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 | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 131 | 113 | 113 | 0 | 424 | 204 | 111 | 312 | 129 |
N.S. |
1 | 1.07 | 0.92 | 0.92 | 0.00 | 3.45 | 1.66 | 0.90 | 2.54 | 1.05 |
time (sec) |
N/A | 0.443 | 0.055 | 0.124 | 0.000 | 0.074 | 0.459 | 0.116 | 0.190 | 17.022 |
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 | 133 | 133 | 133 | 128 | 129 | 129 | 144 | 131 | 135 | 127 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.97 | 0.97 | 1.08 | 0.98 | 1.02 | 0.95 |
time (sec) |
N/A | 0.519 | 0.016 | 0.112 | 0.028 | 0.056 | 0.027 | 0.106 | 0.175 | 0.061 |
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 | 97 | 97 | 97 | 90 | 89 | 89 | 104 | 91 | 94 | 89 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.92 | 0.92 | 1.07 | 0.94 | 0.97 | 0.92 |
time (sec) |
N/A | 0.436 | 0.014 | 0.111 | 0.028 | 0.059 | 0.024 | 0.107 | 0.180 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 60 | 51 | 50 | 50 | 60 | 50 | 53 | 50 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.83 | 0.83 | 1.00 | 0.83 | 0.88 | 0.83 |
time (sec) |
N/A | 0.345 | 0.002 | 0.100 | 0.040 | 0.056 | 0.021 | 0.118 | 0.179 | 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 | 25 | 25 | 25 | 22 | 21 | 21 | 22 | 21 | 24 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.84 | 0.84 | 0.88 | 0.84 | 0.96 | 0.84 |
time (sec) |
N/A | 0.273 | 0.001 | 0.067 | 0.032 | 0.053 | 0.017 | 0.115 | 0.176 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 108 | 97 | 104 | 0 | 268 | 236 | 118 | 155 | 141 |
N.S. |
1 | 1.00 | 0.90 | 0.96 | 0.00 | 2.48 | 2.19 | 1.09 | 1.44 | 1.31 |
time (sec) |
N/A | 0.435 | 0.052 | 0.141 | 0.000 | 0.078 | 0.238 | 0.130 | 0.182 | 16.954 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 142 | 134 | 129 | 0 | 394 | 314 | 144 | 263 | 183 |
N.S. |
1 | 1.08 | 1.02 | 0.98 | 0.00 | 3.01 | 2.40 | 1.10 | 2.01 | 1.40 |
time (sec) |
N/A | 0.778 | 0.079 | 0.125 | 0.000 | 0.072 | 0.427 | 0.151 | 0.173 | 16.944 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 173 | 154 | 152 | 0 | 516 | 257 | 160 | 377 | 164 |
N.S. |
1 | 1.12 | 0.99 | 0.98 | 0.00 | 3.33 | 1.66 | 1.03 | 2.43 | 1.06 |
time (sec) |
N/A | 0.938 | 0.080 | 0.134 | 0.000 | 0.076 | 0.750 | 0.111 | 0.180 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 212 | 174 | 179 | 0 | 662 | 292 | 183 | 504 | 199 |
N.S. |
1 | 1.13 | 0.93 | 0.96 | 0.00 | 3.54 | 1.56 | 0.98 | 2.70 | 1.06 |
time (sec) |
N/A | 0.991 | 0.095 | 0.133 | 0.000 | 0.078 | 1.198 | 0.109 | 0.185 | 17.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 226 | 250 | 200 | 212 | 0 | 806 | 335 | 216 | 631 | 240 |
N.S. |
1 | 1.11 | 0.88 | 0.94 | 0.00 | 3.57 | 1.48 | 0.96 | 2.79 | 1.06 |
time (sec) |
N/A | 1.038 | 0.127 | 0.146 | 0.000 | 0.076 | 2.063 | 0.114 | 0.180 | 17.104 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 353 | 437 | 444 | 118 | 432 | 2878 | 500 | 510 | 812 | 4022 |
N.S. |
1 | 1.24 | 1.26 | 0.33 | 1.22 | 8.15 | 1.42 | 1.44 | 2.30 | 11.39 |
time (sec) |
N/A | 1.094 | 0.228 | 0.115 | 0.114 | 9.624 | 1.811 | 0.116 | 0.199 | 17.782 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 278 | 370 | 360 | 80 | 342 | 2133 | 350 | 411 | 624 | 2712 |
N.S. |
1 | 1.33 | 1.29 | 0.29 | 1.23 | 7.67 | 1.26 | 1.48 | 2.24 | 9.76 |
time (sec) |
N/A | 0.999 | 0.180 | 0.108 | 0.112 | 2.039 | 1.143 | 0.136 | 0.179 | 0.552 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 220 | 297 | 269 | 56 | 288 | 1480 | 238 | 319 | 452 | 1479 |
N.S. |
1 | 1.35 | 1.22 | 0.25 | 1.31 | 6.73 | 1.08 | 1.45 | 2.05 | 6.72 |
time (sec) |
N/A | 0.753 | 0.174 | 0.109 | 0.113 | 0.463 | 0.719 | 0.171 | 0.182 | 17.367 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 230 | 183 | 34 | 221 | 767 | 109 | 241 | 239 | 599 |
N.S. |
1 | 1.28 | 1.02 | 0.19 | 1.23 | 4.26 | 0.61 | 1.34 | 1.33 | 3.33 |
time (sec) |
N/A | 0.713 | 0.036 | 0.099 | 0.114 | 0.085 | 0.335 | 0.114 | 0.188 | 0.362 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 200 | 134 | 27 | 169 | 112 | 20 | 179 | 112 | 33 |
N.S. |
1 | 1.49 | 1.00 | 0.20 | 1.26 | 0.84 | 0.15 | 1.34 | 0.84 | 0.25 |
time (sec) |
N/A | 0.609 | 0.014 | 0.090 | 0.109 | 0.069 | 0.071 | 0.124 | 0.180 | 0.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 336 | 234 | 253 | 0 | 4084 | 0 | 344 | 330 | 4802 |
N.S. |
1 | 1.31 | 0.91 | 0.98 | 0.00 | 15.89 | 0.00 | 1.34 | 1.28 | 18.68 |
time (sec) |
N/A | 0.787 | 0.106 | 0.165 | 0.000 | 0.442 | 0.000 | 0.112 | 0.191 | 18.473 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 336 | 453 | 362 | 307 | 0 | 8409 | 0 | 531 | 1155 | 16369 |
N.S. |
1 | 1.35 | 1.08 | 0.91 | 0.00 | 25.03 | 0.00 | 1.58 | 3.44 | 48.72 |
time (sec) |
N/A | 0.963 | 0.330 | 0.198 | 0.000 | 8.634 | 0.000 | 0.124 | 16.342 | 19.321 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 268 | 323 | 371 | 119 | 292 | 2116 | 352 | 430 | 1304 | 2560 |
N.S. |
1 | 1.21 | 1.38 | 0.44 | 1.09 | 7.90 | 1.31 | 1.60 | 4.87 | 9.55 |
time (sec) |
N/A | 1.068 | 0.176 | 0.112 | 0.113 | 0.730 | 1.428 | 0.136 | 0.186 | 17.638 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 325 | 295 | 97 | 324 | 1596 | 275 | 350 | 957 | 1565 |
N.S. |
1 | 1.31 | 1.18 | 0.39 | 1.30 | 6.41 | 1.10 | 1.41 | 3.84 | 6.29 |
time (sec) |
N/A | 0.973 | 0.117 | 0.112 | 0.111 | 0.505 | 0.922 | 0.111 | 0.178 | 0.537 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 264 | 267 | 67 | 253 | 873 | 136 | 268 | 610 | 637 |
N.S. |
1 | 1.28 | 1.29 | 0.32 | 1.22 | 4.22 | 0.66 | 1.29 | 2.95 | 3.08 |
time (sec) |
N/A | 0.778 | 0.201 | 0.105 | 0.111 | 0.086 | 0.455 | 0.119 | 0.194 | 0.431 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 225 | 183 | 46 | 189 | 183 | 39 | 194 | 305 | 58 |
N.S. |
1 | 1.49 | 1.21 | 0.30 | 1.25 | 1.21 | 0.26 | 1.28 | 2.02 | 0.38 |
time (sec) |
N/A | 0.658 | 0.083 | 0.096 | 0.109 | 0.066 | 0.138 | 0.130 | 0.177 | 17.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 371 | 689 | 429 | 334 | 0 | 9892 | 0 | 621 | 1438 | 17945 |
N.S. |
1 | 1.86 | 1.16 | 0.90 | 0.00 | 26.66 | 0.00 | 1.67 | 3.88 | 48.37 |
time (sec) |
N/A | 1.378 | 0.202 | 0.201 | 0.000 | 11.082 | 0.000 | 0.125 | 0.214 | 19.520 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 492 | 864 | 540 | 402 | 0 | 15292 | 0 | 879 | 3860 | 28923 |
N.S. |
1 | 1.76 | 1.10 | 0.82 | 0.00 | 31.08 | 0.00 | 1.79 | 7.85 | 58.79 |
time (sec) |
N/A | 1.854 | 0.380 | 0.277 | 0.000 | 100.166 | 0.000 | 0.157 | 0.237 | 21.289 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 139 | 118 | 102 | 0 | 236 | 170 | 116 | 167 | 0 |
N.S. |
1 | 0.95 | 0.81 | 0.70 | 0.00 | 1.62 | 1.16 | 0.79 | 1.14 | 0.00 |
time (sec) |
N/A | 0.409 | 0.164 | 0.174 | 0.000 | 0.093 | 0.377 | 0.121 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 117 | 93 | 80 | 0 | 188 | 121 | 88 | 127 | 0 |
N.S. |
1 | 1.03 | 0.82 | 0.70 | 0.00 | 1.65 | 1.06 | 0.77 | 1.11 | 0.00 |
time (sec) |
N/A | 0.385 | 0.118 | 0.147 | 0.000 | 0.083 | 0.303 | 0.117 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 93 | 74 | 62 | 0 | 146 | 100 | 66 | 91 | 0 |
N.S. |
1 | 1.09 | 0.87 | 0.73 | 0.00 | 1.72 | 1.18 | 0.78 | 1.07 | 0.00 |
time (sec) |
N/A | 0.349 | 0.078 | 0.137 | 0.000 | 0.076 | 0.264 | 0.125 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 79 | 77 | 73 | 0 | 201 | 94 | 68 | 165 | 0 |
N.S. |
1 | 1.01 | 0.99 | 0.94 | 0.00 | 2.58 | 1.21 | 0.87 | 2.12 | 0.00 |
time (sec) |
N/A | 0.340 | 0.113 | 0.157 | 0.000 | 0.081 | 2.885 | 0.129 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 98 | 84 | 88 | 0 | 273 | 403 | 84 | 223 | 0 |
N.S. |
1 | 1.14 | 0.98 | 1.02 | 0.00 | 3.17 | 4.69 | 0.98 | 2.59 | 0.00 |
time (sec) |
N/A | 0.383 | 0.148 | 0.189 | 0.000 | 0.092 | 4.829 | 0.143 | 0.207 | 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 | 92 | 91 | 52 | 49 | 119 | 81 | 488 | 58 | 209 | 96 |
N.S. |
1 | 0.99 | 0.57 | 0.53 | 1.29 | 0.88 | 5.30 | 0.63 | 2.27 | 1.04 |
time (sec) |
N/A | 0.363 | 0.114 | 0.123 | 0.033 | 0.079 | 9.555 | 0.129 | 0.263 | 17.137 |
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 | 126 | 117 | 74 | 64 | 154 | 112 | 1469 | 86 | 288 | 126 |
N.S. |
1 | 0.93 | 0.59 | 0.51 | 1.22 | 0.89 | 11.66 | 0.68 | 2.29 | 1.00 |
time (sec) |
N/A | 0.399 | 0.136 | 0.141 | 0.032 | 0.095 | 22.087 | 0.123 | 0.241 | 17.116 |
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 | 160 | 147 | 95 | 83 | 189 | 146 | 3738 | 118 | 367 | 157 |
N.S. |
1 | 0.92 | 0.59 | 0.52 | 1.18 | 0.91 | 23.36 | 0.74 | 2.29 | 0.98 |
time (sec) |
N/A | 0.425 | 0.161 | 0.143 | 0.035 | 0.114 | 47.777 | 0.142 | 0.266 | 17.854 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 245 | 197 | 174 | 0 | 428 | 389 | 225 | 335 | 0 |
N.S. |
1 | 0.91 | 0.73 | 0.64 | 0.00 | 1.59 | 1.44 | 0.83 | 1.24 | 0.00 |
time (sec) |
N/A | 0.774 | 0.302 | 0.214 | 0.000 | 0.232 | 0.497 | 0.124 | 0.342 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 223 | 163 | 141 | 0 | 354 | 280 | 183 | 270 | 0 |
N.S. |
1 | 1.01 | 0.74 | 0.64 | 0.00 | 1.60 | 1.27 | 0.83 | 1.22 | 0.00 |
time (sec) |
N/A | 0.738 | 0.241 | 0.201 | 0.000 | 0.138 | 0.417 | 0.121 | 0.281 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 198 | 138 | 113 | 0 | 282 | 192 | 144 | 209 | 0 |
N.S. |
1 | 1.14 | 0.79 | 0.65 | 0.00 | 1.62 | 1.10 | 0.83 | 1.20 | 0.00 |
time (sec) |
N/A | 0.707 | 0.524 | 0.190 | 0.000 | 0.107 | 0.406 | 0.116 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 181 | 131 | 132 | 0 | 369 | 0 | 150 | 357 | 0 |
N.S. |
1 | 1.14 | 0.82 | 0.83 | 0.00 | 2.32 | 0.00 | 0.94 | 2.25 | 0.00 |
time (sec) |
N/A | 0.890 | 0.218 | 0.207 | 0.000 | 0.112 | 0.000 | 0.130 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 191 | 146 | 147 | 0 | 478 | 0 | 161 | 466 | 0 |
N.S. |
1 | 1.11 | 0.85 | 0.85 | 0.00 | 2.78 | 0.00 | 0.94 | 2.71 | 0.00 |
time (sec) |
N/A | 0.968 | 0.263 | 0.331 | 0.000 | 0.124 | 0.000 | 0.163 | 0.293 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 198 | 139 | 138 | 0 | 459 | 0 | 159 | 505 | 0 |
N.S. |
1 | 1.06 | 0.75 | 0.74 | 0.00 | 2.47 | 0.00 | 0.85 | 2.72 | 0.00 |
time (sec) |
N/A | 0.960 | 0.273 | 0.222 | 0.000 | 0.128 | 0.000 | 0.135 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 235 | 157 | 183 | 0 | 557 | 0 | 192 | 641 | 0 |
N.S. |
1 | 1.12 | 0.75 | 0.87 | 0.00 | 2.65 | 0.00 | 0.91 | 3.05 | 0.00 |
time (sec) |
N/A | 1.057 | 0.360 | 0.315 | 0.000 | 0.194 | 0.000 | 0.125 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 216 | 109 | 100 | 369 | 167 | 0 | 141 | 513 | 287 |
N.S. |
1 | 0.94 | 0.47 | 0.43 | 1.60 | 0.72 | 0.00 | 0.61 | 2.22 | 1.24 |
time (sec) |
N/A | 1.038 | 0.248 | 0.189 | 0.037 | 0.173 | 0.000 | 0.158 | 0.212 | 17.602 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 280 | 249 | 142 | 130 | 428 | 217 | 0 | 190 | 636 | 332 |
N.S. |
1 | 0.89 | 0.51 | 0.46 | 1.53 | 0.78 | 0.00 | 0.68 | 2.27 | 1.19 |
time (sec) |
N/A | 1.073 | 0.293 | 0.191 | 0.037 | 0.251 | 0.000 | 0.132 | 0.214 | 17.669 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 582 | 465 | 357 | 0 | 6742 | 0 | 0 | 114 | 0 |
N.S. |
1 | 2.51 | 2.00 | 1.54 | 0.00 | 29.06 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 1.595 | 0.328 | 0.974 | 0.000 | 52.554 | 0.000 | 0.000 | 0.342 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 428 | 389 | 295 | 0 | 4605 | 0 | 0 | 82 | 0 |
N.S. |
1 | 2.15 | 1.95 | 1.48 | 0.00 | 23.14 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 1.127 | 0.238 | 0.581 | 0.000 | 12.904 | 0.000 | 0.000 | 0.299 | 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 | 170 | 310 | 241 | 257 | 0 | 2793 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.82 | 1.42 | 1.51 | 0.00 | 16.43 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.834 | 0.167 | 0.513 | 0.000 | 1.233 | 0.000 | 0.000 | 0.335 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 239 | 211 | 137 | 0 | 487 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.65 | 1.46 | 0.94 | 0.00 | 3.36 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.609 | 0.126 | 0.460 | 0.000 | 0.187 | 0.000 | 0.000 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 135 | 132 | 102 | 0 | 1225 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.76 | 0.00 | 9.07 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.425 | 0.088 | 0.488 | 0.000 | 0.282 | 0.000 | 0.000 | 0.266 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 227 | 247 | 253 | 0 | 3813 | 0 | 0 | 60 | 0 |
N.S. |
1 | 1.27 | 1.38 | 1.41 | 0.00 | 21.30 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.807 | 0.213 | 0.500 | 0.000 | 11.028 | 0.000 | 0.000 | 0.293 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 222 | 367 | 339 | 315 | 0 | 6571 | 0 | 0 | 100 | 0 |
N.S. |
1 | 1.65 | 1.53 | 1.42 | 0.00 | 29.60 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 1.097 | 0.387 | 0.665 | 0.000 | 45.745 | 0.000 | 0.000 | 37.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 293 | 564 | 473 | 408 | 0 | 0 | 0 | 0 | 140 | 0 |
N.S. |
1 | 1.92 | 1.61 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 1.505 | 1.128 | 0.768 | 0.000 | 0.000 | 0.000 | 0.000 | 0.546 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F(-1) | F | A | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 327 | 0 | 1004 | 426 | 0 | 0 | 0 | 436 | 196 | 0 |
N.S. |
1 | 0.00 | 3.07 | 1.30 | 0.00 | 0.00 | 0.00 | 1.33 | 0.60 | 0.00 |
time (sec) |
N/A | 0.000 | 1.036 | 0.978 | 0.000 | 0.000 | 0.000 | 0.187 | 51.609 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | B | F | A | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 0 | 828 | 389 | 0 | 7084 | 0 | 388 | 154 | 0 |
N.S. |
1 | 0.00 | 2.91 | 1.36 | 0.00 | 24.86 | 0.00 | 1.36 | 0.54 | 0.00 |
time (sec) |
N/A | 0.000 | 0.777 | 0.763 | 0.000 | 69.077 | 0.000 | 0.194 | 3.949 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 0 | 711 | 310 | 0 | 1935 | 0 | 0 | 112 | 0 |
N.S. |
1 | 0.00 | 3.05 | 1.33 | 0.00 | 8.30 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.000 | 0.602 | 0.694 | 0.000 | 10.333 | 0.000 | 0.000 | 3.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | B | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 0 | 516 | 176 | 0 | 641 | 0 | 0 | 70 | 0 |
N.S. |
1 | 0.00 | 2.93 | 1.00 | 0.00 | 3.64 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.000 | 0.433 | 0.566 | 0.000 | 0.736 | 0.000 | 0.000 | 1.502 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | B | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 0 | 421 | 179 | 0 | 2399 | 0 | 0 | 31 | 0 |
N.S. |
1 | 0.00 | 2.02 | 0.86 | 0.00 | 11.53 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.000 | 0.367 | 0.527 | 0.000 | 4.055 | 0.000 | 0.000 | 0.573 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | B | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 0 | 317 | 294 | 0 | 4804 | 0 | 0 | 47 | 0 |
N.S. |
1 | 0.00 | 1.43 | 1.33 | 0.00 | 21.74 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.000 | 0.341 | 0.589 | 0.000 | 25.175 | 0.000 | 0.000 | 0.325 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | B | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 280 | 0 | 708 | 370 | 0 | 7859 | 0 | 0 | 98 | 0 |
N.S. |
1 | 0.00 | 2.53 | 1.32 | 0.00 | 28.07 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.000 | 0.747 | 0.690 | 0.000 | 171.476 | 0.000 | 0.000 | 15.663 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F(-1) | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 341 | 0 | 913 | 488 | 0 | 0 | 0 | 0 | 163 | 0 |
N.S. |
1 | 0.00 | 2.68 | 1.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.000 | 1.578 | 1.079 | 0.000 | 0.000 | 0.000 | 0.000 | 167.398 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F(-1) | F(-1) | B | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 420 | 0 | 2319 | 538 | 0 | 0 | 0 | 1035 | 22 | 0 |
N.S. |
1 | 0.00 | 5.52 | 1.28 | 0.00 | 0.00 | 0.00 | 2.46 | 0.05 | 0.00 |
time (sec) |
N/A | 0.000 | 3.116 | 1.384 | 0.000 | 0.000 | 0.000 | 0.218 | 200.033 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | B | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 356 | 0 | 2220 | 444 | 0 | 3392 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.00 | 6.24 | 1.25 | 0.00 | 9.53 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.000 | 2.946 | 1.198 | 0.000 | 143.234 | 0.000 | 0.000 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | B | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 266 | 0 | 1818 | 363 | 0 | 2082 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.00 | 6.83 | 1.36 | 0.00 | 7.83 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.000 | 2.354 | 1.060 | 0.000 | 28.791 | 0.000 | 0.000 | 200.031 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | B | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 0 | 1766 | 344 | 0 | 2034 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.00 | 6.05 | 1.18 | 0.00 | 6.97 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.000 | 2.188 | 1.138 | 0.000 | 21.976 | 0.000 | 0.000 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | B | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 0 | 1315 | 274 | 0 | 2526 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.00 | 5.28 | 1.10 | 0.00 | 10.14 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.000 | 1.493 | 0.643 | 0.000 | 11.700 | 0.000 | 0.000 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | B | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 0 | 1324 | 355 | 0 | 6046 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.00 | 4.53 | 1.22 | 0.00 | 20.71 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.000 | 1.455 | 0.721 | 0.000 | 117.338 | 0.000 | 0.000 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F(-1) | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 319 | 0 | 1214 | 411 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.00 | 3.81 | 1.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.000 | 1.534 | 0.772 | 0.000 | 0.000 | 0.000 | 0.000 | 200.031 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F(-1) | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 396 | 0 | 2037 | 548 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.00 | 5.14 | 1.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.000 | 2.531 | 1.023 | 0.000 | 0.000 | 0.000 | 0.000 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 139 | 118 | 102 | 0 | 236 | 170 | 116 | 167 | 0 |
N.S. |
1 | 0.97 | 0.82 | 0.71 | 0.00 | 1.64 | 1.18 | 0.81 | 1.16 | 0.00 |
time (sec) |
N/A | 0.402 | 0.155 | 0.154 | 0.000 | 0.101 | 0.346 | 0.257 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 117 | 93 | 80 | 0 | 188 | 121 | 88 | 127 | 0 |
N.S. |
1 | 1.04 | 0.82 | 0.71 | 0.00 | 1.66 | 1.07 | 0.78 | 1.12 | 0.00 |
time (sec) |
N/A | 0.376 | 0.123 | 0.149 | 0.000 | 0.097 | 0.297 | 0.257 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 93 | 82 | 62 | 0 | 146 | 100 | 66 | 91 | 0 |
N.S. |
1 | 1.09 | 0.96 | 0.73 | 0.00 | 1.72 | 1.18 | 0.78 | 1.07 | 0.00 |
time (sec) |
N/A | 0.357 | 0.192 | 0.137 | 0.000 | 0.086 | 0.258 | 0.225 | 0.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 79 | 75 | 72 | 0 | 201 | 94 | 68 | 165 | 0 |
N.S. |
1 | 1.03 | 0.97 | 0.94 | 0.00 | 2.61 | 1.22 | 0.88 | 2.14 | 0.00 |
time (sec) |
N/A | 0.348 | 0.132 | 0.149 | 0.000 | 0.089 | 2.895 | 0.294 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 98 | 86 | 88 | 0 | 277 | 403 | 87 | 223 | 0 |
N.S. |
1 | 1.17 | 1.02 | 1.05 | 0.00 | 3.30 | 4.80 | 1.04 | 2.65 | 0.00 |
time (sec) |
N/A | 0.386 | 0.154 | 0.174 | 0.000 | 0.097 | 4.830 | 0.309 | 0.169 | 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 | 91 | 91 | 52 | 49 | 119 | 80 | 488 | 57 | 209 | 96 |
N.S. |
1 | 1.00 | 0.57 | 0.54 | 1.31 | 0.88 | 5.36 | 0.63 | 2.30 | 1.05 |
time (sec) |
N/A | 0.366 | 0.108 | 0.123 | 0.033 | 0.096 | 9.667 | 0.277 | 0.174 | 17.412 |
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 | 124 | 117 | 74 | 64 | 154 | 112 | 1469 | 86 | 288 | 127 |
N.S. |
1 | 0.94 | 0.60 | 0.52 | 1.24 | 0.90 | 11.85 | 0.69 | 2.32 | 1.02 |
time (sec) |
N/A | 0.402 | 0.139 | 0.130 | 0.036 | 0.096 | 22.093 | 0.276 | 0.171 | 17.373 |
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 | 158 | 147 | 94 | 83 | 189 | 146 | 3738 | 118 | 367 | 158 |
N.S. |
1 | 0.93 | 0.59 | 0.53 | 1.20 | 0.92 | 23.66 | 0.75 | 2.32 | 1.00 |
time (sec) |
N/A | 0.435 | 0.160 | 0.145 | 0.035 | 0.126 | 47.787 | 0.294 | 0.196 | 17.508 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 245 | 197 | 173 | 0 | 428 | 382 | 225 | 335 | 0 |
N.S. |
1 | 0.91 | 0.73 | 0.64 | 0.00 | 1.59 | 1.41 | 0.83 | 1.24 | 0.00 |
time (sec) |
N/A | 0.752 | 0.301 | 0.233 | 0.000 | 0.230 | 0.471 | 0.273 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 223 | 163 | 141 | 0 | 354 | 269 | 183 | 270 | 0 |
N.S. |
1 | 1.01 | 0.74 | 0.64 | 0.00 | 1.60 | 1.22 | 0.83 | 1.22 | 0.00 |
time (sec) |
N/A | 0.729 | 0.238 | 0.211 | 0.000 | 0.152 | 0.380 | 0.253 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 198 | 130 | 113 | 0 | 282 | 192 | 144 | 209 | 0 |
N.S. |
1 | 1.14 | 0.75 | 0.65 | 0.00 | 1.62 | 1.10 | 0.83 | 1.20 | 0.00 |
time (sec) |
N/A | 0.687 | 0.163 | 0.201 | 0.000 | 0.109 | 0.379 | 0.289 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 180 | 131 | 131 | 0 | 369 | 0 | 150 | 357 | 0 |
N.S. |
1 | 1.14 | 0.83 | 0.83 | 0.00 | 2.34 | 0.00 | 0.95 | 2.26 | 0.00 |
time (sec) |
N/A | 0.865 | 0.220 | 0.244 | 0.000 | 0.111 | 0.000 | 0.297 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 190 | 146 | 147 | 0 | 478 | 0 | 161 | 466 | 0 |
N.S. |
1 | 1.11 | 0.85 | 0.86 | 0.00 | 2.80 | 0.00 | 0.94 | 2.73 | 0.00 |
time (sec) |
N/A | 0.960 | 0.256 | 0.355 | 0.000 | 0.131 | 0.000 | 0.302 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 197 | 139 | 138 | 0 | 459 | 0 | 159 | 505 | 0 |
N.S. |
1 | 1.06 | 0.75 | 0.75 | 0.00 | 2.48 | 0.00 | 0.86 | 2.73 | 0.00 |
time (sec) |
N/A | 0.960 | 0.283 | 0.239 | 0.000 | 0.142 | 0.000 | 0.287 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 234 | 158 | 183 | 0 | 557 | 0 | 192 | 641 | 0 |
N.S. |
1 | 1.12 | 0.76 | 0.88 | 0.00 | 2.68 | 0.00 | 0.92 | 3.08 | 0.00 |
time (sec) |
N/A | 1.052 | 0.337 | 0.327 | 0.000 | 0.191 | 0.000 | 0.303 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 215 | 109 | 100 | 369 | 167 | 0 | 141 | 513 | 285 |
N.S. |
1 | 0.94 | 0.48 | 0.44 | 1.62 | 0.73 | 0.00 | 0.62 | 2.25 | 1.25 |
time (sec) |
N/A | 1.051 | 0.249 | 0.178 | 0.040 | 0.174 | 0.000 | 0.306 | 0.192 | 17.434 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 278 | 249 | 142 | 130 | 428 | 217 | 0 | 190 | 636 | 330 |
N.S. |
1 | 0.90 | 0.51 | 0.47 | 1.54 | 0.78 | 0.00 | 0.68 | 2.29 | 1.19 |
time (sec) |
N/A | 1.090 | 0.310 | 0.192 | 0.037 | 0.257 | 0.000 | 0.303 | 0.200 | 17.701 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 555 | 742 | 466 | 990 | 0 | 6799 | 0 | 0 | 110 | 0 |
N.S. |
1 | 1.34 | 0.84 | 1.78 | 0.00 | 12.25 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 2.040 | 0.339 | 3.100 | 0.000 | 53.718 | 0.000 | 0.000 | 0.352 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 474 | 551 | 391 | 826 | 0 | 4661 | 0 | 0 | 79 | 0 |
N.S. |
1 | 1.16 | 0.82 | 1.74 | 0.00 | 9.83 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 1.385 | 0.229 | 1.053 | 0.000 | 13.096 | 0.000 | 0.000 | 0.284 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 442 | 390 | 241 | 783 | 0 | 2849 | 0 | 0 | 48 | 0 |
N.S. |
1 | 0.88 | 0.55 | 1.77 | 0.00 | 6.45 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 1.041 | 0.158 | 0.782 | 0.000 | 1.298 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 287 | 263 | 211 | 551 | 0 | 503 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.92 | 0.74 | 1.92 | 0.00 | 1.75 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.696 | 0.118 | 1.112 | 0.000 | 0.212 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 370 | 151 | 132 | 673 | 0 | 1217 | 0 | 0 | 28 | 0 |
N.S. |
1 | 0.41 | 0.36 | 1.82 | 0.00 | 3.29 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.497 | 0.086 | 0.900 | 0.000 | 0.286 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 399 | 244 | 246 | 773 | 0 | 3803 | 0 | 0 | 58 | 0 |
N.S. |
1 | 0.61 | 0.62 | 1.94 | 0.00 | 9.53 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.968 | 0.194 | 1.013 | 0.000 | 10.930 | 0.000 | 0.000 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 494 | 384 | 335 | 924 | 0 | 6557 | 0 | 0 | 98 | 0 |
N.S. |
1 | 0.78 | 0.68 | 1.87 | 0.00 | 13.27 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 1.348 | 0.386 | 1.004 | 0.000 | 46.717 | 0.000 | 0.000 | 35.860 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | F(-1) | F | A | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 627 | 0 | 1002 | 1175 | 0 | 0 | 0 | 437 | 196 | 0 |
N.S. |
1 | 0.00 | 1.60 | 1.87 | 0.00 | 0.00 | 0.00 | 0.70 | 0.31 | 0.00 |
time (sec) |
N/A | 0.000 | 0.945 | 1.655 | 0.000 | 0.000 | 0.000 | 0.322 | 53.719 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | B | F | A | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 573 | 0 | 827 | 1155 | 0 | 7122 | 0 | 387 | 154 | 0 |
N.S. |
1 | 0.00 | 1.44 | 2.02 | 0.00 | 12.43 | 0.00 | 0.68 | 0.27 | 0.00 |
time (sec) |
N/A | 0.000 | 0.699 | 1.457 | 0.000 | 68.677 | 0.000 | 0.823 | 4.050 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 473 | 0 | 708 | 871 | 0 | 1951 | 0 | 0 | 112 | 0 |
N.S. |
1 | 0.00 | 1.50 | 1.84 | 0.00 | 4.12 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.000 | 0.571 | 1.168 | 0.000 | 10.824 | 0.000 | 0.000 | 3.523 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | B | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 317 | 0 | 502 | 553 | 0 | 647 | 0 | 0 | 70 | 0 |
N.S. |
1 | 0.00 | 1.58 | 1.74 | 0.00 | 2.04 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.000 | 0.450 | 0.880 | 0.000 | 0.747 | 0.000 | 0.000 | 2.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | B | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 395 | 0 | 420 | 839 | 0 | 2397 | 0 | 0 | 31 | 0 |
N.S. |
1 | 0.00 | 1.06 | 2.12 | 0.00 | 6.07 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.000 | 0.348 | 1.398 | 0.000 | 3.656 | 0.000 | 0.000 | 0.862 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | B | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 464 | 0 | 314 | 1041 | 0 | 4777 | 0 | 0 | 47 | 0 |
N.S. |
1 | 0.00 | 0.68 | 2.24 | 0.00 | 10.30 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.000 | 0.322 | 1.316 | 0.000 | 18.116 | 0.000 | 0.000 | 0.383 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | B | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 504 | 0 | 666 | 1116 | 0 | 7841 | 0 | 0 | 98 | 0 |
N.S. |
1 | 0.00 | 1.32 | 2.21 | 0.00 | 15.56 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.000 | 0.889 | 1.950 | 0.000 | 170.297 | 0.000 | 0.000 | 16.802 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | F(-1) | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 630 | 0 | 910 | 1382 | 0 | 0 | 0 | 0 | 163 | 0 |
N.S. |
1 | 0.00 | 1.44 | 2.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.000 | 1.358 | 2.849 | 0.000 | 0.000 | 0.000 | 0.000 | 170.883 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | F(-1) | F(-1) | A | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 748 | 0 | 2315 | 1517 | 0 | 0 | 0 | 1035 | 21 | 0 |
N.S. |
1 | 0.00 | 3.09 | 2.03 | 0.00 | 0.00 | 0.00 | 1.38 | 0.03 | 0.00 |
time (sec) |
N/A | 0.000 | 3.294 | 2.520 | 0.000 | 0.000 | 0.000 | 0.227 | 200.029 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | F(-1) | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 632 | 0 | 2216 | 1244 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 0.00 | 3.51 | 1.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 0.000 | 3.086 | 1.943 | 0.000 | 0.000 | 0.000 | 0.000 | 200.032 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | B | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 505 | 0 | 1814 | 993 | 0 | 2105 | 0 | 0 | 21 | 0 |
N.S. |
1 | 0.00 | 3.59 | 1.97 | 0.00 | 4.17 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.000 | 2.419 | 1.434 | 0.000 | 28.541 | 0.000 | 0.000 | 200.029 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | B | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 512 | 0 | 1763 | 982 | 0 | 2045 | 0 | 0 | 21 | 0 |
N.S. |
1 | 0.00 | 3.44 | 1.92 | 0.00 | 3.99 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.000 | 2.274 | 1.413 | 0.000 | 21.003 | 0.000 | 0.000 | 200.035 | 0.000 |