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 | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 19 | 22 | 20 | 48 | 31 | 22 | 46 | 21 |
N.S. |
1 | 1.00 | 0.79 | 0.92 | 0.83 | 2.00 | 1.29 | 0.92 | 1.92 | 0.88 |
time (sec) |
N/A | 0.318 | 0.220 | 0.358 | 0.028 | 0.089 | 0.232 | 0.109 | 0.261 | 1.913 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 61 | 100 | 0 | 315 | 0 | 66 | 120 | 160 |
N.S. |
1 | 1.00 | 0.94 | 1.54 | 0.00 | 4.85 | 0.00 | 1.02 | 1.85 | 2.46 |
time (sec) |
N/A | 0.390 | 0.198 | 0.637 | 0.000 | 0.122 | 0.000 | 0.120 | 0.283 | 13.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 134 | 101 | 0 | 303 | 0 | 90 | 106 | 974 |
N.S. |
1 | 1.00 | 1.34 | 1.01 | 0.00 | 3.03 | 0.00 | 0.90 | 1.06 | 9.74 |
time (sec) |
N/A | 0.449 | 0.313 | 0.673 | 0.000 | 1.279 | 0.000 | 0.115 | 0.223 | 4.829 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 63 | 59 | 0 | 249 | 0 | 53 | 45 | 636 |
N.S. |
1 | 1.00 | 1.02 | 0.95 | 0.00 | 4.02 | 0.00 | 0.85 | 0.73 | 10.26 |
time (sec) |
N/A | 0.504 | 0.188 | 0.616 | 0.000 | 0.302 | 0.000 | 0.113 | 0.225 | 7.373 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 112 | 116 | 100 | 0 | 298 | 0 | 90 | 108 | 983 |
N.S. |
1 | 1.13 | 1.17 | 1.01 | 0.00 | 3.01 | 0.00 | 0.91 | 1.09 | 9.93 |
time (sec) |
N/A | 0.653 | 0.251 | 1.309 | 0.000 | 1.752 | 0.000 | 0.117 | 0.260 | 4.465 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 81 | 156 | 0 | 405 | 695 | 94 | 25 | 653 |
N.S. |
1 | 1.00 | 0.94 | 1.81 | 0.00 | 4.71 | 8.08 | 1.09 | 0.29 | 7.59 |
time (sec) |
N/A | 0.593 | 0.440 | 1.115 | 0.000 | 0.103 | 15.802 | 0.123 | 0.282 | 3.274 |
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 | 121 | 132 | 115 | 144 | 0 | 1044 | 0 | 155 | 253 | 301 |
N.S. |
1 | 1.09 | 0.95 | 1.19 | 0.00 | 8.63 | 0.00 | 1.28 | 2.09 | 2.49 |
time (sec) |
N/A | 0.622 | 0.548 | 1.864 | 0.000 | 0.104 | 0.000 | 0.138 | 0.260 | 2.695 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 213 | 175 | 273 | 0 | 3636 | 0 | 370 | 688 | 0 |
N.S. |
1 | 1.14 | 0.94 | 1.46 | 0.00 | 19.44 | 0.00 | 1.98 | 3.68 | 0.00 |
time (sec) |
N/A | 0.857 | 0.776 | 6.407 | 0.000 | 0.151 | 0.000 | 0.150 | 0.264 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 260 | 302 | 245 | 459 | 0 | 8531 | 0 | 657 | 1747 | 0 |
N.S. |
1 | 1.16 | 0.94 | 1.77 | 0.00 | 32.81 | 0.00 | 2.53 | 6.72 | 0.00 |
time (sec) |
N/A | 1.197 | 1.854 | 20.825 | 0.000 | 0.331 | 0.000 | 0.162 | 0.334 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 193 | 284 | 487 | 0 | 780 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.01 | 1.49 | 2.55 | 0.00 | 4.08 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.781 | 0.417 | 0.514 | 0.000 | 0.133 | 0.000 | 0.000 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 291 | 275 | 434 | 686 | 0 | 1162 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.95 | 1.49 | 2.36 | 0.00 | 3.99 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.130 | 0.281 | 0.482 | 0.000 | 0.120 | 0.000 | 0.000 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 391 | 355 | 580 | 889 | 0 | 1542 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.91 | 1.48 | 2.27 | 0.00 | 3.94 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.436 | 0.288 | 0.537 | 0.000 | 0.127 | 0.000 | 0.000 | 0.252 | 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 | 58 | 57 | 55 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 0.98 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.419 | 0.051 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.473 | 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 | 58 | 57 | 57 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 0.98 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.381 | 0.027 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.284 | 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 | 26 | 26 | 26 | 0 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.27 | 0.00 |
time (sec) |
N/A | 0.303 | 0.023 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.297 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 36 | 30 | 33 | 32 | 29 | 32 | 33 | 35 |
N.S. |
1 | 1.00 | 1.06 | 0.88 | 0.97 | 0.94 | 0.85 | 0.94 | 0.97 | 1.03 |
time (sec) |
N/A | 0.331 | 8.027 | 0.177 | 0.246 | 0.090 | 4.412 | 0.210 | 0.317 | 2.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 38 | 32 | 121 | 34 | 31 | 34 | 35 | 35 |
N.S. |
1 | 1.00 | 1.06 | 0.89 | 3.36 | 0.94 | 0.86 | 0.94 | 0.97 | 0.97 |
time (sec) |
N/A | 0.374 | 27.737 | 0.215 | 0.243 | 0.080 | 4.823 | 0.276 | 0.392 | 2.238 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 59 | 138 | 0 | 480 | 0 | 0 | 112 | 110 |
N.S. |
1 | 1.00 | 0.98 | 2.30 | 0.00 | 8.00 | 0.00 | 0.00 | 1.87 | 1.83 |
time (sec) |
N/A | 0.338 | 0.096 | 1.364 | 0.000 | 0.115 | 0.000 | 0.000 | 0.307 | 2.122 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 103 | 87 | 231 | 0 | 1692 | 0 | 0 | 924 | 0 |
N.S. |
1 | 1.18 | 1.00 | 2.66 | 0.00 | 19.45 | 0.00 | 0.00 | 10.62 | 0.00 |
time (sec) |
N/A | 0.434 | 0.174 | 5.083 | 0.000 | 0.104 | 0.000 | 0.000 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 41 | 47 | 42 | 67 | 0 | 45 | 35 | 0 |
N.S. |
1 | 1.00 | 0.87 | 1.00 | 0.89 | 1.43 | 0.00 | 0.96 | 0.74 | 0.00 |
time (sec) |
N/A | 0.697 | 0.052 | 2.994 | 0.135 | 0.072 | 0.000 | 0.111 | 0.278 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 202 | 24 | 20 | 24 | 173 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 9.18 | 1.09 | 0.91 | 1.09 | 7.86 | 1.09 |
time (sec) |
N/A | 0.266 | 2.674 | 0.141 | 0.975 | 0.085 | 0.765 | 0.144 | 0.313 | 1.959 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 327 | 337 | 326 | 0 | 0 | 624 | 0 | 0 | 79 | 0 |
N.S. |
1 | 1.03 | 1.00 | 0.00 | 0.00 | 1.91 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 1.409 | 0.029 | 0.000 | 0.000 | 0.114 | 0.000 | 0.000 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 249 | 244 | 0 | 0 | 497 | 0 | 0 | 79 | 0 |
N.S. |
1 | 1.02 | 1.00 | 0.00 | 0.00 | 2.03 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 1.000 | 0.017 | 0.000 | 0.000 | 0.089 | 0.000 | 0.000 | 0.280 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 161 | 160 | 368 | 0 | 354 | 0 | 0 | 75 | 0 |
N.S. |
1 | 1.00 | 0.99 | 2.29 | 0.00 | 2.20 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.627 | 0.010 | 0.736 | 0.000 | 0.093 | 0.000 | 0.000 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 19 | 18 | 44 | 41 | 31 | 18 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 2.44 | 2.28 | 1.72 | 1.00 | 1.00 |
time (sec) |
N/A | 0.215 | 0.141 | 0.352 | 0.027 | 0.099 | 0.573 | 0.117 | 0.245 | 1.914 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 56 | 24 | 19 | 24 | 86 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 2.55 | 1.09 | 0.86 | 1.09 | 3.91 | 1.09 |
time (sec) |
N/A | 0.227 | 8.019 | 0.200 | 0.139 | 0.075 | 4.690 | 0.136 | 0.278 | 1.926 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 26 | 26 | 22 | 26 | 1291 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.08 | 0.92 | 1.08 | 53.79 | 1.08 |
time (sec) |
N/A | 0.242 | 6.934 | 0.407 | 0.228 | 0.077 | 1.276 | 0.141 | 0.329 | 1.947 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | F | F(-2) | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 495 | 463 | 386 | 0 | 0 | 1174 | 0 | 0 | 377 | 0 |
N.S. |
1 | 0.94 | 0.78 | 0.00 | 0.00 | 2.37 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 2.348 | 0.651 | 0.000 | 0.000 | 0.144 | 0.000 | 0.000 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | F | F(-2) | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 370 | 356 | 293 | 0 | 0 | 937 | 0 | 0 | 334 | 0 |
N.S. |
1 | 0.96 | 0.79 | 0.00 | 0.00 | 2.53 | 0.00 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 1.965 | 0.488 | 0.000 | 0.000 | 0.112 | 0.000 | 0.000 | 0.297 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 244 | 242 | 187 | 862 | 0 | 669 | 0 | 0 | 282 | 0 |
N.S. |
1 | 0.99 | 0.77 | 3.53 | 0.00 | 2.74 | 0.00 | 0.00 | 1.16 | 0.00 |
time (sec) |
N/A | 1.250 | 0.681 | 2.917 | 0.000 | 0.099 | 0.000 | 0.000 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 87 | 69 | 129 | 0 | 415 | 1122 | 89 | 89 | 176 |
N.S. |
1 | 1.19 | 0.95 | 1.77 | 0.00 | 5.68 | 15.37 | 1.22 | 1.22 | 2.41 |
time (sec) |
N/A | 0.505 | 0.263 | 1.592 | 0.000 | 0.104 | 57.259 | 0.128 | 0.257 | 2.159 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 92 | 26 | 20 | 26 | 26 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 3.83 | 1.08 | 0.83 | 1.08 | 1.08 | 1.08 |
time (sec) |
N/A | 0.267 | 18.127 | 0.512 | 0.186 | 0.075 | 39.362 | 0.157 | 0.254 | 1.991 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 26 | 26 | 22 | 26 | 2616 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.08 | 0.92 | 1.08 | 109.00 | 1.08 |
time (sec) |
N/A | 0.248 | 9.360 | 0.646 | 0.263 | 0.087 | 2.563 | 0.149 | 0.398 | 2.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 586 | 540 | 951 | 0 | 0 | 2025 | 0 | 0 | 829 | 0 |
N.S. |
1 | 0.92 | 1.62 | 0.00 | 0.00 | 3.46 | 0.00 | 0.00 | 1.41 | 0.00 |
time (sec) |
N/A | 3.138 | 4.342 | 0.000 | 0.000 | 0.118 | 0.000 | 0.000 | 0.302 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 432 | 388 | 758 | 0 | 0 | 1622 | 0 | 0 | 712 | 0 |
N.S. |
1 | 0.90 | 1.75 | 0.00 | 0.00 | 3.75 | 0.00 | 0.00 | 1.65 | 0.00 |
time (sec) |
N/A | 2.151 | 3.071 | 0.000 | 0.000 | 0.112 | 0.000 | 0.000 | 0.318 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 288 | 264 | 374 | 860 | 0 | 1196 | 0 | 0 | 583 | 0 |
N.S. |
1 | 0.92 | 1.30 | 2.99 | 0.00 | 4.15 | 0.00 | 0.00 | 2.02 | 0.00 |
time (sec) |
N/A | 1.381 | 1.519 | 12.735 | 0.000 | 0.104 | 0.000 | 0.000 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 55 | 55 | 55 | 130 | 340 | 0 | 88 | 177 | 122 |
N.S. |
1 | 0.90 | 0.90 | 0.90 | 2.13 | 5.57 | 0.00 | 1.44 | 2.90 | 2.00 |
time (sec) |
N/A | 0.318 | 0.253 | 7.570 | 0.051 | 0.089 | 0.000 | 0.124 | 0.235 | 2.215 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 143 | 26 | 20 | 26 | 183 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 5.96 | 1.08 | 0.83 | 1.08 | 7.62 | 1.08 |
time (sec) |
N/A | 0.271 | 34.173 | 0.706 | 0.348 | 0.075 | 23.283 | 0.192 | 0.309 | 2.184 |
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 | 54 | 54 | 41 | 42 | 51 | 44 | 0 | 47 | 41 | 44 |
N.S. |
1 | 1.00 | 0.76 | 0.78 | 0.94 | 0.81 | 0.00 | 0.87 | 0.76 | 0.81 |
time (sec) |
N/A | 0.227 | 0.044 | 0.465 | 0.054 | 0.083 | 0.000 | 0.115 | 0.290 | 1.963 |
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 | 88 | 88 | 56 | 59 | 67 | 90 | 0 | 169 | 123 | 53 |
N.S. |
1 | 1.00 | 0.64 | 0.67 | 0.76 | 1.02 | 0.00 | 1.92 | 1.40 | 0.60 |
time (sec) |
N/A | 0.270 | 0.062 | 1.794 | 0.060 | 0.107 | 0.000 | 0.128 | 0.269 | 1.951 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 143 | 117 | 357 | 115 | 199 | 0 | 665 | 324 | 94 |
N.S. |
1 | 0.96 | 0.79 | 2.40 | 0.77 | 1.34 | 0.00 | 4.46 | 2.17 | 0.63 |
time (sec) |
N/A | 0.367 | 0.342 | 5.254 | 0.073 | 0.098 | 0.000 | 0.145 | 0.258 | 2.011 |
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 | 191 | 177 | 167 | 184 | 129 | 293 | 0 | 777 | 390 | 102 |
N.S. |
1 | 0.93 | 0.87 | 0.96 | 0.68 | 1.53 | 0.00 | 4.07 | 2.04 | 0.53 |
time (sec) |
N/A | 0.418 | 0.289 | 19.321 | 0.081 | 0.113 | 0.000 | 0.143 | 0.259 | 1.989 |
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 | 73 | 74 | 54 | 68 | 64 | 99 | 0 | 235 | 66 | 55 |
N.S. |
1 | 1.01 | 0.74 | 0.93 | 0.88 | 1.36 | 0.00 | 3.22 | 0.90 | 0.75 |
time (sec) |
N/A | 0.262 | 0.085 | 1.171 | 0.061 | 0.102 | 0.000 | 0.117 | 0.234 | 1.991 |
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 | 120 | 122 | 87 | 94 | 87 | 250 | 0 | 759 | 262 | 73 |
N.S. |
1 | 1.02 | 0.72 | 0.78 | 0.72 | 2.08 | 0.00 | 6.32 | 2.18 | 0.61 |
time (sec) |
N/A | 0.311 | 0.185 | 9.788 | 0.075 | 0.103 | 0.000 | 0.151 | 0.234 | 2.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 188 | 292 | 286 | 138 | 584 | 0 | 3225 | 784 | 117 |
N.S. |
1 | 0.93 | 1.44 | 1.41 | 0.68 | 2.88 | 0.00 | 15.89 | 3.86 | 0.58 |
time (sec) |
N/A | 0.489 | 0.914 | 66.283 | 0.091 | 0.098 | 0.000 | 0.170 | 0.243 | 2.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 266 | 236 | 311 | 0 | 161 | 1123 | 0 | 6880 | 1329 | 134 |
N.S. |
1 | 0.89 | 1.17 | 0.00 | 0.61 | 4.22 | 0.00 | 25.86 | 5.00 | 0.50 |
time (sec) |
N/A | 0.455 | 2.402 | 0.000 | 0.097 | 0.135 | 0.000 | 0.204 | 0.284 | 2.163 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 37 | 19 | 18 | 19 | 34 | 42 | 18 | 18 |
N.S. |
1 | 1.00 | 2.06 | 1.06 | 1.00 | 1.06 | 1.89 | 2.33 | 1.00 | 1.00 |
time (sec) |
N/A | 0.221 | 0.007 | 0.472 | 0.034 | 0.083 | 0.237 | 0.112 | 0.239 | 2.068 |
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 | 39 | 44 | 36 | 30 | 49 | 39 | 0 | 82 | 71 | 32 |
N.S. |
1 | 1.13 | 0.92 | 0.77 | 1.26 | 1.00 | 0.00 | 2.10 | 1.82 | 0.82 |
time (sec) |
N/A | 0.234 | 0.016 | 1.777 | 0.034 | 0.085 | 0.000 | 0.119 | 0.271 | 2.548 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 45 | 42 | 36 | 86 | 53 | 71 | 81 | 85 | 35 |
N.S. |
1 | 1.07 | 1.00 | 0.86 | 2.05 | 1.26 | 1.69 | 1.93 | 2.02 | 0.83 |
time (sec) |
N/A | 0.277 | 0.004 | 7.796 | 0.051 | 0.095 | 1.340 | 0.105 | 0.274 | 2.937 |
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 | 73 | 80 | 51 | 46 | 93 | 84 | 0 | 116 | 107 | 50 |
N.S. |
1 | 1.10 | 0.70 | 0.63 | 1.27 | 1.15 | 0.00 | 1.59 | 1.47 | 0.68 |
time (sec) |
N/A | 0.338 | 0.028 | 32.264 | 0.035 | 0.090 | 0.000 | 0.119 | 0.261 | 3.146 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 64 | 65 | 51 | 130 | 105 | 105 | 116 | 122 | 49 |
N.S. |
1 | 0.98 | 1.00 | 0.78 | 2.00 | 1.62 | 1.62 | 1.78 | 1.88 | 0.75 |
time (sec) |
N/A | 0.268 | 0.007 | 115.650 | 0.039 | 0.096 | 8.155 | 0.117 | 0.277 | 2.839 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 65 | 62 | 256 | 0 | 332 | 0 | 0 | 31 | 0 |
N.S. |
1 | 0.97 | 0.93 | 3.82 | 0.00 | 4.96 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.305 | 0.033 | 7.938 | 0.000 | 0.082 | 0.000 | 0.000 | 0.241 | 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 | 67 | 65 | 114 | 237 | 0 | 170 | 0 | 0 | 29 | 0 |
N.S. |
1 | 0.97 | 1.70 | 3.54 | 0.00 | 2.54 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.303 | 0.089 | 2.944 | 0.000 | 0.088 | 0.000 | 0.000 | 0.270 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 183 | 0 | 58 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.00 | 1.00 | 6.54 | 0.00 | 2.07 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.232 | 0.011 | 1.897 | 0.000 | 0.082 | 0.000 | 0.000 | 0.279 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 183 | 0 | 39 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 1.00 | 6.54 | 0.00 | 1.39 | 0.00 | 0.00 | 1.11 | 0.00 |
time (sec) |
N/A | 0.230 | 0.009 | 1.003 | 0.000 | 0.088 | 0.000 | 0.000 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 61 | 58 | 141 | 0 | 243 | 0 | 0 | 31 | 0 |
N.S. |
1 | 0.97 | 0.92 | 2.24 | 0.00 | 3.86 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.300 | 0.035 | 1.260 | 0.000 | 0.090 | 0.000 | 0.000 | 0.280 | 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 | 67 | 65 | 122 | 258 | 0 | 501 | 0 | 0 | 31 | 0 |
N.S. |
1 | 0.97 | 1.82 | 3.85 | 0.00 | 7.48 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.299 | 0.050 | 1.605 | 0.000 | 0.115 | 0.000 | 0.000 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 203 | 85 | 0 | 0 | 187 | 0 | 0 | 40 | 0 |
N.S. |
1 | 0.99 | 0.41 | 0.00 | 0.00 | 0.91 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.465 | 0.236 | 0.000 | 0.000 | 0.097 | 0.000 | 0.000 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 152 | 75 | 0 | 0 | 177 | 0 | 0 | 38 | 0 |
N.S. |
1 | 0.89 | 0.44 | 0.00 | 0.00 | 1.04 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.385 | 0.214 | 0.000 | 0.000 | 0.113 | 0.000 | 0.000 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 109 | 74 | 0 | 0 | 141 | 0 | 0 | 80 | 0 |
N.S. |
1 | 1.07 | 0.73 | 0.00 | 0.00 | 1.38 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.360 | 0.213 | 0.000 | 0.000 | 0.091 | 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 | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 61 | 0 | 0 | 68 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.00 | 1.45 | 0.00 | 0.00 | 1.62 | 0.00 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.366 | 0.085 | 0.000 | 0.000 | 0.091 | 0.000 | 0.000 | 0.266 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 141 | 121 | 0 | 0 | 128 | 0 | 80 | 40 | 0 |
N.S. |
1 | 1.62 | 1.39 | 0.00 | 0.00 | 1.47 | 0.00 | 0.92 | 0.46 | 0.00 |
time (sec) |
N/A | 0.412 | 0.149 | 0.000 | 0.000 | 0.094 | 0.000 | 3.298 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | B | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 116 | 305 | 347 | 0 | 171 | 0 | 764 | 1338 | 0 |
N.S. |
1 | 1.15 | 3.02 | 3.44 | 0.00 | 1.69 | 0.00 | 7.56 | 13.25 | 0.00 |
time (sec) |
N/A | 0.726 | 1.261 | 0.734 | 0.000 | 0.097 | 0.000 | 1.702 | 0.299 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | B | F | B | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 122 | 475 | 358 | 0 | 366 | 0 | 749 | 1575 | 0 |
N.S. |
1 | 1.14 | 4.44 | 3.35 | 0.00 | 3.42 | 0.00 | 7.00 | 14.72 | 0.00 |
time (sec) |
N/A | 0.656 | 2.979 | 3.539 | 0.000 | 0.109 | 0.000 | 6.438 | 0.296 | 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 | 83 | 71 | 62 | 45 | 68 | 113 | 139 | 60 | 67 | 58 |
N.S. |
1 | 0.86 | 0.75 | 0.54 | 0.82 | 1.36 | 1.67 | 0.72 | 0.81 | 0.70 |
time (sec) |
N/A | 0.226 | 0.031 | 3.088 | 0.046 | 0.079 | 2.347 | 0.115 | 0.242 | 0.553 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 47 | 53 | 47 | 53 | 95 | 207 | 57 | 55 | 42 |
N.S. |
1 | 0.82 | 0.93 | 0.82 | 0.93 | 1.67 | 3.63 | 1.00 | 0.96 | 0.74 |
time (sec) |
N/A | 0.217 | 0.021 | 1.648 | 0.036 | 0.087 | 0.994 | 0.116 | 0.268 | 0.294 |
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 | 49 | 43 | 39 | 35 | 40 | 54 | 78 | 34 | 38 | 34 |
N.S. |
1 | 0.88 | 0.80 | 0.71 | 0.82 | 1.10 | 1.59 | 0.69 | 0.78 | 0.69 |
time (sec) |
N/A | 0.198 | 0.017 | 0.865 | 0.037 | 0.078 | 0.475 | 0.111 | 0.272 | 0.117 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 30 | 23 | 19 | 24 | 50 | 63 | 22 | 38 | 18 |
N.S. |
1 | 1.30 | 1.00 | 0.83 | 1.04 | 2.17 | 2.74 | 0.96 | 1.65 | 0.78 |
time (sec) |
N/A | 0.192 | 0.010 | 0.393 | 0.030 | 0.081 | 0.229 | 0.107 | 0.262 | 2.219 |
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 | 17 | 17 | 17 | 17 | 16 | 30 | 0 | 16 | 17 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.94 | 1.76 | 0.00 | 0.94 | 1.00 | 0.94 |
time (sec) |
N/A | 0.177 | 0.011 | 0.309 | 0.111 | 0.076 | 0.000 | 0.105 | 0.213 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 43 | 38 | 25 | 37 | 105 | 0 | 35 | 56 | 48 |
N.S. |
1 | 1.08 | 0.95 | 0.62 | 0.92 | 2.62 | 0.00 | 0.88 | 1.40 | 1.20 |
time (sec) |
N/A | 0.189 | 0.044 | 0.674 | 0.139 | 0.086 | 0.000 | 0.107 | 0.300 | 0.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 22 | 68 | 86 | 0 | 31 | 41 | 31 |
N.S. |
1 | 1.00 | 1.00 | 0.76 | 2.34 | 2.97 | 0.00 | 1.07 | 1.41 | 1.07 |
time (sec) |
N/A | 0.178 | 0.015 | 1.083 | 0.035 | 0.077 | 0.000 | 0.107 | 0.268 | 2.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 106 | 64 | 37 | 83 | 513 | 0 | 60 | 147 | 130 |
N.S. |
1 | 1.12 | 0.67 | 0.39 | 0.87 | 5.40 | 0.00 | 0.63 | 1.55 | 1.37 |
time (sec) |
N/A | 0.214 | 0.057 | 4.105 | 0.112 | 0.089 | 0.000 | 0.112 | 0.239 | 2.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 44 | 35 | 172 | 233 | 0 | 42 | 81 | 42 |
N.S. |
1 | 1.00 | 0.73 | 0.58 | 2.87 | 3.88 | 0.00 | 0.70 | 1.35 | 0.70 |
time (sec) |
N/A | 0.217 | 0.026 | 3.250 | 0.042 | 0.089 | 0.000 | 0.115 | 0.277 | 2.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 28 | 26 | 17 | 17 | 47 | 42 | 17 | 25 | 17 |
N.S. |
1 | 1.08 | 1.00 | 0.65 | 0.65 | 1.81 | 1.62 | 0.65 | 0.96 | 0.65 |
time (sec) |
N/A | 0.196 | 0.011 | 0.572 | 0.028 | 0.075 | 0.154 | 0.110 | 0.270 | 0.087 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 21 | 16 | 14 | 13 | 26 | 20 | 13 | 18 | 12 |
N.S. |
1 | 1.11 | 0.84 | 0.74 | 0.68 | 1.37 | 1.05 | 0.68 | 0.95 | 0.63 |
time (sec) |
N/A | 0.180 | 0.008 | 0.262 | 0.027 | 0.088 | 0.101 | 0.107 | 0.249 | 2.006 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 104 | 24 | 25 | 76 | 90 | 0 | 76 | 70 | 77 |
N.S. |
1 | 1.60 | 0.37 | 0.38 | 1.17 | 1.38 | 0.00 | 1.17 | 1.08 | 1.18 |
time (sec) |
N/A | 0.319 | 0.009 | 0.645 | 0.114 | 0.081 | 0.000 | 0.109 | 0.232 | 0.235 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 125 | 106 | 36 | 88 | 345 | 0 | 88 | 186 | 85 |
N.S. |
1 | 1.45 | 1.23 | 0.42 | 1.02 | 4.01 | 0.00 | 1.02 | 2.16 | 0.99 |
time (sec) |
N/A | 0.335 | 0.061 | 1.348 | 0.111 | 0.102 | 0.000 | 0.116 | 0.238 | 2.284 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 28 | 26 | 17 | 17 | 67 | 42 | 17 | 25 | 17 |
N.S. |
1 | 1.08 | 1.00 | 0.65 | 0.65 | 2.58 | 1.62 | 0.65 | 0.96 | 0.65 |
time (sec) |
N/A | 0.187 | 0.013 | 0.596 | 0.026 | 0.085 | 0.155 | 0.119 | 0.263 | 1.967 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 23 | 16 | 14 | 13 | 38 | 20 | 13 | 18 | 12 |
N.S. |
1 | 1.21 | 0.84 | 0.74 | 0.68 | 2.00 | 1.05 | 0.68 | 0.95 | 0.63 |
time (sec) |
N/A | 0.182 | 0.008 | 0.407 | 0.028 | 0.081 | 0.099 | 0.133 | 0.234 | 1.893 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | A | A | F | A | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 35 | 24 | 79 | 71 | 83 | 0 | 44 | 72 | 65 |
N.S. |
1 | 0.64 | 0.44 | 1.44 | 1.29 | 1.51 | 0.00 | 0.80 | 1.31 | 1.18 |
time (sec) |
N/A | 0.250 | 0.010 | 0.653 | 0.112 | 0.080 | 0.000 | 0.114 | 0.268 | 2.013 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 121 | 34 | 59 | 79 | 481 | 0 | 79 | 175 | 84 |
N.S. |
1 | 1.42 | 0.40 | 0.69 | 0.93 | 5.66 | 0.00 | 0.93 | 2.06 | 0.99 |
time (sec) |
N/A | 0.364 | 0.017 | 1.462 | 0.137 | 0.088 | 0.000 | 0.122 | 0.251 | 0.334 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 28 | 26 | 17 | 17 | 87 | 42 | 17 | 25 | 17 |
N.S. |
1 | 1.08 | 1.00 | 0.65 | 0.65 | 3.35 | 1.62 | 0.65 | 0.96 | 0.65 |
time (sec) |
N/A | 0.209 | 0.012 | 0.681 | 0.033 | 0.092 | 0.155 | 0.117 | 0.252 | 1.920 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 23 | 19 | 14 | 13 | 46 | 20 | 13 | 18 | 14 |
N.S. |
1 | 1.21 | 1.00 | 0.74 | 0.68 | 2.42 | 1.05 | 0.68 | 0.95 | 0.74 |
time (sec) |
N/A | 0.199 | 0.008 | 0.489 | 0.029 | 0.076 | 0.100 | 0.119 | 0.240 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 289 | 389 | 24 | 25 | 0 | 167 | 0 | 249 | 469 | 479 |
N.S. |
1 | 1.35 | 0.08 | 0.09 | 0.00 | 0.58 | 0.00 | 0.86 | 1.62 | 1.66 |
time (sec) |
N/A | 0.727 | 0.010 | 0.756 | 0.000 | 0.098 | 0.000 | 0.161 | 0.258 | 5.838 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 293 | 390 | 34 | 36 | 0 | 1215 | 0 | 261 | 506 | 473 |
N.S. |
1 | 1.33 | 0.12 | 0.12 | 0.00 | 4.15 | 0.00 | 0.89 | 1.73 | 1.61 |
time (sec) |
N/A | 0.752 | 0.015 | 1.364 | 0.000 | 0.106 | 0.000 | 0.136 | 0.285 | 4.750 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | C | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 190 | 159 | 148 | 134 | 2218 | 1610 | 1211 | 23 | 154 |
N.S. |
1 | 0.94 | 0.79 | 0.73 | 0.66 | 10.98 | 7.97 | 6.00 | 0.11 | 0.76 |
time (sec) |
N/A | 0.517 | 0.427 | 2.319 | 0.050 | 0.170 | 3.305 | 0.174 | 0.232 | 3.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | C | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 132 | 85 | 90 | 94 | 699 | 707 | 889 | 23 | 100 |
N.S. |
1 | 1.00 | 0.64 | 0.68 | 0.71 | 5.30 | 5.36 | 6.73 | 0.17 | 0.76 |
time (sec) |
N/A | 0.370 | 0.137 | 1.041 | 0.053 | 0.089 | 1.165 | 0.172 | 0.274 | 2.388 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 50 | 52 | 63 | 246 | 265 | 597 | 51 | 74 |
N.S. |
1 | 1.00 | 0.67 | 0.69 | 0.84 | 3.28 | 3.53 | 7.96 | 0.68 | 0.99 |
time (sec) |
N/A | 0.240 | 0.063 | 0.373 | 0.041 | 0.105 | 0.655 | 0.138 | 0.254 | 2.141 |
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 | 68 | 68 | 70 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.244 | 0.016 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.271 | 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 | 70 | 70 | 70 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.228 | 0.013 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.252 | 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 | 124 | 139 | 96 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.12 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.361 | 0.151 | 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 | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 148 | 101 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.11 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.370 | 0.128 | 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 | A | A | A | F(-1) | A | B | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 102 | 109 | 326 | 112 | 218 | 0 | 99 | 97 | 0 |
N.S. |
1 | 0.41 | 0.44 | 1.30 | 0.45 | 0.87 | 0.00 | 0.40 | 0.39 | 0.00 |
time (sec) |
N/A | 0.467 | 0.073 | 8.348 | 0.036 | 0.098 | 0.000 | 0.122 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 74 | 81 | 216 | 74 | 126 | 0 | 71 | 67 | 0 |
N.S. |
1 | 0.46 | 0.50 | 1.33 | 0.46 | 0.78 | 0.00 | 0.44 | 0.41 | 0.00 |
time (sec) |
N/A | 0.394 | 0.047 | 1.206 | 0.037 | 0.076 | 0.000 | 0.129 | 0.262 | 0.000 |
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 | 74 | 59 | 48 | 106 | 29 | 66 | 163 | 25 | 55 | 76 |
N.S. |
1 | 0.80 | 0.65 | 1.43 | 0.39 | 0.89 | 2.20 | 0.34 | 0.74 | 1.03 |
time (sec) |
N/A | 0.357 | 0.025 | 1.251 | 0.038 | 0.081 | 2.183 | 0.121 | 0.281 | 0.134 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 42 | 29 | 21 | 42 | 0 | 21 | 22 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.66 | 0.48 | 0.95 | 0.00 | 0.48 | 0.50 | 0.00 |
time (sec) |
N/A | 0.338 | 0.037 | 0.622 | 0.121 | 0.081 | 0.000 | 0.128 | 0.284 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 46 | 69 | 84 | 120 | 0 | 38 | 50 | 76 |
N.S. |
1 | 1.00 | 0.82 | 1.23 | 1.50 | 2.14 | 0.00 | 0.68 | 0.89 | 1.36 |
time (sec) |
N/A | 0.345 | 0.050 | 1.275 | 0.045 | 0.073 | 0.000 | 0.130 | 0.277 | 1.939 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 87 | 72 | 80 | 209 | 315 | 0 | 51 | 96 | 89 |
N.S. |
1 | 0.62 | 0.51 | 0.57 | 1.48 | 2.23 | 0.00 | 0.36 | 0.68 | 0.63 |
time (sec) |
N/A | 0.419 | 0.048 | 1.264 | 0.037 | 0.090 | 0.000 | 0.132 | 0.294 | 0.116 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 105 | 84 | 91 | 386 | 589 | 0 | 64 | 138 | 345 |
N.S. |
1 | 0.55 | 0.44 | 0.48 | 2.02 | 3.08 | 0.00 | 0.34 | 0.72 | 1.81 |
time (sec) |
N/A | 0.446 | 0.057 | 1.331 | 0.039 | 0.083 | 0.000 | 0.129 | 0.240 | 0.120 |
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 | 41 | 41 | 28 | 28 | 0 | 45 | 99 | 32 | 28 | 45 |
N.S. |
1 | 1.00 | 0.68 | 0.68 | 0.00 | 1.10 | 2.41 | 0.78 | 0.68 | 1.10 |
time (sec) |
N/A | 0.200 | 0.035 | 0.575 | 0.000 | 0.075 | 0.239 | 0.116 | 0.267 | 1.962 |