | 0.348 | 0.095 | 0.572 | 0.034 | 0.092 | 0.696 | 0.133 | 0.160 | 4.102 |
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 | 229 | 192 | 175 | 182 | 353 | 218 | 301 | 735 | 192 | 260 |
N.S. |
1 | 0.84 | 0.76 | 0.79 | 1.54 | 0.95 | 1.31 | 3.21 | 0.84 | 1.14 |
time (sec) |
N/A | 0.540 | 0.101 | 0.585 | 0.032 | 0.100 | 0.870 | 0.137 | 0.165 | 4.104 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 195 | 129 | 162 | 0 | 0 | 0 | 0 | 64 | 0 |
N.S. |
1 | 1.10 | 0.73 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 1.853 | 0.357 | 0.315 | 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 | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 138 | 97 | 132 | 0 | 0 | 0 | 0 | 54 | 0 |
N.S. |
1 | 0.95 | 0.67 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 1.219 | 0.237 | 0.238 | 0.000 | 0.000 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 91 | 75 | 106 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 0.97 | 0.80 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.514 | 0.170 | 0.194 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 52 | 78 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 1.02 | 1.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.314 | 0.144 | 0.161 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 55 | 115 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.00 | 1.20 | 2.50 | 0.00 | 0.00 | 0.00 | 0.00 | 1.13 | 0.00 |
time (sec) |
N/A | 0.291 | 0.165 | 0.227 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 89 | 93 | 156 | 0 | 0 | 0 | 0 | 49 | 0 |
N.S. |
1 | 0.96 | 1.00 | 1.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.566 | 0.206 | 0.259 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 126 | 133 | 188 | 0 | 0 | 0 | 0 | 67 | 0 |
N.S. |
1 | 0.86 | 0.91 | 1.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.855 | 0.298 | 0.335 | 0.000 | 0.000 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 181 | 172 | 218 | 0 | 0 | 0 | 0 | 182 | 0 |
N.S. |
1 | 0.98 | 0.93 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 1.275 | 0.362 | 0.376 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 181 | 142 | 163 | 0 | 0 | 0 | 0 | 121 | 0 |
N.S. |
1 | 1.00 | 0.78 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.465 | 0.540 | 0.349 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 149 | 121 | 137 | 0 | 0 | 0 | 0 | 109 | 0 |
N.S. |
1 | 1.00 | 0.81 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.427 | 0.438 | 0.289 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 106 | 99 | 123 | 0 | 0 | 0 | 0 | 95 | 0 |
N.S. |
1 | 1.00 | 0.93 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.368 | 0.306 | 0.280 | 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 | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 55 | 64 | 41 | 96 | 49 | 95 | 63 | 73 | 45 |
N.S. |
1 | 0.96 | 1.12 | 0.72 | 1.68 | 0.86 | 1.67 | 1.11 | 1.28 | 0.79 |
time (sec) |
N/A | 0.249 | 0.091 | 0.211 | 0.030 | 0.082 | 0.576 | 0.123 | 0.160 | 3.882 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 124 | 101 | 159 | 0 | 0 | 0 | 0 | 196 | 0 |
N.S. |
1 | 1.00 | 0.81 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 1.58 | 0.00 |
time (sec) |
N/A | 0.417 | 0.315 | 0.304 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 171 | 140 | 184 | 0 | 0 | 0 | 0 | 243 | 0 |
N.S. |
1 | 1.00 | 0.82 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 1.42 | 0.00 |
time (sec) |
N/A | 0.558 | 0.574 | 0.364 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 212 | 189 | 218 | 0 | 0 | 0 | 0 | 321 | 0 |
N.S. |
1 | 1.00 | 0.89 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 1.51 | 0.00 |
time (sec) |
N/A | 0.835 | 0.755 | 0.493 | 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 | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 227 | 189 | 197 | 0 | 0 | 0 | 0 | 209 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.843 | 0.585 | 0.509 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 194 | 167 | 170 | 0 | 0 | 0 | 0 | 201 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.751 | 0.518 | 0.416 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 150 | 145 | 157 | 0 | 0 | 0 | 0 | 190 | 0 |
N.S. |
1 | 1.00 | 0.97 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 1.27 | 0.00 |
time (sec) |
N/A | 0.490 | 0.393 | 0.414 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 75 | 99 | 68 | 152 | 84 | 277 | 114 | 126 | 81 |
N.S. |
1 | 0.97 | 1.29 | 0.88 | 1.97 | 1.09 | 3.60 | 1.48 | 1.64 | 1.05 |
time (sec) |
N/A | 0.339 | 0.086 | 0.342 | 0.037 | 0.082 | 0.835 | 0.118 | 0.169 | 4.401 |
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 | 74 | 86 | 72 | 134 | 75 | 224 | 118 | 130 | 123 |
N.S. |
1 | 0.96 | 1.12 | 0.94 | 1.74 | 0.97 | 2.91 | 1.53 | 1.69 | 1.60 |
time (sec) |
N/A | 0.266 | 0.088 | 0.306 | 0.036 | 0.083 | 0.813 | 0.117 | 0.164 | 4.103 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 161 | 147 | 190 | 0 | 0 | 0 | 0 | 343 | 0 |
N.S. |
1 | 1.00 | 0.91 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | 2.13 | 0.00 |
time (sec) |
N/A | 0.465 | 0.382 | 0.415 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 218 | 218 | 186 | 222 | 0 | 0 | 0 | 0 | 434 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 1.99 | 0.00 |
time (sec) |
N/A | 0.545 | 0.801 | 0.490 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 268 | 268 | 220 | 256 | 0 | 0 | 0 | 0 | 458 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 1.71 | 0.00 |
time (sec) |
N/A | 0.603 | 0.987 | 0.721 | 0.000 | 0.000 | 0.000 | 0.000 | 0.170 | 0.000 |
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 | 80 | 82 | 75 | 75 | 132 | 91 | 294 | 161 | 156 | 139 |
N.S. |
1 | 1.02 | 0.94 | 0.94 | 1.65 | 1.14 | 3.68 | 2.01 | 1.95 | 1.74 |
time (sec) |
N/A | 0.272 | 0.099 | 0.356 | 0.037 | 0.090 | 1.192 | 0.124 | 0.176 | 3.865 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 39 | 88 | 120 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 0.95 | 2.15 | 2.93 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.299 | 0.140 | 0.231 | 0.032 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 270 | 271 | 306 | 0 | 0 | 0 | 0 | 296 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 1.10 | 0.00 |
time (sec) |
N/A | 0.913 | 0.472 | 0.533 | 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 | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 236 | 236 | 234 | 278 | 402 | 0 | 0 | 0 | 259 | 0 |
N.S. |
1 | 1.00 | 0.99 | 1.18 | 1.70 | 0.00 | 0.00 | 0.00 | 1.10 | 0.00 |
time (sec) |
N/A | 1.098 | 0.343 | 0.456 | 0.279 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 196 | 201 | 249 | 0 | 0 | 0 | 0 | 224 | 0 |
N.S. |
1 | 1.00 | 1.03 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.14 | 0.00 |
time (sec) |
N/A | 0.985 | 0.389 | 0.397 | 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 | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 122 | 156 | 211 | 290 | 0 | 0 | 0 | 178 | 0 |
N.S. |
1 | 1.09 | 1.39 | 1.88 | 2.59 | 0.00 | 0.00 | 0.00 | 1.59 | 0.00 |
time (sec) |
N/A | 0.554 | 0.274 | 0.330 | 0.200 | 0.000 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 191 | 228 | 1827 | 0 | 0 | 0 | 0 | 90 | 0 |
N.S. |
1 | 1.00 | 1.19 | 9.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.788 | 0.312 | 2.622 | 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 | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 201 | 249 | 1857 | 0 | 0 | 0 | 0 | 133 | 0 |
N.S. |
1 | 1.00 | 1.24 | 9.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.739 | 0.333 | 2.806 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 151 | 206 | 276 | 0 | 0 | 0 | 0 | 235 | 0 |
N.S. |
1 | 1.00 | 1.36 | 1.83 | 0.00 | 0.00 | 0.00 | 0.00 | 1.56 | 0.00 |
time (sec) |
N/A | 0.598 | 0.205 | 0.625 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 206 | 246 | 308 | 417 | 0 | 0 | 0 | 235 | 0 |
N.S. |
1 | 1.00 | 1.19 | 1.50 | 2.02 | 0.00 | 0.00 | 0.00 | 1.14 | 0.00 |
time (sec) |
N/A | 0.747 | 0.315 | 0.625 | 0.470 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 356 | 356 | 329 | 374 | 766 | 0 | 0 | 1135 | 376 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.05 | 2.15 | 0.00 | 0.00 | 3.19 | 1.06 | 0.00 |
time (sec) |
N/A | 1.265 | 0.650 | 0.750 | 0.299 | 0.000 | 0.000 | 2.251 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 312 | 312 | 297 | 345 | 604 | 0 | 0 | 0 | 339 | 0 |
N.S. |
1 | 1.00 | 0.95 | 1.11 | 1.94 | 0.00 | 0.00 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 1.393 | 0.641 | 0.674 | 0.291 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 280 | 280 | 263 | 318 | 610 | 0 | 0 | 761 | 303 | 0 |
N.S. |
1 | 1.00 | 0.94 | 1.14 | 2.18 | 0.00 | 0.00 | 2.72 | 1.08 | 0.00 |
time (sec) |
N/A | 1.232 | 0.708 | 0.598 | 0.285 | 0.000 | 0.000 | 1.452 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 170 | 227 | 223 | 464 | 0 | 0 | 0 | 251 | 0 |
N.S. |
1 | 0.97 | 1.30 | 1.27 | 2.65 | 0.00 | 0.00 | 0.00 | 1.43 | 0.00 |
time (sec) |
N/A | 0.651 | 0.608 | 0.469 | 0.207 | 0.000 | 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 | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 278 | 278 | 324 | 895 | 0 | 0 | 0 | 0 | 189 | 0 |
N.S. |
1 | 1.00 | 1.17 | 3.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.995 | 0.433 | 2.454 | 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 | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 283 | 283 | 341 | 2519 | 0 | 0 | 0 | 0 | 151 | 0 |
N.S. |
1 | 1.00 | 1.20 | 8.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.933 | 0.351 | 2.183 | 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 | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 313 | 313 | 370 | 952 | 0 | 0 | 0 | 0 | 278 | 0 |
N.S. |
1 | 1.00 | 1.18 | 3.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.981 | 0.573 | 4.342 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 244 | 227 | 270 | 350 | 555 | 0 | 0 | 0 | 301 | 0 |
N.S. |
1 | 0.93 | 1.11 | 1.43 | 2.27 | 0.00 | 0.00 | 0.00 | 1.23 | 0.00 |
time (sec) |
N/A | 0.528 | 0.424 | 0.812 | 0.477 | 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 | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 415 | 415 | 385 | 436 | 928 | 0 | 0 | 0 | 454 | 0 |
N.S. |
1 | 1.00 | 0.93 | 1.05 | 2.24 | 0.00 | 0.00 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 2.045 | 1.051 | 1.032 | 0.313 | 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 | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 377 | 377 | 356 | 408 | 775 | 0 | 0 | 0 | 418 | 0 |
N.S. |
1 | 1.00 | 0.94 | 1.08 | 2.06 | 0.00 | 0.00 | 0.00 | 1.11 | 0.00 |
time (sec) |
N/A | 2.086 | 0.802 | 0.917 | 0.298 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 286 | 286 | 325 | 377 | 780 | 0 | 0 | 0 | 382 | 0 |
N.S. |
1 | 1.00 | 1.14 | 1.32 | 2.73 | 0.00 | 0.00 | 0.00 | 1.34 | 0.00 |
time (sec) |
N/A | 0.971 | 1.701 | 0.893 | 0.291 | 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 | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 197 | 293 | 276 | 627 | 0 | 0 | 0 | 333 | 0 |
N.S. |
1 | 0.96 | 1.42 | 1.34 | 3.04 | 0.00 | 0.00 | 0.00 | 1.62 | 0.00 |
time (sec) |
N/A | 0.474 | 1.497 | 0.654 | 0.210 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 355 | 355 | 448 | 959 | 0 | 0 | 0 | 0 | 278 | 0 |
N.S. |
1 | 1.00 | 1.26 | 2.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 1.140 | 0.540 | 3.385 | 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 | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 361 | 361 | 479 | 1012 | 0 | 0 | 0 | 0 | 286 | 0 |
N.S. |
1 | 1.00 | 1.33 | 2.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 1.112 | 0.437 | 4.543 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 385 | 385 | 461 | 1086 | 0 | 0 | 0 | 0 | 322 | 0 |
N.S. |
1 | 1.00 | 1.20 | 2.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 1.100 | 0.739 | 4.485 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 396 | 396 | 569 | 1197 | 0 | 0 | 0 | 0 | 357 | 0 |
N.S. |
1 | 1.00 | 1.44 | 3.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 1.796 | 0.465 | 5.590 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 256 | 343 | 412 | 813 | 0 | 0 | 0 | 379 | 0 |
N.S. |
1 | 0.94 | 1.27 | 1.52 | 3.00 | 0.00 | 0.00 | 0.00 | 1.40 | 0.00 |
time (sec) |
N/A | 0.780 | 0.550 | 1.103 | 0.485 | 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 | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 352 | 330 | 372 | 440 | 783 | 0 | 0 | 0 | 415 | 0 |
N.S. |
1 | 0.94 | 1.06 | 1.25 | 2.22 | 0.00 | 0.00 | 0.00 | 1.18 | 0.00 |
time (sec) |
N/A | 0.945 | 0.755 | 1.135 | 0.499 | 0.000 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 479 | 449 | 402 | 468 | 961 | 0 | 0 | 0 | 451 | 0 |
N.S. |
1 | 0.94 | 0.84 | 0.98 | 2.01 | 0.00 | 0.00 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 0.969 | 0.911 | 1.165 | 0.506 | 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 | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 329 | 423 | 347 | 967 | 0 | 0 | 0 | 0 | 100 | 0 |
N.S. |
1 | 1.29 | 1.05 | 2.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 5.103 | 0.684 | 5.903 | 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 | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 247 | 271 | 260 | 905 | 0 | 0 | 0 | 0 | 88 | 0 |
N.S. |
1 | 1.10 | 1.05 | 3.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 3.587 | 0.470 | 3.576 | 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 | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 183 | 140 | 2602 | 0 | 0 | 0 | 0 | 71 | 0 |
N.S. |
1 | 1.06 | 0.81 | 15.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 1.751 | 0.546 | 1.826 | 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 | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 85 | 102 | 287 | 0 | 0 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.01 | 1.21 | 3.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.621 | 0.454 | 0.487 | 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 | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 84 | 132 | 1148 | 0 | 0 | 0 | 0 | 96 | 0 |
N.S. |
1 | 1.09 | 1.71 | 14.91 | 0.00 | 0.00 | 0.00 | 0.00 | 1.25 | 0.00 |
time (sec) |
N/A | 0.621 | 0.691 | 1.006 | 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 | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 166 | 225 | 4135 | 0 | 0 | 0 | 0 | 82 | 0 |
N.S. |
1 | 1.02 | 1.39 | 25.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 1.694 | 0.580 | 2.601 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 0.000 |