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 | B | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 447 | 458 | 375 | 288 | 2367 | 538 | 0 | 0 | 74 | 0 |
N.S. |
1 | 1.02 | 0.84 | 0.64 | 5.30 | 1.20 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 1.028 | 3.218 | 7.570 | 0.441 | 0.092 | 0.000 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 278 | 373 | 338 | 266 | 1871 | 420 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.34 | 1.22 | 0.96 | 6.73 | 1.51 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.644 | 2.816 | 7.559 | 0.421 | 0.089 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 398 | 411 | 401 | 286 | 1462 | 460 | 0 | 0 | 76 | 0 |
N.S. |
1 | 1.03 | 1.01 | 0.72 | 3.67 | 1.16 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.855 | 2.570 | 7.573 | 0.366 | 0.088 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 38 | 31 | 76 | 76 | 0 | 0 | 76 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 2.00 | 2.00 | 0.00 | 0.00 | 2.00 | 0.00 |
time (sec) |
N/A | 0.250 | 0.732 | 7.229 | 0.169 | 0.074 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 84 | 63 | 59 | 79 | 0 | 0 | 76 | 102 |
N.S. |
1 | 1.00 | 1.04 | 0.78 | 0.73 | 0.98 | 0.00 | 0.00 | 0.94 | 1.26 |
time (sec) |
N/A | 0.387 | 1.099 | 6.063 | 0.282 | 0.075 | 0.000 | 0.000 | 0.203 | 1.833 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 128 | 98 | 80 | 84 | 91 | 0 | 0 | 76 | 110 |
N.S. |
1 | 1.02 | 0.78 | 0.64 | 0.67 | 0.73 | 0.00 | 0.00 | 0.61 | 0.88 |
time (sec) |
N/A | 0.593 | 1.385 | 6.148 | 0.245 | 0.070 | 0.000 | 0.000 | 0.165 | 2.274 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 174 | 113 | 90 | 160 | 103 | 0 | 0 | 76 | 125 |
N.S. |
1 | 1.04 | 0.68 | 0.54 | 0.96 | 0.62 | 0.00 | 0.00 | 0.46 | 0.75 |
time (sec) |
N/A | 0.796 | 1.490 | 6.156 | 0.291 | 0.076 | 0.000 | 0.000 | 0.194 | 2.892 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 488 | 503 | 386 | 316 | 3005 | 635 | 0 | 0 | 115 | 0 |
N.S. |
1 | 1.03 | 0.79 | 0.65 | 6.16 | 1.30 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 1.266 | 2.815 | 7.692 | 0.469 | 0.093 | 0.000 | 0.000 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 327 | 418 | 387 | 289 | 2431 | 525 | 0 | 0 | 96 | 0 |
N.S. |
1 | 1.28 | 1.18 | 0.88 | 7.43 | 1.61 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.829 | 3.698 | 7.799 | 0.454 | 0.093 | 0.000 | 0.000 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 437 | 454 | 359 | 305 | 2013 | 484 | 0 | 0 | 118 | 0 |
N.S. |
1 | 1.04 | 0.82 | 0.70 | 4.61 | 1.11 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 1.033 | 3.122 | 7.940 | 0.329 | 0.091 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 280 | 372 | 343 | 296 | 1492 | 505 | 0 | 0 | 118 | 0 |
N.S. |
1 | 1.33 | 1.22 | 1.06 | 5.33 | 1.80 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.670 | 3.553 | 7.652 | 0.332 | 0.117 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 38 | 31 | 76 | 80 | 0 | 0 | 118 | 104 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 2.00 | 2.11 | 0.00 | 0.00 | 3.11 | 2.74 |
time (sec) |
N/A | 0.243 | 1.124 | 8.380 | 0.181 | 0.071 | 0.000 | 0.000 | 0.180 | 1.747 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 92 | 82 | 94 | 94 | 0 | 0 | 118 | 112 |
N.S. |
1 | 1.00 | 1.14 | 1.01 | 1.16 | 1.16 | 0.00 | 0.00 | 1.46 | 1.38 |
time (sec) |
N/A | 0.431 | 1.354 | 6.214 | 0.265 | 0.074 | 0.000 | 0.000 | 0.183 | 2.174 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 128 | 104 | 89 | 96 | 99 | 0 | 0 | 118 | 127 |
N.S. |
1 | 1.02 | 0.83 | 0.71 | 0.77 | 0.79 | 0.00 | 0.00 | 0.94 | 1.02 |
time (sec) |
N/A | 0.555 | 1.421 | 6.247 | 0.242 | 0.069 | 0.000 | 0.000 | 0.183 | 2.817 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 175 | 121 | 97 | 124 | 99 | 0 | 0 | 118 | 133 |
N.S. |
1 | 1.04 | 0.72 | 0.57 | 0.73 | 0.59 | 0.00 | 0.00 | 0.70 | 0.79 |
time (sec) |
N/A | 0.806 | 1.574 | 6.467 | 0.251 | 0.072 | 0.000 | 0.000 | 0.182 | 3.359 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 283 | 375 | 350 | 307 | 2258 | 461 | 0 | 0 | 162 | 0 |
N.S. |
1 | 1.33 | 1.24 | 1.08 | 7.98 | 1.63 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.671 | 3.419 | 10.243 | 0.430 | 0.092 | 0.000 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 361 | 373 | 302 | 232 | 726 | 385 | 0 | 0 | 191 | 0 |
N.S. |
1 | 1.03 | 0.84 | 0.64 | 2.01 | 1.07 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.664 | 1.643 | 10.137 | 0.307 | 0.094 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 36 | 31 | 76 | 64 | 0 | 0 | 50 | 40 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 2.11 | 1.78 | 0.00 | 0.00 | 1.39 | 1.11 |
time (sec) |
N/A | 0.233 | 0.475 | 11.037 | 0.186 | 0.084 | 0.000 | 0.000 | 0.170 | 1.510 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 48 | 42 | 80 | 78 | 0 | 0 | 111 | 78 |
N.S. |
1 | 1.00 | 0.60 | 0.52 | 1.00 | 0.98 | 0.00 | 0.00 | 1.39 | 0.98 |
time (sec) |
N/A | 0.384 | 0.582 | 6.161 | 0.384 | 0.083 | 0.000 | 0.000 | 0.180 | 1.391 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 127 | 68 | 62 | 130 | 89 | 0 | 0 | 119 | 86 |
N.S. |
1 | 1.05 | 0.56 | 0.51 | 1.07 | 0.74 | 0.00 | 0.00 | 0.98 | 0.71 |
time (sec) |
N/A | 0.600 | 0.795 | 6.121 | 0.246 | 0.076 | 0.000 | 0.000 | 0.178 | 1.135 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 173 | 79 | 70 | 178 | 100 | 0 | 0 | 119 | 101 |
N.S. |
1 | 1.05 | 0.48 | 0.42 | 1.08 | 0.61 | 0.00 | 0.00 | 0.72 | 0.61 |
time (sec) |
N/A | 0.758 | 0.998 | 6.152 | 0.311 | 0.075 | 0.000 | 0.000 | 0.179 | 1.357 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 220 | 87 | 88 | 226 | 111 | 0 | 0 | 119 | 109 |
N.S. |
1 | 1.07 | 0.42 | 0.43 | 1.10 | 0.54 | 0.00 | 0.00 | 0.58 | 0.53 |
time (sec) |
N/A | 0.956 | 1.279 | 6.282 | 0.336 | 0.071 | 0.000 | 0.000 | 0.178 | 1.510 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 403 | 464 | 337 | 289 | 1817 | 483 | 0 | 0 | 349 | 0 |
N.S. |
1 | 1.15 | 0.84 | 0.72 | 4.51 | 1.20 | 0.00 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 1.076 | 3.532 | 10.368 | 0.387 | 0.095 | 0.000 | 0.000 | 0.436 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 283 | 378 | 338 | 275 | 778 | 539 | 0 | 0 | 202 | 0 |
N.S. |
1 | 1.34 | 1.19 | 0.97 | 2.75 | 1.90 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.680 | 3.681 | 10.567 | 0.356 | 0.112 | 0.000 | 0.000 | 0.404 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 38 | 31 | 76 | 67 | 0 | 0 | 178 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 2.00 | 1.76 | 0.00 | 0.00 | 4.68 | 0.00 |
time (sec) |
N/A | 0.251 | 0.930 | 10.669 | 0.153 | 0.072 | 0.000 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 63 | 62 | 80 | 75 | 0 | 0 | 201 | 84 |
N.S. |
1 | 1.00 | 0.79 | 0.78 | 1.00 | 0.94 | 0.00 | 0.00 | 2.51 | 1.05 |
time (sec) |
N/A | 0.388 | 0.732 | 8.696 | 0.238 | 0.069 | 0.000 | 0.000 | 0.236 | 1.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 126 | 83 | 70 | 130 | 89 | 0 | 0 | 171 | 104 |
N.S. |
1 | 1.04 | 0.69 | 0.58 | 1.07 | 0.74 | 0.00 | 0.00 | 1.41 | 0.86 |
time (sec) |
N/A | 0.538 | 0.903 | 6.306 | 0.244 | 0.072 | 0.000 | 0.000 | 0.243 | 1.278 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 173 | 100 | 91 | 178 | 100 | 0 | 0 | 187 | 112 |
N.S. |
1 | 1.05 | 0.61 | 0.55 | 1.08 | 0.61 | 0.00 | 0.00 | 1.13 | 0.68 |
time (sec) |
N/A | 0.809 | 1.195 | 6.319 | 0.271 | 0.072 | 0.000 | 0.000 | 0.220 | 1.421 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 209 | 219 | 100 | 103 | 226 | 111 | 0 | 0 | 187 | 127 |
N.S. |
1 | 1.05 | 0.48 | 0.49 | 1.08 | 0.53 | 0.00 | 0.00 | 0.89 | 0.61 |
time (sec) |
N/A | 0.953 | 1.328 | 6.354 | 0.247 | 0.081 | 0.000 | 0.000 | 0.232 | 1.736 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 325 | 426 | 370 | 314 | 2449 | 541 | 0 | 0 | 88 | 0 |
N.S. |
1 | 1.31 | 1.14 | 0.97 | 7.54 | 1.66 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.924 | 5.053 | 11.130 | 0.373 | 0.125 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 405 | 420 | 357 | 313 | 1466 | 543 | 0 | 0 | 88 | 0 |
N.S. |
1 | 1.04 | 0.88 | 0.77 | 3.62 | 1.34 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.862 | 3.878 | 10.958 | 0.396 | 0.126 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 38 | 31 | 76 | 71 | 0 | 0 | 88 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 2.00 | 1.87 | 0.00 | 0.00 | 2.32 | 0.00 |
time (sec) |
N/A | 0.256 | 1.151 | 11.606 | 0.178 | 0.071 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 63 | 79 | 86 | 79 | 0 | 0 | 84 | 102 |
N.S. |
1 | 1.00 | 0.79 | 0.99 | 1.08 | 0.99 | 0.00 | 0.00 | 1.05 | 1.28 |
time (sec) |
N/A | 0.416 | 1.199 | 9.253 | 0.238 | 0.070 | 0.000 | 0.000 | 0.187 | 1.328 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 126 | 85 | 87 | 130 | 86 | 0 | 0 | 77 | 109 |
N.S. |
1 | 1.04 | 0.70 | 0.72 | 1.07 | 0.71 | 0.00 | 0.00 | 0.64 | 0.90 |
time (sec) |
N/A | 0.561 | 1.090 | 9.154 | 0.242 | 0.076 | 0.000 | 0.000 | 0.213 | 1.428 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 172 | 102 | 97 | 178 | 89 | 0 | 0 | 92 | 118 |
N.S. |
1 | 1.06 | 0.63 | 0.60 | 1.10 | 0.55 | 0.00 | 0.00 | 0.57 | 0.73 |
time (sec) |
N/A | 0.757 | 1.186 | 6.627 | 0.269 | 0.076 | 0.000 | 0.000 | 0.153 | 1.688 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 219 | 107 | 115 | 226 | 111 | 0 | 0 | 113 | 135 |
N.S. |
1 | 1.06 | 0.52 | 0.56 | 1.10 | 0.54 | 0.00 | 0.00 | 0.55 | 0.66 |
time (sec) |
N/A | 1.029 | 1.488 | 6.612 | 0.252 | 0.086 | 0.000 | 0.000 | 0.154 | 1.953 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 118 | 0 | 0 | 0 | 0 | 0 | 140 | 0 |
N.S. |
1 | 1.00 | 1.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.63 | 0.00 |
time (sec) |
N/A | 0.503 | 1.447 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 116 | 0 | 0 | 0 | 0 | 0 | 142 | 0 |
N.S. |
1 | 1.00 | 1.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.65 | 0.00 |
time (sec) |
N/A | 0.476 | 1.168 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 85 | 116 | 0 | 0 | 0 | 0 | 0 | 142 | 0 |
N.S. |
1 | 0.99 | 1.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.65 | 0.00 |
time (sec) |
N/A | 0.491 | 0.976 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 83 | 95 | 0 | 0 | 0 | 0 | 0 | 142 | 0 |
N.S. |
1 | 0.99 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.69 | 0.00 |
time (sec) |
N/A | 0.477 | 0.922 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 83 | 95 | 0 | 0 | 0 | 0 | 0 | 103 | 0 |
N.S. |
1 | 0.99 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.23 | 0.00 |
time (sec) |
N/A | 0.479 | 1.189 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.254 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 88 | 112 | 0 | 0 | 0 | 0 | 0 | 103 | 0 |
N.S. |
1 | 1.02 | 1.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.20 | 0.00 |
time (sec) |
N/A | 0.499 | 1.189 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.262 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | A | F(-1) | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 437 | 248 | 240 | 0 | 3902 | 528 | 0 | 0 | 78 | 0 |
N.S. |
1 | 0.57 | 0.55 | 0.00 | 8.93 | 1.21 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.712 | 2.339 | 0.000 | 0.427 | 0.096 | 0.000 | 0.000 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 378 | 201 | 220 | 0 | 1906 | 515 | 0 | 0 | 53 | 0 |
N.S. |
1 | 0.53 | 0.58 | 0.00 | 5.04 | 1.36 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.665 | 1.798 | 0.000 | 0.306 | 0.093 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 340 | 154 | 161 | 0 | 1753 | 367 | 0 | 0 | 30 | 0 |
N.S. |
1 | 0.45 | 0.47 | 0.00 | 5.16 | 1.08 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.466 | 1.064 | 0.000 | 0.320 | 0.104 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | A | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 47 | 0 | 107 | 55 | 0 | 0 | 30 | 81 |
N.S. |
1 | 1.00 | 1.27 | 0.00 | 2.89 | 1.49 | 0.00 | 0.00 | 0.81 | 2.19 |
time (sec) |
N/A | 0.269 | 0.873 | 0.000 | 0.219 | 0.091 | 0.000 | 0.000 | 0.176 | 2.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 70 | 0 | 316 | 58 | 0 | 0 | 62 | 90 |
N.S. |
1 | 1.00 | 0.86 | 0.00 | 3.90 | 0.72 | 0.00 | 0.00 | 0.77 | 1.11 |
time (sec) |
N/A | 0.425 | 0.991 | 0.000 | 0.212 | 0.077 | 0.000 | 0.000 | 0.196 | 1.294 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 126 | 100 | 0 | 402 | 107 | 0 | 0 | 96 | 122 |
N.S. |
1 | 1.03 | 0.82 | 0.00 | 3.30 | 0.88 | 0.00 | 0.00 | 0.79 | 1.00 |
time (sec) |
N/A | 0.572 | 1.339 | 0.000 | 0.252 | 0.073 | 0.000 | 0.000 | 0.208 | 2.494 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 171 | 116 | 0 | 983 | 133 | 0 | 0 | 130 | 303 |
N.S. |
1 | 1.05 | 0.71 | 0.00 | 6.03 | 0.82 | 0.00 | 0.00 | 0.80 | 1.86 |
time (sec) |
N/A | 0.762 | 1.961 | 0.000 | 0.240 | 0.078 | 0.000 | 0.000 | 0.238 | 5.313 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 88 | 210 | 0 | 0 | 0 | 0 | 0 | 335 | 0 |
N.S. |
1 | 1.02 | 2.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.90 | 0.00 |
time (sec) |
N/A | 0.463 | 4.894 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 88 | 147 | 0 | 0 | 0 | 0 | 0 | 139 | 0 |
N.S. |
1 | 1.02 | 1.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.62 | 0.00 |
time (sec) |
N/A | 0.455 | 1.078 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 114 | 114 | 0 | 0 | 0 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.33 | 1.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.469 | 0.320 | 0.000 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 114 | 67 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.39 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.424 | 0.143 | 0.000 | 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 | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 88 | 152 | 0 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.02 | 1.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.460 | 1.318 | 0.000 | 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 | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 88 | 156 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.02 | 1.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.473 | 1.378 | 0.000 | 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 | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 88 | 153 | 0 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.02 | 1.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.467 | 1.584 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 121 | 186 | 0 | 0 | 0 | 0 | 0 | 167 | 0 |
N.S. |
1 | 1.13 | 1.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.56 | 0.00 |
time (sec) |
N/A | 0.516 | 2.998 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.280 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 121 | 186 | 0 | 0 | 0 | 0 | 0 | 133 | 0 |
N.S. |
1 | 1.13 | 1.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.24 | 0.00 |
time (sec) |
N/A | 0.478 | 3.239 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 114 | 186 | 0 | 0 | 0 | 0 | 0 | 95 | 0 |
N.S. |
1 | 1.07 | 1.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.500 | 1.622 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 114 | 174 | 0 | 0 | 0 | 0 | 0 | 94 | 0 |
N.S. |
1 | 1.07 | 1.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.453 | 1.044 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 118 | 174 | 0 | 0 | 0 | 0 | 0 | 236 | 0 |
N.S. |
1 | 1.10 | 1.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.21 | 0.00 |
time (sec) |
N/A | 0.482 | 1.463 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 121 | 178 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.13 | 1.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.496 | 1.955 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.023 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 121 | 178 | 0 | 0 | 0 | 0 | 0 | 79 | 0 |
N.S. |
1 | 1.13 | 1.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.497 | 3.362 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 105 | 165 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 0.96 | 1.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.443 | 6.237 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 86 | 80 | 272 | 0 | 247 | 0 | 623 | 24 | 168 |
N.S. |
1 | 0.89 | 0.82 | 2.80 | 0.00 | 2.55 | 0.00 | 6.42 | 0.25 | 1.73 |
time (sec) |
N/A | 0.277 | 0.555 | 1.835 | 0.000 | 0.102 | 0.000 | 0.622 | 0.176 | 5.641 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 60 | 60 | 150 | 0 | 142 | 0 | 206 | 24 | 216 |
N.S. |
1 | 0.92 | 0.92 | 2.31 | 0.00 | 2.18 | 0.00 | 3.17 | 0.37 | 3.32 |
time (sec) |
N/A | 0.257 | 0.169 | 1.166 | 0.000 | 0.083 | 0.000 | 0.488 | 0.187 | 2.663 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 31 | 28 | 60 | 0 | 28 | 24 | 104 |
N.S. |
1 | 1.00 | 1.00 | 0.97 | 0.88 | 1.88 | 0.00 | 0.88 | 0.75 | 3.25 |
time (sec) |
N/A | 0.227 | 0.115 | 0.556 | 0.034 | 0.085 | 0.000 | 0.358 | 0.150 | 0.461 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 60 | 54 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.07 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.249 | 0.137 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 64 | 58 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.07 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.243 | 0.183 | 0.000 | 0.000 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 64 | 58 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.07 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.245 | 0.326 | 0.000 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 94 | 149 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.02 | 1.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.497 | 12.486 | 0.000 | 0.000 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 149 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 1.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.457 | 11.820 | 0.000 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 146 | 0 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 1.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.415 | 6.347 | 0.000 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 85 | 146 | 0 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.97 | 1.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.458 | 12.163 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 94 | 149 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.02 | 1.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.473 | 13.253 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 94 | 149 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.02 | 1.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.472 | 14.246 | 0.000 | 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 | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 96 | 181 | 0 | 0 | 0 | 0 | 0 | 126 | 0 |
N.S. |
1 | 1.00 | 1.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.31 | 0.00 |
time (sec) |
N/A | 0.482 | 6.950 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.279 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 96 | 170 | 0 | 0 | 0 | 0 | 0 | 118 | 0 |
N.S. |
1 | 1.00 | 1.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.23 | 0.00 |
time (sec) |
N/A | 0.474 | 6.852 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.298 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 170 | 0 | 0 | 0 | 0 | 0 | 98 | 0 |
N.S. |
1 | 1.00 | 1.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.456 | 6.255 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 91 | 143 | 0 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 0.97 | 1.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.479 | 7.108 | 0.000 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 93 | 143 | 0 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 0.97 | 1.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.485 | 7.765 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 98 | 157 | 0 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.02 | 1.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.488 | 8.031 | 0.000 | 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 | C | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 269 | 259 | 165 | 4331 | 435 | 335 | 0 | 0 | 43 | 511 |
N.S. |
1 | 0.96 | 0.61 | 16.10 | 1.62 | 1.25 | 0.00 | 0.00 | 0.16 | 1.90 |
time (sec) |
N/A | 1.113 | 1.527 | 6.088 | 0.275 | 0.115 | 0.000 | 0.000 | 0.202 | 7.387 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 209 | 119 | 4982 | 346 | 265 | 0 | 0 | 43 | 425 |
N.S. |
1 | 1.02 | 0.58 | 24.30 | 1.69 | 1.29 | 0.00 | 0.00 | 0.21 | 2.07 |
time (sec) |
N/A | 0.875 | 1.529 | 5.841 | 0.260 | 0.084 | 0.000 | 0.000 | 0.181 | 6.523 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 147 | 82 | 2581 | 175 | 178 | 0 | 0 | 43 | 227 |
N.S. |
1 | 0.99 | 0.55 | 17.44 | 1.18 | 1.20 | 0.00 | 0.00 | 0.29 | 1.53 |
time (sec) |
N/A | 0.620 | 1.212 | 5.471 | 0.231 | 0.109 | 0.000 | 0.000 | 0.168 | 6.673 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 97 | 58 | 2484 | 113 | 129 | 246 | 0 | 43 | 121 |
N.S. |
1 | 1.03 | 0.62 | 26.43 | 1.20 | 1.37 | 2.62 | 0.00 | 0.46 | 1.29 |
time (sec) |
N/A | 0.424 | 0.954 | 5.898 | 0.227 | 0.082 | 0.536 | 0.000 | 0.168 | 2.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 37 | 36 | 86 | 84 | 49 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.97 | 2.32 | 2.27 | 1.32 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.236 | 0.233 | 5.298 | 0.204 | 0.086 | 3.957 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 156 | 87 | 0 | 0 | 0 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.29 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.538 | 3.667 | 0.000 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 146 | 112 | 0 | 0 | 0 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.29 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.506 | 8.815 | 0.000 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 156 | 116 | 0 | 0 | 0 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.29 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.574 | 12.358 | 0.000 | 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 | F | B | A | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 159 | 122 | 0 | 1067 | 166 | 0 | 0 | 47 | 318 |
N.S. |
1 | 1.02 | 0.78 | 0.00 | 6.84 | 1.06 | 0.00 | 0.00 | 0.30 | 2.04 |
time (sec) |
N/A | 0.650 | 2.610 | 0.000 | 1.298 | 0.082 | 0.000 | 0.000 | 0.191 | 7.667 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 142 | 166 | 0 | 0 | 0 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.38 | 1.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.559 | 10.658 | 0.000 | 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 | A | F | B | A | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 102 | 91 | 0 | 595 | 134 | 0 | 0 | 47 | 174 |
N.S. |
1 | 1.04 | 0.93 | 0.00 | 6.07 | 1.37 | 0.00 | 0.00 | 0.48 | 1.78 |
time (sec) |
N/A | 0.434 | 1.989 | 0.000 | 0.368 | 0.087 | 0.000 | 0.000 | 0.189 | 2.951 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 140 | 166 | 0 | 0 | 0 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.36 | 1.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.540 | 9.486 | 0.000 | 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 | A | F | B | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 59 | 0 | 217 | 109 | 0 | 0 | 47 | 106 |
N.S. |
1 | 1.00 | 1.28 | 0.00 | 4.72 | 2.37 | 0.00 | 0.00 | 1.02 | 2.30 |
time (sec) |
N/A | 0.246 | 1.360 | 0.000 | 0.203 | 0.085 | 0.000 | 0.000 | 0.158 | 1.507 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 138 | 154 | 0 | 0 | 0 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.37 | 1.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.532 | 6.334 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 69 | 146 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.06 | 2.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.341 | 1.291 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 137 | 157 | 0 | 0 | 0 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.36 | 1.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.540 | 9.880 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 78 | 151 | 0 | 0 | 0 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.05 | 2.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.575 | 9.896 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 142 | 166 | 0 | 0 | 0 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.38 | 1.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.565 | 11.465 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 0.000 |