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 | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 144 | 144 | 125 | 135 | 0 | 891 | 0 | 158 | 1428 |
N.S. |
1 | 1.00 | 0.87 | 0.94 | 0.00 | 6.19 | 0.00 | 1.10 | 9.92 |
time (sec) |
N/A | 0.168 | 0.239 | 3.142 | 0.000 | 0.942 | 0.000 | 0.320 | 6.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 130 | 130 | 145 | 138 | 0 | 901 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.12 | 1.06 | 0.00 | 6.93 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.123 | 0.377 | 3.116 | 0.000 | 0.491 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 88 | 90 | 0 | 390 | 0 | 105 | 100 |
N.S. |
1 | 1.00 | 0.88 | 0.90 | 0.00 | 3.90 | 0.00 | 1.05 | 1.00 |
time (sec) |
N/A | 0.077 | 0.162 | 3.009 | 0.000 | 0.285 | 0.000 | 0.296 | 5.385 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 69 | 71 | 0 | 306 | 0 | 64 | 57 |
N.S. |
1 | 1.00 | 1.01 | 1.04 | 0.00 | 4.50 | 0.00 | 0.94 | 0.84 |
time (sec) |
N/A | 0.046 | 0.078 | 2.946 | 0.000 | 0.266 | 0.000 | 0.297 | 5.274 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 48 | 38 | 0 | 231 | 85 | 39 | 39 |
N.S. |
1 | 1.00 | 0.98 | 0.78 | 0.00 | 4.71 | 1.73 | 0.80 | 0.80 |
time (sec) |
N/A | 0.030 | 0.040 | 2.924 | 0.000 | 0.277 | 3.112 | 0.296 | 5.302 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 78 | 78 | 0 | 603 | 109 | 70 | 651 |
N.S. |
1 | 1.00 | 0.98 | 0.98 | 0.00 | 7.54 | 1.36 | 0.88 | 8.14 |
time (sec) |
N/A | 0.054 | 0.112 | 3.010 | 0.000 | 0.315 | 4.102 | 0.284 | 5.517 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 115 | 109 | 115 | 0 | 734 | 0 | 103 | 396 |
N.S. |
1 | 1.00 | 0.95 | 1.00 | 0.00 | 6.38 | 0.00 | 0.90 | 3.44 |
time (sec) |
N/A | 0.081 | 0.238 | 3.035 | 0.000 | 0.327 | 0.000 | 0.286 | 5.801 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 114 | 114 | 375 | 112 | 0 | 717 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 3.29 | 0.98 | 0.00 | 6.29 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.067 | 2.142 | 3.035 | 0.000 | 0.350 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 342 | 84 | 0 | 616 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 4.17 | 1.02 | 0.00 | 7.51 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.034 | 1.224 | 2.947 | 0.000 | 0.304 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 70 | 41 | 0 | 241 | 0 | 70 | 0 |
N.S. |
1 | 1.00 | 1.43 | 0.84 | 0.00 | 4.92 | 0.00 | 1.43 | 0.00 |
time (sec) |
N/A | 0.015 | 0.014 | 2.911 | 0.000 | 0.283 | 0.000 | 0.306 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 93 | 78 | 0 | 324 | 0 | 111 | 0 |
N.S. |
1 | 1.00 | 1.26 | 1.05 | 0.00 | 4.38 | 0.00 | 1.50 | 0.00 |
time (sec) |
N/A | 0.042 | 0.165 | 2.931 | 0.000 | 0.291 | 0.000 | 0.295 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 117 | 87 | 0 | 414 | 0 | 195 | 0 |
N.S. |
1 | 1.00 | 1.06 | 0.79 | 0.00 | 3.76 | 0.00 | 1.77 | 0.00 |
time (sec) |
N/A | 0.090 | 0.251 | 3.033 | 0.000 | 0.308 | 0.000 | 1.024 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | B | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 666 | 117 | 0 | 977 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 6.11 | 1.07 | 0.00 | 8.96 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.078 | 2.429 | 3.015 | 0.000 | 0.403 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 76 | 87 | 0 | 428 | 0 | 78 | 64 |
N.S. |
1 | 1.00 | 0.99 | 1.13 | 0.00 | 5.56 | 0.00 | 1.01 | 0.83 |
time (sec) |
N/A | 0.051 | 0.132 | 2.934 | 0.000 | 0.270 | 0.000 | 0.296 | 5.575 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 319 | 87 | 0 | 334 | 0 | 103 | 0 |
N.S. |
1 | 1.00 | 4.31 | 1.18 | 0.00 | 4.51 | 0.00 | 1.39 | 0.00 |
time (sec) |
N/A | 0.034 | 1.378 | 2.917 | 0.000 | 0.302 | 0.000 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 72 | 82 | 0 | 323 | 114 | 71 | 61 |
N.S. |
1 | 1.00 | 1.00 | 1.14 | 0.00 | 4.49 | 1.58 | 0.99 | 0.85 |
time (sec) |
N/A | 0.038 | 0.092 | 2.940 | 0.000 | 0.309 | 5.974 | 0.283 | 5.571 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 99 | 92 | 0 | 442 | 0 | 107 | 0 |
N.S. |
1 | 1.00 | 1.25 | 1.16 | 0.00 | 5.59 | 0.00 | 1.35 | 0.00 |
time (sec) |
N/A | 0.025 | 0.052 | 2.902 | 0.000 | 0.335 | 0.000 | 0.312 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 106 | 101 | 0 | 959 | 141 | 110 | 2296 |
N.S. |
1 | 1.00 | 0.99 | 0.94 | 0.00 | 8.96 | 1.32 | 1.03 | 21.46 |
time (sec) |
N/A | 0.078 | 0.240 | 2.989 | 0.000 | 0.452 | 5.976 | 0.283 | 6.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 124 | 127 | 107 | 0 | 560 | 0 | 152 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.86 | 0.00 | 4.52 | 0.00 | 1.23 | 0.00 |
time (sec) |
N/A | 0.081 | 0.390 | 3.008 | 0.000 | 0.344 | 0.000 | 0.763 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 156 | 156 | 142 | 159 | 0 | 1291 | 0 | 172 | 3025 |
N.S. |
1 | 1.00 | 0.91 | 1.02 | 0.00 | 8.28 | 0.00 | 1.10 | 19.39 |
time (sec) |
N/A | 0.152 | 0.394 | 3.166 | 0.000 | 0.608 | 0.000 | 0.300 | 6.758 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 176 | 176 | 175 | 125 | 0 | 706 | 0 | 275 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.71 | 0.00 | 4.01 | 0.00 | 1.56 | 0.00 |
time (sec) |
N/A | 0.148 | 0.495 | 3.052 | 0.000 | 0.421 | 0.000 | 0.859 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 117 | 117 | 351 | 107 | 0 | 524 | 0 | 304 | 0 |
N.S. |
1 | 1.00 | 3.00 | 0.91 | 0.00 | 4.48 | 0.00 | 2.60 | 0.00 |
time (sec) |
N/A | 0.072 | 1.843 | 2.964 | 0.000 | 0.483 | 0.000 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 100 | 109 | 0 | 535 | 0 | 127 | 110 |
N.S. |
1 | 1.00 | 0.97 | 1.06 | 0.00 | 5.19 | 0.00 | 1.23 | 1.07 |
time (sec) |
N/A | 0.067 | 0.220 | 3.059 | 0.000 | 0.294 | 0.000 | 0.301 | 5.667 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 115 | 122 | 116 | 0 | 550 | 0 | 291 | 0 |
N.S. |
1 | 1.00 | 1.06 | 1.01 | 0.00 | 4.78 | 0.00 | 2.53 | 0.00 |
time (sec) |
N/A | 0.058 | 0.391 | 2.983 | 0.000 | 0.427 | 0.000 | 0.311 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 90 | 102 | 0 | 511 | 139 | 118 | 103 |
N.S. |
1 | 1.00 | 0.92 | 1.04 | 0.00 | 5.21 | 1.42 | 1.20 | 1.05 |
time (sec) |
N/A | 0.053 | 0.144 | 2.962 | 0.000 | 0.325 | 7.413 | 0.279 | 5.610 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 122 | 122 | 132 | 122 | 0 | 764 | 0 | 321 | 0 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 0.00 | 6.26 | 0.00 | 2.63 | 0.00 |
time (sec) |
N/A | 0.070 | 0.338 | 2.974 | 0.000 | 0.485 | 0.000 | 0.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 145 | 145 | 138 | 141 | 0 | 1711 | 182 | 176 | 4558 |
N.S. |
1 | 1.00 | 0.95 | 0.97 | 0.00 | 11.80 | 1.26 | 1.21 | 31.43 |
time (sec) |
N/A | 0.129 | 0.382 | 3.031 | 0.000 | 0.835 | 7.574 | 0.285 | 7.294 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 178 | 178 | 180 | 144 | 0 | 934 | 0 | 366 | 0 |
N.S. |
1 | 1.00 | 1.01 | 0.81 | 0.00 | 5.25 | 0.00 | 2.06 | 0.00 |
time (sec) |
N/A | 0.171 | 0.519 | 3.148 | 0.000 | 0.512 | 0.000 | 0.792 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 211 | 211 | 194 | 190 | 0 | 2219 | 0 | 211 | 5409 |
N.S. |
1 | 1.00 | 0.92 | 0.90 | 0.00 | 10.52 | 0.00 | 1.00 | 25.64 |
time (sec) |
N/A | 0.230 | 0.666 | 3.181 | 0.000 | 1.453 | 0.000 | 0.288 | 8.144 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 245 | 245 | 233 | 238 | 0 | 1128 | 0 | 490 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.97 | 0.00 | 4.60 | 0.00 | 2.00 | 0.00 |
time (sec) |
N/A | 0.239 | 0.827 | 3.128 | 0.000 | 0.674 | 0.000 | 0.973 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 150 | 150 | 134 | 145 | 0 | 1002 | 0 | 283 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.97 | 0.00 | 6.68 | 0.00 | 1.89 | 0.00 |
time (sec) |
N/A | 0.114 | 10.122 | 3.219 | 0.000 | 0.363 | 0.000 | 0.312 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 136 | 136 | 98 | 99 | 0 | 436 | 0 | 101 | 102 |
N.S. |
1 | 1.00 | 0.72 | 0.73 | 0.00 | 3.21 | 0.00 | 0.74 | 0.75 |
time (sec) |
N/A | 0.080 | 0.227 | 3.034 | 0.000 | 0.287 | 0.000 | 0.289 | 5.530 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 120 | 120 | 138 | 99 | 0 | 1069 | 0 | 251 | 0 |
N.S. |
1 | 1.00 | 1.15 | 0.82 | 0.00 | 8.91 | 0.00 | 2.09 | 0.00 |
time (sec) |
N/A | 0.055 | 0.437 | 3.020 | 0.000 | 0.334 | 0.000 | 0.316 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 80 | 65 | 0 | 356 | 0 | 79 | 70 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.00 | 4.45 | 0.00 | 0.99 | 0.88 |
time (sec) |
N/A | 0.043 | 0.230 | 2.987 | 0.000 | 0.273 | 0.000 | 0.286 | 5.348 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 102 | 73 | 0 | 369 | 0 | 218 | 0 |
N.S. |
1 | 1.00 | 1.24 | 0.89 | 0.00 | 4.50 | 0.00 | 2.66 | 0.00 |
time (sec) |
N/A | 0.022 | 0.364 | 2.938 | 0.000 | 0.305 | 0.000 | 0.818 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 119 | 111 | 120 | 0 | 1054 | 0 | 113 | 996 |
N.S. |
1 | 1.00 | 0.93 | 1.01 | 0.00 | 8.86 | 0.00 | 0.95 | 8.37 |
time (sec) |
N/A | 0.078 | 0.460 | 3.014 | 0.000 | 0.351 | 0.000 | 0.281 | 5.653 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 1650 | 92 | 0 | 458 | 0 | 329 | 0 |
N.S. |
1 | 1.00 | 14.60 | 0.81 | 0.00 | 4.05 | 0.00 | 2.91 | 0.00 |
time (sec) |
N/A | 0.078 | 7.995 | 3.061 | 0.000 | 0.328 | 0.000 | 0.866 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 132 | 153 | 0 | 1043 | 0 | 183 | 1193 |
N.S. |
1 | 1.00 | 0.83 | 0.96 | 0.00 | 6.56 | 0.00 | 1.15 | 7.50 |
time (sec) |
N/A | 0.145 | 0.657 | 3.103 | 0.000 | 0.403 | 0.000 | 0.319 | 6.204 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 147 | 147 | 154 | 116 | 0 | 602 | 0 | 361 | 0 |
N.S. |
1 | 1.00 | 1.05 | 0.79 | 0.00 | 4.10 | 0.00 | 2.46 | 0.00 |
time (sec) |
N/A | 0.146 | 0.873 | 3.101 | 0.000 | 0.348 | 0.000 | 1.076 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 197 | 197 | 3517 | 164 | 0 | 1249 | 0 | 389 | 0 |
N.S. |
1 | 1.00 | 17.85 | 0.83 | 0.00 | 6.34 | 0.00 | 1.97 | 0.00 |
time (sec) |
N/A | 0.230 | 14.751 | 3.116 | 0.000 | 0.437 | 0.000 | 0.318 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 163 | 163 | 125 | 133 | 0 | 413 | 0 | 173 | 183 |
N.S. |
1 | 1.00 | 0.77 | 0.82 | 0.00 | 2.53 | 0.00 | 1.06 | 1.12 |
time (sec) |
N/A | 0.098 | 0.279 | 3.100 | 0.000 | 0.301 | 0.000 | 0.283 | 5.593 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 149 | 149 | 1365 | 152 | 0 | 996 | 0 | 336 | 0 |
N.S. |
1 | 1.00 | 9.16 | 1.02 | 0.00 | 6.68 | 0.00 | 2.26 | 0.00 |
time (sec) |
N/A | 0.125 | 5.975 | 3.110 | 0.000 | 0.358 | 0.000 | 0.310 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 99 | 99 | 96 | 109 | 0 | 333 | 0 | 122 | 117 |
N.S. |
1 | 1.00 | 0.97 | 1.10 | 0.00 | 3.36 | 0.00 | 1.23 | 1.18 |
time (sec) |
N/A | 0.055 | 0.220 | 3.056 | 0.000 | 0.282 | 0.000 | 0.283 | 5.515 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 131 | 131 | 148 | 114 | 0 | 903 | 0 | 315 | 0 |
N.S. |
1 | 1.00 | 1.13 | 0.87 | 0.00 | 6.89 | 0.00 | 2.40 | 0.00 |
time (sec) |
N/A | 0.063 | 0.484 | 3.047 | 0.000 | 0.347 | 0.000 | 0.307 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 129 | 129 | 122 | 140 | 0 | 883 | 0 | 154 | 488 |
N.S. |
1 | 1.00 | 0.95 | 1.09 | 0.00 | 6.84 | 0.00 | 1.19 | 3.78 |
time (sec) |
N/A | 0.106 | 0.317 | 3.054 | 0.000 | 0.438 | 0.000 | 0.295 | 7.187 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 128 | 128 | 122 | 97 | 0 | 351 | 0 | 412 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.76 | 0.00 | 2.74 | 0.00 | 3.22 | 0.00 |
time (sec) |
N/A | 0.089 | 0.414 | 3.050 | 0.000 | 0.279 | 0.000 | 0.841 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 170 | 170 | 154 | 165 | 0 | 1034 | 0 | 216 | 441 |
N.S. |
1 | 1.00 | 0.91 | 0.97 | 0.00 | 6.08 | 0.00 | 1.27 | 2.59 |
time (sec) |
N/A | 0.183 | 0.554 | 3.109 | 0.000 | 0.445 | 0.000 | 0.292 | 7.565 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 166 | 166 | 1668 | 132 | 0 | 443 | 0 | 442 | 0 |
N.S. |
1 | 1.00 | 10.05 | 0.80 | 0.00 | 2.67 | 0.00 | 2.66 | 0.00 |
time (sec) |
N/A | 0.166 | 7.264 | 3.108 | 0.000 | 0.318 | 0.000 | 1.064 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 258 | 258 | 219 | 219 | 0 | 1697 | 0 | 516 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.85 | 0.00 | 6.58 | 0.00 | 2.00 | 0.00 |
time (sec) |
N/A | 0.337 | 10.204 | 3.211 | 0.000 | 1.691 | 0.000 | 0.354 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 198 | 198 | 183 | 176 | 0 | 573 | 0 | 264 | 276 |
N.S. |
1 | 1.00 | 0.92 | 0.89 | 0.00 | 2.89 | 0.00 | 1.33 | 1.39 |
time (sec) |
N/A | 0.133 | 0.347 | 3.089 | 0.000 | 0.305 | 0.000 | 0.297 | 5.812 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 195 | 195 | 173 | 169 | 0 | 1379 | 0 | 446 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.87 | 0.00 | 7.07 | 0.00 | 2.29 | 0.00 |
time (sec) |
N/A | 0.173 | 10.146 | 3.252 | 0.000 | 0.862 | 0.000 | 0.334 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 126 | 126 | 128 | 139 | 0 | 453 | 0 | 197 | 172 |
N.S. |
1 | 1.00 | 1.02 | 1.10 | 0.00 | 3.60 | 0.00 | 1.56 | 1.37 |
time (sec) |
N/A | 0.075 | 0.318 | 3.094 | 0.000 | 0.300 | 0.000 | 0.295 | 5.658 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 174 | 174 | 191 | 156 | 0 | 1228 | 0 | 407 | 0 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 0.00 | 7.06 | 0.00 | 2.34 | 0.00 |
time (sec) |
N/A | 0.147 | 0.565 | 3.180 | 0.000 | 0.669 | 0.000 | 0.303 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 160 | 160 | 146 | 165 | 0 | 1132 | 0 | 206 | 1321 |
N.S. |
1 | 1.00 | 0.91 | 1.03 | 0.00 | 7.08 | 0.00 | 1.29 | 8.26 |
time (sec) |
N/A | 0.165 | 0.349 | 3.121 | 0.000 | 1.017 | 0.000 | 0.299 | 6.378 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 168 | 168 | 192 | 181 | 0 | 1184 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.14 | 1.08 | 0.00 | 7.05 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.131 | 0.529 | 3.247 | 0.000 | 0.528 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 180 | 180 | 160 | 187 | 0 | 1266 | 0 | 283 | 1152 |
N.S. |
1 | 1.00 | 0.89 | 1.04 | 0.00 | 7.03 | 0.00 | 1.57 | 6.40 |
time (sec) |
N/A | 0.191 | 0.476 | 3.233 | 0.000 | 1.057 | 0.000 | 0.304 | 6.750 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 176 | 176 | 157 | 155 | 0 | 483 | 0 | 496 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.88 | 0.00 | 2.74 | 0.00 | 2.82 | 0.00 |
time (sec) |
N/A | 0.183 | 0.616 | 3.337 | 0.000 | 0.345 | 0.000 | 1.098 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 132 | 132 | 148 | 115 | 0 | 1053 | 0 | 284 | 0 |
N.S. |
1 | 1.00 | 1.12 | 0.87 | 0.00 | 7.98 | 0.00 | 2.15 | 0.00 |
time (sec) |
N/A | 0.077 | 0.704 | 3.023 | 0.000 | 0.480 | 0.000 | 0.341 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 99 | 99 | 100 | 83 | 0 | 450 | 0 | 116 | 93 |
N.S. |
1 | 1.00 | 1.01 | 0.84 | 0.00 | 4.55 | 0.00 | 1.17 | 0.94 |
time (sec) |
N/A | 0.062 | 0.218 | 3.014 | 0.000 | 0.279 | 0.000 | 0.304 | 5.691 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 608 | 79 | 0 | 418 | 0 | 231 | 0 |
N.S. |
1 | 1.00 | 6.83 | 0.89 | 0.00 | 4.70 | 0.00 | 2.60 | 0.00 |
time (sec) |
N/A | 0.035 | 3.002 | 2.989 | 0.000 | 0.317 | 0.000 | 0.838 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 86 | 90 | 0 | 404 | 0 | 93 | 82 |
N.S. |
1 | 1.00 | 0.99 | 1.03 | 0.00 | 4.64 | 0.00 | 1.07 | 0.94 |
time (sec) |
N/A | 0.047 | 0.166 | 2.975 | 0.000 | 0.272 | 0.000 | 0.281 | 5.525 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 122 | 88 | 0 | 459 | 0 | 225 | 0 |
N.S. |
1 | 1.00 | 1.22 | 0.88 | 0.00 | 4.59 | 0.00 | 2.25 | 0.00 |
time (sec) |
N/A | 0.036 | 0.046 | 3.007 | 0.000 | 0.335 | 0.000 | 0.295 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 130 | 130 | 124 | 145 | 0 | 1037 | 0 | 138 | 3023 |
N.S. |
1 | 1.00 | 0.95 | 1.12 | 0.00 | 7.98 | 0.00 | 1.06 | 23.25 |
time (sec) |
N/A | 0.092 | 0.336 | 3.050 | 0.000 | 0.557 | 0.000 | 0.284 | 6.286 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 147 | 147 | 156 | 109 | 0 | 600 | 0 | 396 | 0 |
N.S. |
1 | 1.00 | 1.06 | 0.74 | 0.00 | 4.08 | 0.00 | 2.69 | 0.00 |
time (sec) |
N/A | 0.098 | 0.659 | 3.072 | 0.000 | 0.353 | 0.000 | 0.852 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 185 | 185 | 163 | 189 | 0 | 1407 | 0 | 257 | 3837 |
N.S. |
1 | 1.00 | 0.88 | 1.02 | 0.00 | 7.61 | 0.00 | 1.39 | 20.74 |
time (sec) |
N/A | 0.170 | 0.675 | 3.147 | 0.000 | 0.831 | 0.000 | 0.280 | 7.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 206 | 206 | 199 | 131 | 0 | 758 | 0 | 375 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.64 | 0.00 | 3.68 | 0.00 | 1.82 | 0.00 |
time (sec) |
N/A | 0.175 | 0.865 | 3.116 | 0.000 | 0.435 | 0.000 | 0.988 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 130 | 130 | 672 | 95 | 0 | 552 | 0 | 298 | 0 |
N.S. |
1 | 1.00 | 5.17 | 0.73 | 0.00 | 4.25 | 0.00 | 2.29 | 0.00 |
time (sec) |
N/A | 0.073 | 10.798 | 3.000 | 0.000 | 0.431 | 0.000 | 0.897 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 134 | 134 | 110 | 125 | 0 | 732 | 0 | 181 | 142 |
N.S. |
1 | 1.00 | 0.82 | 0.93 | 0.00 | 5.46 | 0.00 | 1.35 | 1.06 |
time (sec) |
N/A | 0.082 | 0.314 | 3.027 | 0.000 | 0.317 | 0.000 | 0.294 | 5.422 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 123 | 123 | 1437 | 97 | 0 | 744 | 0 | 299 | 0 |
N.S. |
1 | 1.00 | 11.68 | 0.79 | 0.00 | 6.05 | 0.00 | 2.43 | 0.00 |
time (sec) |
N/A | 0.065 | 9.768 | 3.036 | 0.000 | 0.477 | 0.000 | 0.884 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 102 | 88 | 0 | 537 | 0 | 153 | 130 |
N.S. |
1 | 1.00 | 0.90 | 0.78 | 0.00 | 4.75 | 0.00 | 1.35 | 1.15 |
time (sec) |
N/A | 0.064 | 0.328 | 3.032 | 0.000 | 0.312 | 0.000 | 0.292 | 5.298 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 142 | 142 | 154 | 109 | 0 | 854 | 0 | 318 | 0 |
N.S. |
1 | 1.00 | 1.08 | 0.77 | 0.00 | 6.01 | 0.00 | 2.24 | 0.00 |
time (sec) |
N/A | 0.077 | 0.541 | 3.024 | 0.000 | 0.515 | 0.000 | 0.861 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 170 | 170 | 157 | 199 | 0 | 1992 | 0 | 225 | 5227 |
N.S. |
1 | 1.00 | 0.92 | 1.17 | 0.00 | 11.72 | 0.00 | 1.32 | 30.75 |
time (sec) |
N/A | 0.153 | 0.697 | 3.088 | 0.000 | 1.724 | 0.000 | 0.292 | 7.466 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 205 | 205 | 216 | 141 | 0 | 1018 | 0 | 554 | 0 |
N.S. |
1 | 1.00 | 1.05 | 0.69 | 0.00 | 4.97 | 0.00 | 2.70 | 0.00 |
time (sec) |
N/A | 0.185 | 0.845 | 3.131 | 0.000 | 0.583 | 0.000 | 0.934 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 241 | 241 | 223 | 269 | 0 | 2554 | 0 | 367 | 4286 |
N.S. |
1 | 1.00 | 0.93 | 1.12 | 0.00 | 10.60 | 0.00 | 1.52 | 17.78 |
time (sec) |
N/A | 0.239 | 0.894 | 3.334 | 0.000 | 3.151 | 0.000 | 0.281 | 9.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 277 | 277 | 265 | 158 | 0 | 1252 | 0 | 486 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.57 | 0.00 | 4.52 | 0.00 | 1.75 | 0.00 |
time (sec) |
N/A | 0.276 | 1.330 | 3.213 | 0.000 | 0.795 | 0.000 | 1.061 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 174 | 174 | 133 | 146 | 0 | 1008 | 0 | 594 | 0 |
N.S. |
1 | 1.00 | 0.76 | 0.84 | 0.00 | 5.79 | 0.00 | 3.41 | 0.00 |
time (sec) |
N/A | 0.153 | 11.011 | 3.130 | 0.000 | 0.704 | 0.000 | 0.883 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 170 | 170 | 154 | 162 | 0 | 993 | 0 | 260 | 193 |
N.S. |
1 | 1.00 | 0.91 | 0.95 | 0.00 | 5.84 | 0.00 | 1.53 | 1.14 |
time (sec) |
N/A | 0.106 | 0.461 | 3.130 | 0.000 | 0.364 | 0.000 | 0.289 | 5.657 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 163 | 163 | 183 | 143 | 0 | 1292 | 0 | 595 | 0 |
N.S. |
1 | 1.00 | 1.12 | 0.88 | 0.00 | 7.93 | 0.00 | 3.65 | 0.00 |
time (sec) |
N/A | 0.112 | 0.851 | 3.206 | 0.000 | 1.128 | 0.000 | 0.939 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 140 | 140 | 137 | 134 | 0 | 895 | 0 | 226 | 171 |
N.S. |
1 | 1.00 | 0.98 | 0.96 | 0.00 | 6.39 | 0.00 | 1.61 | 1.22 |
time (sec) |
N/A | 0.077 | 0.316 | 3.096 | 0.000 | 0.455 | 0.000 | 0.283 | 5.729 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 201 | 201 | 214 | 158 | 0 | 1434 | 0 | 619 | 0 |
N.S. |
1 | 1.00 | 1.06 | 0.79 | 0.00 | 7.13 | 0.00 | 3.08 | 0.00 |
time (sec) |
N/A | 0.149 | 0.962 | 3.097 | 0.000 | 0.901 | 0.000 | 0.903 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 225 | 225 | 215 | 257 | 0 | 3403 | 0 | 298 | 8467 |
N.S. |
1 | 1.00 | 0.96 | 1.14 | 0.00 | 15.12 | 0.00 | 1.32 | 37.63 |
time (sec) |
N/A | 0.252 | 0.810 | 3.506 | 0.000 | 4.278 | 0.000 | 0.279 | 9.956 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 279 | 279 | 287 | 176 | 0 | 1662 | 0 | 938 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.63 | 0.00 | 5.96 | 0.00 | 3.36 | 0.00 |
time (sec) |
N/A | 0.325 | 1.089 | 3.351 | 0.000 | 1.077 | 0.000 | 1.010 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 304 | 304 | 294 | 288 | 0 | 4115 | 0 | 505 | 5800 |
N.S. |
1 | 1.00 | 0.97 | 0.95 | 0.00 | 13.54 | 0.00 | 1.66 | 19.08 |
time (sec) |
N/A | 0.350 | 1.265 | 3.389 | 0.000 | 7.957 | 0.000 | 0.280 | 11.321 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 362 | 362 | 348 | 367 | 0 | 1890 | 0 | 789 | 0 |
N.S. |
1 | 1.00 | 0.96 | 1.01 | 0.00 | 5.22 | 0.00 | 2.18 | 0.00 |
time (sec) |
N/A | 0.411 | 1.597 | 3.306 | 0.000 | 1.549 | 0.000 | 1.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 212 | 212 | 110 | 214 | 0 | 101 | 97 | 0 | 0 |
N.S. |
1 | 1.00 | 0.52 | 1.01 | 0.00 | 0.48 | 0.46 | 0.00 | 0.00 |
time (sec) |
N/A | 0.118 | 10.115 | 3.188 | 0.000 | 0.083 | 5.562 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 337 | 337 | 93 | 238 | 0 | 80 | 97 | 0 | 0 |
N.S. |
1 | 1.00 | 0.28 | 0.71 | 0.00 | 0.24 | 0.29 | 0.00 | 0.00 |
time (sec) |
N/A | 0.187 | 10.075 | 3.073 | 0.000 | 0.085 | 2.375 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 176 | 176 | 93 | 184 | 0 | 73 | 97 | 0 | 0 |
N.S. |
1 | 1.00 | 0.53 | 1.05 | 0.00 | 0.41 | 0.55 | 0.00 | 0.00 |
time (sec) |
N/A | 0.083 | 10.044 | 3.013 | 0.000 | 0.081 | 2.477 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 333 | 333 | 96 | 228 | 0 | 72 | 100 | 0 | 0 |
N.S. |
1 | 1.00 | 0.29 | 0.68 | 0.00 | 0.22 | 0.30 | 0.00 | 0.00 |
time (sec) |
N/A | 0.177 | 8.296 | 3.063 | 0.000 | 0.092 | 3.328 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 172 | 172 | 82 | 179 | 0 | 64 | 100 | 0 | 0 |
N.S. |
1 | 1.00 | 0.48 | 1.04 | 0.00 | 0.37 | 0.58 | 0.00 | 0.00 |
time (sec) |
N/A | 0.083 | 8.928 | 3.032 | 0.000 | 0.083 | 4.626 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 338 | 338 | 95 | 242 | 0 | 79 | 107 | 0 | 0 |
N.S. |
1 | 1.00 | 0.28 | 0.72 | 0.00 | 0.23 | 0.32 | 0.00 | 0.00 |
time (sec) |
N/A | 0.187 | 10.042 | 3.069 | 0.000 | 0.096 | 12.845 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 152 | 152 | 79 | 177 | 0 | 67 | 97 | 0 | 0 |
N.S. |
1 | 1.00 | 0.52 | 1.16 | 0.00 | 0.44 | 0.64 | 0.00 | 0.00 |
time (sec) |
N/A | 0.064 | 10.063 | 3.060 | 0.000 | 0.083 | 10.596 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 331 | 331 | 80 | 250 | 0 | 99 | 100 | 0 | 0 |
N.S. |
1 | 1.00 | 0.24 | 0.76 | 0.00 | 0.30 | 0.30 | 0.00 | 0.00 |
time (sec) |
N/A | 0.170 | 10.066 | 3.095 | 0.000 | 0.083 | 28.951 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 187 | 187 | 80 | 201 | 0 | 92 | 100 | 0 | 0 |
N.S. |
1 | 1.00 | 0.43 | 1.07 | 0.00 | 0.49 | 0.53 | 0.00 | 0.00 |
time (sec) |
N/A | 0.076 | 10.074 | 3.103 | 0.000 | 0.077 | 77.502 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 252 | 252 | 114 | 238 | 0 | 124 | 199 | 0 | 0 |
N.S. |
1 | 1.00 | 0.45 | 0.94 | 0.00 | 0.49 | 0.79 | 0.00 | 0.00 |
time (sec) |
N/A | 0.117 | 10.132 | 3.163 | 0.000 | 0.087 | 14.241 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 377 | 377 | 97 | 262 | 0 | 105 | 199 | 0 | 0 |
N.S. |
1 | 1.00 | 0.26 | 0.69 | 0.00 | 0.28 | 0.53 | 0.00 | 0.00 |
time (sec) |
N/A | 0.208 | 10.080 | 3.062 | 0.000 | 0.092 | 5.744 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 214 | 214 | 96 | 208 | 0 | 96 | 199 | 0 | 0 |
N.S. |
1 | 1.00 | 0.45 | 0.97 | 0.00 | 0.45 | 0.93 | 0.00 | 0.00 |
time (sec) |
N/A | 0.093 | 10.054 | 3.042 | 0.000 | 0.089 | 5.424 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 367 | 367 | 84 | 245 | 0 | 95 | 202 | 0 | 0 |
N.S. |
1 | 1.00 | 0.23 | 0.67 | 0.00 | 0.26 | 0.55 | 0.00 | 0.00 |
time (sec) |
N/A | 0.202 | 10.052 | 3.080 | 0.000 | 0.087 | 8.323 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 210 | 210 | 85 | 199 | 0 | 89 | 202 | 0 | 0 |
N.S. |
1 | 1.00 | 0.40 | 0.95 | 0.00 | 0.42 | 0.96 | 0.00 | 0.00 |
time (sec) |
N/A | 0.106 | 10.051 | 3.034 | 0.000 | 0.088 | 9.854 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 365 | 365 | 84 | 242 | 0 | 84 | 212 | 0 | 0 |
N.S. |
1 | 1.00 | 0.23 | 0.66 | 0.00 | 0.23 | 0.58 | 0.00 | 0.00 |
time (sec) |
N/A | 0.208 | 10.046 | 3.074 | 0.000 | 0.089 | 23.278 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 338 | 338 | 96 | 242 | 0 | 92 | 94 | 0 | 0 |
N.S. |
1 | 1.00 | 0.28 | 0.72 | 0.00 | 0.27 | 0.28 | 0.00 | 0.00 |
time (sec) |
N/A | 0.191 | 10.091 | 3.049 | 0.000 | 0.086 | 13.208 | 0.000 | 0.000 |