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 | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 134 | 94 | 157 | 119 | 97 | 0 | 105 | 140 | 485 |
N.S. |
1 | 1.11 | 0.78 | 1.30 | 0.98 | 0.80 | 0.00 | 0.87 | 1.16 | 4.01 |
time (sec) |
N/A | 0.453 | 0.321 | 0.678 | 0.109 | 0.081 | 0.000 | 0.133 | 0.145 | 10.639 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 95 | 75 | 139 | 87 | 78 | 0 | 76 | 100 | 244 |
N.S. |
1 | 1.03 | 0.82 | 1.51 | 0.95 | 0.85 | 0.00 | 0.83 | 1.09 | 2.65 |
time (sec) |
N/A | 0.365 | 0.275 | 0.607 | 0.120 | 0.082 | 0.000 | 0.128 | 0.143 | 6.927 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 65 | 64 | 117 | 57 | 67 | 0 | 60 | 76 | 232 |
N.S. |
1 | 1.03 | 1.02 | 1.86 | 0.90 | 1.06 | 0.00 | 0.95 | 1.21 | 3.68 |
time (sec) |
N/A | 0.240 | 0.240 | 0.601 | 0.107 | 0.071 | 0.000 | 0.129 | 0.144 | 6.752 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 73 | 96 | 57 | 81 | 245 | 196 | 148 | 122 |
N.S. |
1 | 1.00 | 1.52 | 2.00 | 1.19 | 1.69 | 5.10 | 4.08 | 3.08 | 2.54 |
time (sec) |
N/A | 0.384 | 0.181 | 0.604 | 0.110 | 0.078 | 28.622 | 0.182 | 0.148 | 4.801 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 73 | 97 | 57 | 84 | 221 | 282 | 148 | 114 |
N.S. |
1 | 1.00 | 1.52 | 2.02 | 1.19 | 1.75 | 4.60 | 5.88 | 3.08 | 2.38 |
time (sec) |
N/A | 0.382 | 0.205 | 0.678 | 0.111 | 0.076 | 28.367 | 0.206 | 0.146 | 4.532 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 74 | 70 | 108 | 98 | 65 | 0 | 407 | 273 | 312 |
N.S. |
1 | 1.04 | 0.99 | 1.52 | 1.38 | 0.92 | 0.00 | 5.73 | 3.85 | 4.39 |
time (sec) |
N/A | 0.408 | 0.201 | 0.639 | 0.113 | 0.074 | 0.000 | 0.211 | 0.151 | 5.587 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 105 | 77 | 126 | 108 | 78 | 0 | 619 | 204 | 304 |
N.S. |
1 | 1.06 | 0.78 | 1.27 | 1.09 | 0.79 | 0.00 | 6.25 | 2.06 | 3.07 |
time (sec) |
N/A | 0.428 | 0.245 | 0.700 | 0.116 | 0.073 | 0.000 | 0.259 | 0.152 | 5.343 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 141 | 107 | 144 | 161 | 96 | 0 | 861 | 350 | 684 |
N.S. |
1 | 1.06 | 0.80 | 1.08 | 1.21 | 0.72 | 0.00 | 6.47 | 2.63 | 5.14 |
time (sec) |
N/A | 0.484 | 0.280 | 0.746 | 0.109 | 0.079 | 0.000 | 0.282 | 0.159 | 7.394 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 175 | 93 | 124 | 150 | 91 | 0 | 145 | 147 | 767 |
N.S. |
1 | 1.10 | 0.58 | 0.78 | 0.94 | 0.57 | 0.00 | 0.91 | 0.92 | 4.82 |
time (sec) |
N/A | 0.477 | 0.201 | 0.636 | 0.030 | 0.075 | 0.000 | 0.136 | 0.144 | 18.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 137 | 74 | 108 | 100 | 73 | 0 | 105 | 102 | 318 |
N.S. |
1 | 1.26 | 0.68 | 0.99 | 0.92 | 0.67 | 0.00 | 0.96 | 0.94 | 2.92 |
time (sec) |
N/A | 0.400 | 0.173 | 0.408 | 0.029 | 0.079 | 0.000 | 0.138 | 0.144 | 11.084 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 70 | 63 | 96 | 90 | 61 | 0 | 80 | 85 | 312 |
N.S. |
1 | 0.91 | 0.82 | 1.25 | 1.17 | 0.79 | 0.00 | 1.04 | 1.10 | 4.05 |
time (sec) |
N/A | 0.201 | 0.134 | 0.413 | 0.028 | 0.073 | 0.000 | 0.127 | 0.144 | 11.322 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | C | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 89 | 69 | 95 | 56 | 73 | 240 | 71 | 84 | 118 |
N.S. |
1 | 1.62 | 1.25 | 1.73 | 1.02 | 1.33 | 4.36 | 1.29 | 1.53 | 2.15 |
time (sec) |
N/A | 0.405 | 0.141 | 0.701 | 0.111 | 0.086 | 30.253 | 0.133 | 0.141 | 4.336 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 89 | 69 | 95 | 56 | 82 | 216 | 83 | 92 | 118 |
N.S. |
1 | 1.62 | 1.25 | 1.73 | 1.02 | 1.49 | 3.93 | 1.51 | 1.67 | 2.15 |
time (sec) |
N/A | 0.411 | 0.137 | 0.401 | 0.137 | 0.085 | 29.683 | 0.133 | 0.142 | 4.139 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 102 | 60 | 76 | 61 | 69 | 0 | 145 | 126 | 316 |
N.S. |
1 | 1.23 | 0.72 | 0.92 | 0.73 | 0.83 | 0.00 | 1.75 | 1.52 | 3.81 |
time (sec) |
N/A | 0.410 | 0.128 | 0.405 | 0.128 | 0.082 | 0.000 | 0.143 | 0.145 | 8.837 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 133 | 71 | 89 | 86 | 90 | 0 | 187 | 140 | 304 |
N.S. |
1 | 1.15 | 0.61 | 0.77 | 0.74 | 0.78 | 0.00 | 1.61 | 1.21 | 2.62 |
time (sec) |
N/A | 0.453 | 0.173 | 0.413 | 0.120 | 0.079 | 0.000 | 0.141 | 0.145 | 8.122 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 168 | 93 | 107 | 122 | 101 | 0 | 325 | 202 | 695 |
N.S. |
1 | 1.09 | 0.60 | 0.69 | 0.79 | 0.66 | 0.00 | 2.11 | 1.31 | 4.51 |
time (sec) |
N/A | 0.493 | 0.230 | 0.419 | 0.108 | 0.079 | 0.000 | 0.154 | 0.151 | 19.236 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 234 | 149 | 145 | 295 | 138 | 367 | 228 | 142 | 287 |
N.S. |
1 | 1.11 | 0.71 | 0.69 | 1.40 | 0.66 | 1.75 | 1.09 | 0.68 | 1.37 |
time (sec) |
N/A | 0.457 | 0.290 | 0.915 | 0.118 | 0.083 | 21.950 | 0.175 | 0.157 | 4.135 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 186 | 116 | 109 | 217 | 104 | 367 | 164 | 106 | 215 |
N.S. |
1 | 1.17 | 0.73 | 0.69 | 1.36 | 0.65 | 2.31 | 1.03 | 0.67 | 1.35 |
time (sec) |
N/A | 0.401 | 0.231 | 0.779 | 0.112 | 0.080 | 13.016 | 0.172 | 0.151 | 5.112 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 139 | 80 | 73 | 139 | 71 | 350 | 102 | 70 | 143 |
N.S. |
1 | 1.28 | 0.73 | 0.67 | 1.28 | 0.65 | 3.21 | 0.94 | 0.64 | 1.31 |
time (sec) |
N/A | 0.334 | 0.167 | 0.790 | 0.112 | 0.080 | 10.705 | 0.164 | 0.145 | 3.924 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | C | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 107 | 106 | 143 | 105 | 80 | 304 | 189 | 199 | 161 |
N.S. |
1 | 1.07 | 1.06 | 1.43 | 1.05 | 0.80 | 3.04 | 1.89 | 1.99 | 1.61 |
time (sec) |
N/A | 0.355 | 0.220 | 0.838 | 0.114 | 0.083 | 20.090 | 0.278 | 0.156 | 4.826 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 149 | 85 | 137 | 123 | 98 | 0 | 374 | 344 | 422 |
N.S. |
1 | 1.51 | 0.86 | 1.38 | 1.24 | 0.99 | 0.00 | 3.78 | 3.47 | 4.26 |
time (sec) |
N/A | 0.373 | 0.245 | 0.876 | 0.115 | 0.081 | 0.000 | 0.317 | 0.159 | 6.333 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 180 | 102 | 143 | 193 | 102 | 0 | 767 | 505 | 932 |
N.S. |
1 | 1.43 | 0.81 | 1.13 | 1.53 | 0.81 | 0.00 | 6.09 | 4.01 | 7.40 |
time (sec) |
N/A | 0.400 | 0.242 | 0.875 | 0.118 | 0.083 | 0.000 | 0.430 | 0.167 | 11.168 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 226 | 141 | 179 | 271 | 137 | 0 | 1434 | 589 | 1621 |
N.S. |
1 | 1.26 | 0.78 | 0.99 | 1.51 | 0.76 | 0.00 | 7.97 | 3.27 | 9.01 |
time (sec) |
N/A | 0.435 | 0.351 | 0.880 | 0.114 | 0.096 | 0.000 | 0.612 | 0.182 | 19.642 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 192 | 134 | 161 | 226 | 134 | 0 | 177 | 214 | 1132 |
N.S. |
1 | 0.89 | 0.62 | 0.75 | 1.05 | 0.62 | 0.00 | 0.82 | 0.99 | 5.24 |
time (sec) |
N/A | 0.393 | 0.284 | 0.857 | 0.117 | 0.095 | 0.000 | 0.163 | 0.150 | 21.807 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 155 | 98 | 128 | 146 | 100 | 0 | 115 | 141 | 651 |
N.S. |
1 | 1.28 | 0.81 | 1.06 | 1.21 | 0.83 | 0.00 | 0.95 | 1.17 | 5.38 |
time (sec) |
N/A | 0.311 | 0.197 | 0.823 | 0.121 | 0.085 | 0.000 | 0.171 | 0.147 | 12.556 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 126 | 86 | 116 | 94 | 90 | 0 | 239 | 105 | 306 |
N.S. |
1 | 1.34 | 0.91 | 1.23 | 1.00 | 0.96 | 0.00 | 2.54 | 1.12 | 3.26 |
time (sec) |
N/A | 0.318 | 0.179 | 0.892 | 0.122 | 0.083 | 0.000 | 0.209 | 0.157 | 7.610 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 135 | 81 | 107 | 94 | 90 | 257 | 530 | 103 | 138 |
N.S. |
1 | 1.35 | 0.81 | 1.07 | 0.94 | 0.90 | 2.57 | 5.30 | 1.03 | 1.38 |
time (sec) |
N/A | 0.325 | 0.167 | 0.847 | 0.109 | 0.081 | 19.145 | 0.259 | 0.160 | 4.497 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 156 | 87 | 82 | 148 | 76 | 0 | 1055 | 79 | 146 |
N.S. |
1 | 1.26 | 0.70 | 0.66 | 1.19 | 0.61 | 0.00 | 8.51 | 0.64 | 1.18 |
time (sec) |
N/A | 0.338 | 0.140 | 0.882 | 0.123 | 0.085 | 0.000 | 0.359 | 0.163 | 4.197 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 193 | 124 | 118 | 226 | 110 | 0 | 1451 | 115 | 218 |
N.S. |
1 | 1.08 | 0.70 | 0.66 | 1.27 | 0.62 | 0.00 | 8.15 | 0.65 | 1.22 |
time (sec) |
N/A | 0.362 | 0.182 | 0.888 | 0.110 | 0.105 | 0.000 | 0.494 | 0.173 | 4.258 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 230 | 158 | 154 | 304 | 144 | 0 | 1847 | 151 | 290 |
N.S. |
1 | 0.99 | 0.68 | 0.66 | 1.31 | 0.62 | 0.00 | 7.96 | 0.65 | 1.25 |
time (sec) |
N/A | 0.385 | 0.234 | 1.013 | 0.116 | 0.149 | 0.000 | 0.721 | 0.184 | 4.661 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 404 | 383 | 373 | 508 | 444 | 406 | 0 | 1539 | 869 | 3993 |
N.S. |
1 | 0.95 | 0.92 | 1.26 | 1.10 | 1.00 | 0.00 | 3.81 | 2.15 | 9.88 |
time (sec) |
N/A | 0.836 | 1.682 | 0.528 | 0.118 | 0.095 | 0.000 | 0.296 | 0.179 | 43.844 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 284 | 271 | 262 | 358 | 307 | 279 | 0 | 1059 | 577 | 2920 |
N.S. |
1 | 0.95 | 0.92 | 1.26 | 1.08 | 0.98 | 0.00 | 3.73 | 2.03 | 10.28 |
time (sec) |
N/A | 0.672 | 1.267 | 0.482 | 0.118 | 0.083 | 0.000 | 0.240 | 0.160 | 30.933 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 169 | 159 | 231 | 174 | 170 | 0 | 631 | 320 | 736 |
N.S. |
1 | 1.03 | 0.97 | 1.41 | 1.06 | 1.04 | 0.00 | 3.85 | 1.95 | 4.49 |
time (sec) |
N/A | 0.457 | 0.696 | 0.440 | 0.117 | 0.081 | 0.000 | 0.201 | 0.159 | 10.332 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 91 | 89 | 155 | 93 | 95 | 0 | 284 | 140 | 361 |
N.S. |
1 | 0.96 | 0.94 | 1.63 | 0.98 | 1.00 | 0.00 | 2.99 | 1.47 | 3.80 |
time (sec) |
N/A | 0.257 | 0.286 | 0.444 | 0.131 | 0.073 | 0.000 | 0.156 | 0.150 | 7.482 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 227 | 225 | 423 | 0 | 591 | 0 | 0 | 662 | 13115 |
N.S. |
1 | 1.11 | 1.10 | 2.06 | 0.00 | 2.88 | 0.00 | 0.00 | 3.23 | 63.98 |
time (sec) |
N/A | 0.679 | 0.754 | 0.859 | 0.000 | 5.752 | 0.000 | 0.000 | 0.229 | 32.886 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 322 | 356 | 244 | 648 | 0 | 1358 | 0 | 0 | 1966 | 11177 |
N.S. |
1 | 1.11 | 0.76 | 2.01 | 0.00 | 4.22 | 0.00 | 0.00 | 6.11 | 34.71 |
time (sec) |
N/A | 0.810 | 1.180 | 0.785 | 0.000 | 26.661 | 0.000 | 0.000 | 0.298 | 38.554 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 301 | 320 | 310 | 1156 | 0 | 2201 | 0 | 0 | 3422 | 21781 |
N.S. |
1 | 1.06 | 1.03 | 3.84 | 0.00 | 7.31 | 0.00 | 0.00 | 11.37 | 72.36 |
time (sec) |
N/A | 0.764 | 2.030 | 0.812 | 0.000 | 63.351 | 0.000 | 0.000 | 0.332 | 70.716 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 332 | 359 | 259 | 361 | 355 | 286 | 0 | 374 | 565 | 2606 |
N.S. |
1 | 1.08 | 0.78 | 1.09 | 1.07 | 0.86 | 0.00 | 1.13 | 1.70 | 7.85 |
time (sec) |
N/A | 0.858 | 0.999 | 0.793 | 0.124 | 0.084 | 0.000 | 0.171 | 0.161 | 31.508 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 244 | 178 | 256 | 231 | 192 | 0 | 232 | 357 | 1732 |
N.S. |
1 | 1.07 | 0.78 | 1.12 | 1.01 | 0.84 | 0.00 | 1.02 | 1.57 | 7.60 |
time (sec) |
N/A | 0.684 | 0.659 | 0.741 | 0.127 | 0.088 | 0.000 | 0.156 | 0.151 | 26.441 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 140 | 107 | 173 | 131 | 114 | 0 | 112 | 184 | 492 |
N.S. |
1 | 1.10 | 0.84 | 1.36 | 1.03 | 0.90 | 0.00 | 0.88 | 1.45 | 3.87 |
time (sec) |
N/A | 0.458 | 0.459 | 0.661 | 0.112 | 0.084 | 0.000 | 0.140 | 0.148 | 10.187 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 65 | 64 | 117 | 57 | 67 | 0 | 60 | 76 | 232 |
N.S. |
1 | 1.03 | 1.02 | 1.86 | 0.90 | 1.06 | 0.00 | 0.95 | 1.21 | 3.68 |
time (sec) |
N/A | 0.249 | 0.242 | 0.702 | 0.113 | 0.080 | 0.000 | 0.132 | 0.146 | 7.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 127 | 156 | 289 | 0 | 493 | 0 | 0 | 535 | 5803 |
N.S. |
1 | 1.04 | 1.28 | 2.37 | 0.00 | 4.04 | 0.00 | 0.00 | 4.39 | 47.57 |
time (sec) |
N/A | 0.478 | 0.591 | 1.130 | 0.000 | 3.660 | 0.000 | 0.000 | 0.173 | 17.472 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | B | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 184 | 197 | 899 | 0 | 1025 | 0 | 0 | 1375 | 10198 |
N.S. |
1 | 1.13 | 1.21 | 5.52 | 0.00 | 6.29 | 0.00 | 0.00 | 8.44 | 62.56 |
time (sec) |
N/A | 0.550 | 0.894 | 1.155 | 0.000 | 14.648 | 0.000 | 0.000 | 0.188 | 34.200 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | B | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 263 | 228 | 1449 | 0 | 1580 | 0 | 0 | 2499 | 9097 |
N.S. |
1 | 1.06 | 0.92 | 5.84 | 0.00 | 6.37 | 0.00 | 0.00 | 10.08 | 36.68 |
time (sec) |
N/A | 0.613 | 1.226 | 1.108 | 0.000 | 0.141 | 0.000 | 0.000 | 0.257 | 42.008 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 554 | 512 | 402 | 575 | 584 | 1001 | 0 | 2671 | 951 | 0 |
N.S. |
1 | 0.92 | 0.73 | 1.04 | 1.05 | 1.81 | 0.00 | 4.82 | 1.72 | 0.00 |
time (sec) |
N/A | 1.345 | 0.936 | 0.687 | 0.122 | 0.134 | 0.000 | 2.190 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 415 | 398 | 286 | 401 | 417 | 703 | 0 | 1868 | 637 | 4853 |
N.S. |
1 | 0.96 | 0.69 | 0.97 | 1.00 | 1.69 | 0.00 | 4.50 | 1.53 | 11.69 |
time (sec) |
N/A | 1.014 | 0.667 | 0.649 | 0.121 | 0.122 | 0.000 | 1.684 | 0.165 | 140.458 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 284 | 183 | 253 | 248 | 441 | 0 | 1142 | 356 | 1765 |
N.S. |
1 | 1.11 | 0.72 | 0.99 | 0.97 | 1.73 | 0.00 | 4.48 | 1.40 | 6.92 |
time (sec) |
N/A | 0.622 | 0.412 | 0.607 | 0.122 | 0.098 | 0.000 | 1.130 | 0.157 | 26.594 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 153 | 123 | 163 | 140 | 265 | 0 | 527 | 161 | 876 |
N.S. |
1 | 0.90 | 0.72 | 0.96 | 0.82 | 1.56 | 0.00 | 3.10 | 0.95 | 5.15 |
time (sec) |
N/A | 0.283 | 0.210 | 0.598 | 0.113 | 0.091 | 0.000 | 0.611 | 0.155 | 15.290 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 316 | 345 | 271 | 452 | 0 | 0 | 0 | 0 | 3341 | 24910 |
N.S. |
1 | 1.09 | 0.86 | 1.43 | 0.00 | 0.00 | 0.00 | 0.00 | 10.57 | 78.83 |
time (sec) |
N/A | 0.886 | 0.782 | 1.046 | 0.000 | 0.000 | 0.000 | 0.000 | 5.833 | 70.997 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 444 | 462 | 260 | 707 | 0 | 0 | 0 | 631 | 10007 | 21612 |
N.S. |
1 | 1.04 | 0.59 | 1.59 | 0.00 | 0.00 | 0.00 | 1.42 | 22.54 | 48.68 |
time (sec) |
N/A | 1.057 | 0.800 | 1.050 | 0.000 | 0.000 | 0.000 | 0.459 | 13.029 | 83.799 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 390 | 441 | 326 | 1278 | 0 | 0 | 0 | 1592 | 20805 | 0 |
N.S. |
1 | 1.13 | 0.84 | 3.28 | 0.00 | 0.00 | 0.00 | 4.08 | 53.35 | 0.00 |
time (sec) |
N/A | 1.017 | 1.429 | 1.050 | 0.000 | 0.000 | 0.000 | 0.741 | 9.974 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 465 | 482 | 283 | 390 | 471 | 700 | 0 | 571 | 622 | 4167 |
N.S. |
1 | 1.04 | 0.61 | 0.84 | 1.01 | 1.51 | 0.00 | 1.23 | 1.34 | 8.96 |
time (sec) |
N/A | 1.283 | 0.601 | 0.766 | 0.121 | 0.121 | 0.000 | 0.263 | 0.168 | 95.584 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 335 | 362 | 200 | 270 | 317 | 482 | 0 | 363 | 399 | 2799 |
N.S. |
1 | 1.08 | 0.60 | 0.81 | 0.95 | 1.44 | 0.00 | 1.08 | 1.19 | 8.36 |
time (sec) |
N/A | 0.967 | 0.420 | 0.746 | 0.123 | 0.110 | 0.000 | 0.240 | 0.162 | 49.721 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 248 | 128 | 175 | 189 | 302 | 0 | 191 | 209 | 1011 |
N.S. |
1 | 1.22 | 0.63 | 0.86 | 0.93 | 1.49 | 0.00 | 0.94 | 1.03 | 4.98 |
time (sec) |
N/A | 0.617 | 0.231 | 0.678 | 0.112 | 0.104 | 0.000 | 0.222 | 0.153 | 19.951 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 116 | 90 | 126 | 88 | 196 | 0 | 106 | 93 | 489 |
N.S. |
1 | 0.93 | 0.72 | 1.01 | 0.70 | 1.57 | 0.00 | 0.85 | 0.74 | 3.91 |
time (sec) |
N/A | 0.269 | 0.137 | 0.682 | 0.108 | 0.096 | 0.000 | 0.202 | 0.147 | 11.521 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 233 | 178 | 299 | 0 | 0 | 0 | 0 | 3194 | 9298 |
N.S. |
1 | 1.25 | 0.96 | 1.61 | 0.00 | 0.00 | 0.00 | 0.00 | 17.17 | 49.99 |
time (sec) |
N/A | 0.671 | 0.405 | 1.220 | 0.000 | 0.000 | 0.000 | 0.000 | 0.768 | 28.702 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 308 | 229 | 1166 | 0 | 0 | 0 | 526 | 8629 | 106511 |
N.S. |
1 | 1.31 | 0.97 | 4.96 | 0.00 | 0.00 | 0.00 | 2.24 | 36.72 | 453.24 |
time (sec) |
N/A | 0.772 | 0.708 | 1.234 | 0.000 | 0.000 | 0.000 | 0.304 | 0.928 | 121.924 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 301 | 357 | 252 | 1794 | 0 | 1355 | 0 | 1425 | 15212 | 9344 |
N.S. |
1 | 1.19 | 0.84 | 5.96 | 0.00 | 4.50 | 0.00 | 4.73 | 50.54 | 31.04 |
time (sec) |
N/A | 0.829 | 0.991 | 1.321 | 0.000 | 38.127 | 0.000 | 0.636 | 3.089 | 67.450 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 230 | 185 | 1095 | 0 | 1186 | 0 | 627 | 3120 | 7235 |
N.S. |
1 | 1.10 | 0.88 | 5.21 | 0.00 | 5.65 | 0.00 | 2.99 | 14.86 | 34.45 |
time (sec) |
N/A | 0.547 | 0.547 | 0.942 | 0.000 | 0.128 | 0.000 | 0.363 | 0.229 | 46.166 |
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 | 25 | 25 | 19 | 20 | 19 | 19 | 19 | 22 | 19 | 19 |
N.S. |
1 | 1.00 | 0.76 | 0.80 | 0.76 | 0.76 | 0.76 | 0.88 | 0.76 | 0.76 |
time (sec) |
N/A | 0.224 | 0.010 | 0.476 | 0.025 | 0.075 | 0.063 | 0.128 | 0.147 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 141 | 141 | 141 | 170 | 0 | 0 | 170 | 300 | 166 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.21 | 0.00 | 0.00 | 1.21 | 2.13 | 1.18 |
time (sec) |
N/A | 0.454 | 0.059 | 0.853 | 0.040 | 0.000 | 0.000 | 0.130 | 0.149 | 6.856 |
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 | 254 | 254 | 278 | 253 | 339 | 368 | 517 | 475 | 310 | 279 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.33 | 1.45 | 2.04 | 1.87 | 1.22 | 1.10 |
time (sec) |
N/A | 0.569 | 0.242 | 1.541 | 0.036 | 0.078 | 1.471 | 0.128 | 0.148 | 0.076 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1353 | 815 | 1253 | 5734 | 0 | 3096 | 0 | 4456 | 34 | 0 |
N.S. |
1 | 0.60 | 0.93 | 4.24 | 0.00 | 2.29 | 0.00 | 3.29 | 0.03 | 0.00 |
time (sec) |
N/A | 1.355 | 5.964 | 0.623 | 0.000 | 1.312 | 0.000 | 0.709 | 200.021 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 715 | 461 | 662 | 3025 | 0 | 1620 | 0 | 2481 | 32 | 0 |
N.S. |
1 | 0.64 | 0.93 | 4.23 | 0.00 | 2.27 | 0.00 | 3.47 | 0.04 | 0.00 |
time (sec) |
N/A | 0.721 | 2.586 | 0.571 | 0.000 | 0.413 | 0.000 | 0.452 | 200.023 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 330 | 249 | 283 | 1207 | 0 | 840 | 0 | 1035 | 1024 | 0 |
N.S. |
1 | 0.75 | 0.86 | 3.66 | 0.00 | 2.55 | 0.00 | 3.14 | 3.10 | 0.00 |
time (sec) |
N/A | 0.383 | 0.879 | 0.535 | 0.000 | 0.137 | 0.000 | 0.274 | 2.861 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 453 | 481 | 404 | 3898 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.06 | 0.89 | 8.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.297 | 1.482 | 0.845 | 0.000 | 0.000 | 0.000 | 0.000 | 200.024 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 524 | 546 | 358 | 4680 | 0 | 0 | 0 | 1507 | 34 | 0 |
N.S. |
1 | 1.04 | 0.68 | 8.93 | 0.00 | 0.00 | 0.00 | 2.88 | 0.06 | 0.00 |
time (sec) |
N/A | 1.329 | 2.052 | 0.844 | 0.000 | 0.000 | 0.000 | 1.388 | 200.023 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 660 | 695 | 536 | 11204 | 0 | 0 | 0 | 8241 | 34 | 0 |
N.S. |
1 | 1.05 | 0.81 | 16.98 | 0.00 | 0.00 | 0.00 | 12.49 | 0.05 | 0.00 |
time (sec) |
N/A | 1.643 | 4.622 | 0.882 | 0.000 | 0.000 | 0.000 | 4.816 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1035 | 778 | 3220 | 3958 | 0 | 2176 | 0 | 1509 | 34 | 0 |
N.S. |
1 | 0.75 | 3.11 | 3.82 | 0.00 | 2.10 | 0.00 | 1.46 | 0.03 | 0.00 |
time (sec) |
N/A | 1.331 | 16.908 | 0.635 | 0.000 | 2.491 | 0.000 | 0.270 | 200.022 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 535 | 419 | 474 | 2002 | 0 | 1114 | 0 | 733 | 1525 | 0 |
N.S. |
1 | 0.78 | 0.89 | 3.74 | 0.00 | 2.08 | 0.00 | 1.37 | 2.85 | 0.00 |
time (sec) |
N/A | 0.696 | 9.424 | 0.546 | 0.000 | 0.592 | 0.000 | 0.193 | 47.982 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 208 | 217 | 763 | 0 | 576 | 0 | 313 | 648 | 1832 |
N.S. |
1 | 0.85 | 0.88 | 3.10 | 0.00 | 2.34 | 0.00 | 1.27 | 2.63 | 7.45 |
time (sec) |
N/A | 0.349 | 3.551 | 0.533 | 0.000 | 0.201 | 0.000 | 0.159 | 0.194 | 61.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 312 | 465 | 1822 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.07 | 1.59 | 6.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.789 | 12.036 | 0.923 | 0.000 | 0.000 | 0.000 | 0.000 | 200.018 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 364 | 396 | 417 | 3670 | 0 | 0 | 0 | 1354 | 34 | 0 |
N.S. |
1 | 1.09 | 1.15 | 10.08 | 0.00 | 0.00 | 0.00 | 3.72 | 0.09 | 0.00 |
time (sec) |
N/A | 0.944 | 11.353 | 0.977 | 0.000 | 0.000 | 0.000 | 1.234 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 446 | 533 | 523 | 9100 | 0 | 0 | 0 | 7922 | 34 | 0 |
N.S. |
1 | 1.20 | 1.17 | 20.40 | 0.00 | 0.00 | 0.00 | 17.76 | 0.08 | 0.00 |
time (sec) |
N/A | 1.125 | 13.113 | 1.010 | 0.000 | 0.000 | 0.000 | 16.992 | 200.016 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 685 | 719 | 657 | 15990 | 0 | 0 | 0 | 25338 | 34 | 0 |
N.S. |
1 | 1.05 | 0.96 | 23.34 | 0.00 | 0.00 | 0.00 | 36.99 | 0.05 | 0.00 |
time (sec) |
N/A | 1.724 | 15.142 | 1.102 | 0.000 | 0.000 | 0.000 | 79.236 | 200.028 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 723 | 735 | 632 | 2528 | 0 | 1436 | 0 | 946 | 34 | 0 |
N.S. |
1 | 1.02 | 0.87 | 3.50 | 0.00 | 1.99 | 0.00 | 1.31 | 0.05 | 0.00 |
time (sec) |
N/A | 1.260 | 2.516 | 0.758 | 0.000 | 1.103 | 0.000 | 0.210 | 200.025 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 365 | 381 | 314 | 1199 | 0 | 720 | 0 | 441 | 932 | 2621 |
N.S. |
1 | 1.04 | 0.86 | 3.28 | 0.00 | 1.97 | 0.00 | 1.21 | 2.55 | 7.18 |
time (sec) |
N/A | 0.680 | 0.933 | 0.648 | 0.000 | 0.306 | 0.000 | 0.166 | 0.205 | 70.691 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 167 | 141 | 425 | 0 | 380 | 0 | 190 | 359 | 833 |
N.S. |
1 | 1.02 | 0.86 | 2.59 | 0.00 | 2.32 | 0.00 | 1.16 | 2.19 | 5.08 |
time (sec) |
N/A | 0.316 | 0.327 | 0.685 | 0.000 | 0.155 | 0.000 | 0.146 | 0.149 | 18.246 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 204 | 183 | 746 | 0 | 0 | 0 | 0 | 88 | 96118 |
N.S. |
1 | 1.09 | 0.97 | 3.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 511.27 |
time (sec) |
N/A | 0.528 | 0.498 | 1.062 | 0.000 | 0.000 | 0.000 | 0.000 | 1.345 | 159.396 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 254 | 299 | 249 | 2973 | 0 | 0 | 0 | 1319 | 5671 | 0 |
N.S. |
1 | 1.18 | 0.98 | 11.70 | 0.00 | 0.00 | 0.00 | 5.19 | 22.33 | 0.00 |
time (sec) |
N/A | 0.626 | 1.086 | 0.967 | 0.000 | 0.000 | 0.000 | 0.868 | 1.686 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 403 | 445 | 420 | 7119 | 0 | 4058 | 0 | 7939 | 34 | 0 |
N.S. |
1 | 1.10 | 1.04 | 17.67 | 0.00 | 10.07 | 0.00 | 19.70 | 0.08 | 0.00 |
time (sec) |
N/A | 0.946 | 2.438 | 1.119 | 0.000 | 157.369 | 0.000 | 33.364 | 200.025 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 770 | 869 | 1036 | 18802 | 0 | 0 | 0 | 25632 | 34 | 0 |
N.S. |
1 | 1.13 | 1.35 | 24.42 | 0.00 | 0.00 | 0.00 | 33.29 | 0.04 | 0.00 |
time (sec) |
N/A | 1.760 | 9.260 | 1.368 | 0.000 | 0.000 | 0.000 | 78.859 | 200.018 | 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 | 1183 | 1213 | 1422 | 2077 | 0 | 1916 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.03 | 1.20 | 1.76 | 0.00 | 1.62 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 2.829 | 33.717 | 3.129 | 0.000 | 0.158 | 0.000 | 0.000 | 200.019 | 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 | 762 | 789 | 917 | 1205 | 0 | 1393 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.04 | 1.20 | 1.58 | 0.00 | 1.83 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.791 | 29.022 | 4.142 | 0.000 | 0.142 | 0.000 | 0.000 | 200.025 | 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 | 708 | 729 | 633 | 1163 | 0 | 1463 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.03 | 0.89 | 1.64 | 0.00 | 2.07 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.528 | 26.108 | 4.939 | 0.000 | 0.159 | 0.000 | 0.000 | 200.021 | 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 | 687 | 697 | 815 | 1378 | 0 | 2588 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.01 | 1.19 | 2.01 | 0.00 | 3.77 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.480 | 29.223 | 6.862 | 0.000 | 0.271 | 0.000 | 0.000 | 200.027 | 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 | 961 | 996 | 1444 | 2292 | 0 | 4721 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.04 | 1.50 | 2.39 | 0.00 | 4.91 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 2.282 | 33.932 | 8.046 | 0.000 | 0.846 | 0.000 | 0.000 | 200.024 | 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 | 1714 | 1770 | 15963 | 3900 | 0 | 9150 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.03 | 9.31 | 2.28 | 0.00 | 5.34 | 0.00 | 0.00 | 0.02 | 0.00 |
time (sec) |
N/A | 4.404 | 36.985 | 8.695 | 0.000 | 2.801 | 0.000 | 0.000 | 200.018 | 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 | 1233 | 1268 | 1470 | 2108 | 0 | 1931 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.03 | 1.19 | 1.71 | 0.00 | 1.57 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 3.130 | 34.507 | 7.332 | 0.000 | 0.154 | 0.000 | 0.000 | 200.018 | 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 | 767 | 792 | 922 | 1205 | 0 | 1392 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.03 | 1.20 | 1.57 | 0.00 | 1.81 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.678 | 29.063 | 3.990 | 0.000 | 0.179 | 0.000 | 0.000 | 200.018 | 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 | 529 | 545 | 562 | 812 | 0 | 1036 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 1.06 | 1.53 | 0.00 | 1.96 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.983 | 27.042 | 4.427 | 0.000 | 0.124 | 0.000 | 0.000 | 108.086 | 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 | 540 | 555 | 551 | 861 | 0 | 1336 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.03 | 1.02 | 1.59 | 0.00 | 2.47 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.092 | 25.117 | 6.114 | 0.000 | 0.147 | 0.000 | 0.000 | 200.028 | 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 | 596 | 630 | 724 | 1269 | 0 | 2429 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.06 | 1.21 | 2.13 | 0.00 | 4.08 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.236 | 28.269 | 8.326 | 0.000 | 0.311 | 0.000 | 0.000 | 200.026 | 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 | 1034 | 1073 | 1449 | 2330 | 0 | 4867 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.04 | 1.40 | 2.25 | 0.00 | 4.71 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 2.552 | 33.577 | 21.716 | 0.000 | 0.961 | 0.000 | 0.000 | 200.028 | 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 | 825 | 857 | 1000 | 1233 | 0 | 1388 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.04 | 1.21 | 1.49 | 0.00 | 1.68 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.698 | 29.492 | 6.516 | 0.000 | 0.139 | 0.000 | 0.000 | 200.018 | 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 | 524 | 542 | 615 | 812 | 0 | 1036 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 1.17 | 1.55 | 0.00 | 1.98 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.992 | 25.859 | 4.455 | 0.000 | 0.132 | 0.000 | 0.000 | 109.348 | 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 | 384 | 394 | 418 | 615 | 0 | 807 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 1.09 | 1.60 | 0.00 | 2.10 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.676 | 24.575 | 5.247 | 0.000 | 0.126 | 0.000 | 0.000 | 32.353 | 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 | 422 | 445 | 477 | 784 | 0 | 1240 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 1.13 | 1.86 | 0.00 | 2.94 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.779 | 24.178 | 7.748 | 0.000 | 0.141 | 0.000 | 0.000 | 38.619 | 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 | 642 | 672 | 699 | 1249 | 0 | 2344 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 1.09 | 1.95 | 0.00 | 3.65 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.369 | 27.496 | 21.469 | 0.000 | 0.284 | 0.000 | 0.000 | 141.002 | 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 | 1116 | 1176 | 1520 | 2283 | 0 | 5108 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.05 | 1.36 | 2.05 | 0.00 | 4.58 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 2.529 | 33.378 | 24.109 | 0.000 | 1.005 | 0.000 | 0.000 | 200.026 | 0.000 |