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 | C | B | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 60 | 242 | 0 | 103 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.83 | 3.36 | 0.00 | 1.43 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.326 | 0.058 | 0.592 | 0.000 | 0.099 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 104 | 59 | 365 | 0 | 120 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.59 | 3.65 | 0.00 | 1.20 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.424 | 0.052 | 1.027 | 0.000 | 0.102 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 108 | 59 | 396 | 0 | 114 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 0.59 | 3.96 | 0.00 | 1.14 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.425 | 0.047 | 1.371 | 0.000 | 0.100 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 44 | 57 | 37 | 36 | 34 | 73 | 53 | 0 |
N.S. |
1 | 0.98 | 1.27 | 0.82 | 0.80 | 0.76 | 1.62 | 1.18 | 0.00 |
time (sec) |
N/A | 0.218 | 0.208 | 0.066 | 0.193 | 0.316 | 0.862 | 0.332 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 42 | 57 | 37 | 36 | 28 | 71 | 46 | 0 |
N.S. |
1 | 0.98 | 1.33 | 0.86 | 0.84 | 0.65 | 1.65 | 1.07 | 0.00 |
time (sec) |
N/A | 0.221 | 0.126 | 0.072 | 0.185 | 0.279 | 0.781 | 0.341 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 42 | 46 | 36 | 35 | 36 | 70 | 0 | 0 |
N.S. |
1 | 0.98 | 1.07 | 0.84 | 0.81 | 0.84 | 1.63 | 0.00 | 0.00 |
time (sec) |
N/A | 0.226 | 0.053 | 0.051 | 0.187 | 0.277 | 0.773 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 42 | 48 | 35 | 34 | 38 | 71 | 0 | 66 |
N.S. |
1 | 0.98 | 1.12 | 0.81 | 0.79 | 0.88 | 1.65 | 0.00 | 1.53 |
time (sec) |
N/A | 0.234 | 0.069 | 0.055 | 0.189 | 0.287 | 3.543 | 0.000 | 0.810 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 42 | 70 | 37 | 37 | 38 | 71 | 0 | 93 |
N.S. |
1 | 0.98 | 1.63 | 0.86 | 0.86 | 0.88 | 1.65 | 0.00 | 2.16 |
time (sec) |
N/A | 0.227 | 0.187 | 0.052 | 0.190 | 0.264 | 30.187 | 0.000 | 3.460 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 44 | 70 | 37 | 37 | 38 | 0 | 0 | 93 |
N.S. |
1 | 0.98 | 1.56 | 0.82 | 0.82 | 0.84 | 0.00 | 0.00 | 2.07 |
time (sec) |
N/A | 0.229 | 0.202 | 0.048 | 0.184 | 0.269 | 0.000 | 0.000 | 3.662 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 44 | 94 | 37 | 37 | 38 | 0 | 0 | 279 |
N.S. |
1 | 0.98 | 2.09 | 0.82 | 0.82 | 0.84 | 0.00 | 0.00 | 6.20 |
time (sec) |
N/A | 0.231 | 0.374 | 0.052 | 0.200 | 0.297 | 0.000 | 0.000 | 5.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 156 | 172 | 57 | 275 | 0 | 133 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 0.37 | 1.76 | 0.00 | 0.85 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.704 | 0.101 | 13.672 | 0.000 | 0.132 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 156 | 172 | 57 | 262 | 0 | 121 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 0.37 | 1.68 | 0.00 | 0.78 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.702 | 0.064 | 11.613 | 0.000 | 0.113 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 128 | 138 | 65 | 249 | 0 | 120 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 0.51 | 1.95 | 0.00 | 0.94 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.597 | 0.054 | 11.091 | 0.000 | 0.121 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 128 | 138 | 65 | 255 | 0 | 102 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 0.51 | 1.99 | 0.00 | 0.80 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.571 | 0.073 | 1.274 | 0.000 | 0.111 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 99 | 104 | 58 | 221 | 0 | 100 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.59 | 2.23 | 0.00 | 1.01 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.440 | 0.045 | 0.952 | 0.000 | 0.100 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 99 | 104 | 58 | 208 | 0 | 88 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.59 | 2.10 | 0.00 | 0.89 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.454 | 0.051 | 0.387 | 0.000 | 0.096 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 103 | 60 | 213 | 0 | 115 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.60 | 2.13 | 0.00 | 1.15 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.454 | 0.046 | 0.480 | 0.000 | 0.104 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 105 | 60 | 286 | 0 | 113 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.59 | 2.80 | 0.00 | 1.11 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.454 | 0.050 | 0.469 | 0.000 | 0.105 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 106 | 65 | 366 | 0 | 120 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.64 | 3.59 | 0.00 | 1.18 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.487 | 0.051 | 0.552 | 0.000 | 0.130 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 110 | 65 | 398 | 0 | 114 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 0.64 | 3.90 | 0.00 | 1.12 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.478 | 0.047 | 0.534 | 0.000 | 0.101 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 52 | 48 | 111 | 37 | 36 | 44 | 0 | 0 | 35 |
N.S. |
1 | 0.92 | 2.13 | 0.71 | 0.69 | 0.85 | 0.00 | 0.00 | 0.67 |
time (sec) |
N/A | 0.203 | 0.186 | 0.092 | 0.203 | 0.305 | 0.000 | 0.000 | 0.374 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 94 | 83 | 331 | 98 | 313 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 0.83 | 3.31 | 0.98 | 3.13 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.263 | 0.380 | 0.404 | 0.286 | 0.389 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 99 | 92 | 80 | 292 | 98 | 299 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.81 | 2.95 | 0.99 | 3.02 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.274 | 0.268 | 0.368 | 0.275 | 0.402 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 78 | 73 | 68 | 253 | 83 | 281 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 0.87 | 3.24 | 1.06 | 3.60 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.263 | 0.220 | 0.362 | 0.267 | 0.416 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 71 | 65 | 212 | 83 | 259 | 0 | 0 | 0 |
N.S. |
1 | 0.92 | 0.84 | 2.75 | 1.08 | 3.36 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.256 | 0.160 | 0.108 | 0.271 | 0.371 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 58 | 51 | 51 | 182 | 67 | 238 | 0 | 48 | 0 |
N.S. |
1 | 0.88 | 0.88 | 3.14 | 1.16 | 4.10 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.238 | 0.142 | 0.095 | 0.279 | 0.335 | 0.000 | 0.339 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 51 | 50 | 181 | 68 | 246 | 0 | 52 | 0 |
N.S. |
1 | 0.86 | 0.85 | 3.07 | 1.15 | 4.17 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.246 | 0.131 | 0.101 | 0.270 | 0.344 | 0.000 | 0.348 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 78 | 74 | 66 | 441 | 79 | 309 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.85 | 5.65 | 1.01 | 3.96 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.259 | 0.168 | 0.102 | 0.271 | 0.315 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 76 | 70 | 649 | 80 | 318 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 0.86 | 8.01 | 0.99 | 3.93 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.255 | 0.209 | 0.129 | 0.288 | 0.334 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 98 | 81 | 862 | 100 | 342 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.81 | 8.62 | 1.00 | 3.42 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.276 | 0.287 | 0.135 | 0.291 | 0.352 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 103 | 100 | 87 | 1057 | 102 | 342 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.84 | 10.26 | 0.99 | 3.32 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.281 | 0.335 | 0.161 | 0.287 | 0.343 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 136 | 89 | 242 | 0 | 122 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 0.72 | 1.95 | 0.00 | 0.98 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.577 | 0.723 | 3.504 | 0.000 | 0.115 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 96 | 102 | 74 | 229 | 0 | 121 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.77 | 2.39 | 0.00 | 1.26 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.458 | 0.485 | 2.852 | 0.000 | 0.112 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 96 | 102 | 73 | 216 | 0 | 109 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.76 | 2.25 | 0.00 | 1.14 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.442 | 0.384 | 2.441 | 0.000 | 0.104 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 58 | 203 | 0 | 105 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.88 | 3.08 | 0.00 | 1.59 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.333 | 0.307 | 2.115 | 0.000 | 0.102 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 56 | 190 | 0 | 91 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.85 | 2.88 | 0.00 | 1.38 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.343 | 0.237 | 0.405 | 0.000 | 0.109 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 56 | 203 | 0 | 102 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.86 | 3.12 | 0.00 | 1.57 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.321 | 0.228 | 0.429 | 0.000 | 0.113 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-1) | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 47 | 188 | 0 | 93 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.73 | 2.94 | 0.00 | 1.45 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.330 | 0.230 | 0.394 | 0.000 | 0.097 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 94 | 99 | 65 | 209 | 0 | 131 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.69 | 2.22 | 0.00 | 1.39 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.449 | 0.305 | 0.500 | 0.000 | 0.101 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 103 | 62 | 190 | 0 | 129 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.63 | 1.94 | 0.00 | 1.32 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.453 | 0.309 | 0.701 | 0.000 | 0.097 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 126 | 135 | 82 | 408 | 0 | 145 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.65 | 3.24 | 0.00 | 1.15 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.563 | 0.342 | 1.064 | 0.000 | 0.100 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 135 | 134 | 137 | 407 | 133 | 419 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 1.01 | 3.01 | 0.99 | 3.10 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.297 | 1.868 | 6.099 | 0.276 | 0.465 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | A | B | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 115 | 78 | 371 | 118 | 405 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.69 | 3.28 | 1.04 | 3.58 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.277 | 0.769 | 6.062 | 0.279 | 0.419 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 118 | 310 | 118 | 393 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.04 | 2.74 | 1.04 | 3.48 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.289 | 1.039 | 6.025 | 0.279 | 0.419 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | A | B | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 93 | 65 | 286 | 103 | 380 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.71 | 3.14 | 1.13 | 4.18 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.274 | 0.391 | 5.921 | 0.280 | 0.383 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | A | B | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 93 | 76 | 280 | 103 | 347 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.84 | 3.08 | 1.13 | 3.81 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.278 | 0.283 | 0.085 | 0.270 | 0.334 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | A | B | F | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 93 | 99 | 62 | 275 | 102 | 340 | 0 | 95 | 0 |
N.S. |
1 | 1.06 | 0.67 | 2.96 | 1.10 | 3.66 | 0.00 | 1.02 | 0.00 |
time (sec) |
N/A | 0.272 | 0.338 | 0.085 | 0.275 | 0.356 | 0.000 | 0.333 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | A | B | F | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 93 | 99 | 69 | 283 | 103 | 334 | 0 | 91 | 0 |
N.S. |
1 | 1.06 | 0.74 | 3.04 | 1.11 | 3.59 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 0.286 | 0.327 | 0.091 | 0.278 | 0.360 | 0.000 | 0.377 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | A | B | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 122 | 91 | 689 | 117 | 406 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.79 | 5.99 | 1.02 | 3.53 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.297 | 0.350 | 0.115 | 0.284 | 0.341 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | A | B | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 124 | 92 | 885 | 117 | 418 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 0.80 | 7.70 | 1.02 | 3.63 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.294 | 0.448 | 0.134 | 0.275 | 0.360 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | A | A | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 146 | 102 | 1140 | 134 | 438 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.74 | 8.32 | 0.98 | 3.20 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.305 | 0.534 | 0.181 | 0.286 | 0.365 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 19 | 18 | 21 | 37 | 21 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.82 | 0.95 | 1.68 | 0.95 | 0.82 |
time (sec) |
N/A | 0.190 | 0.014 | 0.031 | 0.202 | 0.297 | 1.566 | 0.324 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 18 | 14 | 13 | 14 | 170 | 13 | 25 |
N.S. |
1 | 1.00 | 0.86 | 0.67 | 0.62 | 0.67 | 8.10 | 0.62 | 1.19 |
time (sec) |
N/A | 0.196 | 0.012 | 0.071 | 0.196 | 0.328 | 3.658 | 0.312 | 0.217 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 18 | 14 | 13 | 20 | 24 | 13 | 25 |
N.S. |
1 | 1.00 | 0.86 | 0.67 | 0.62 | 0.95 | 1.14 | 0.62 | 1.19 |
time (sec) |
N/A | 0.206 | 0.011 | 0.047 | 0.205 | 0.310 | 3.275 | 0.318 | 0.191 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 18 | 14 | 13 | 20 | 24 | 13 | 25 |
N.S. |
1 | 1.00 | 0.86 | 0.67 | 0.62 | 0.95 | 1.14 | 0.62 | 1.19 |
time (sec) |
N/A | 0.194 | 0.010 | 5.122 | 0.204 | 0.309 | 32.682 | 0.326 | 0.171 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 16 | 14 | 13 | 12 | 323 | 13 | 25 |
N.S. |
1 | 1.00 | 0.84 | 0.74 | 0.68 | 0.63 | 17.00 | 0.68 | 1.32 |
time (sec) |
N/A | 0.193 | 0.008 | 0.033 | 0.196 | 0.288 | 4.339 | 0.318 | 0.188 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 132 | 138 | 70 | 423 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.53 | 3.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.576 | 0.081 | 0.906 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 95 | 95 | 70 | 409 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.74 | 4.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.410 | 0.063 | 0.342 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 67 | 393 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.26 | 7.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.274 | 0.043 | 0.258 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 70 | 357 | 0 | 172 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.75 | 3.84 | 0.00 | 1.85 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.411 | 0.076 | 0.500 | 0.000 | 0.135 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 134 | 138 | 70 | 412 | 0 | 193 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.52 | 3.07 | 0.00 | 1.44 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.562 | 0.097 | 0.309 | 0.000 | 0.131 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 320 | 325 | 70 | 437 | 0 | 1033 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.22 | 1.37 | 0.00 | 3.23 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.609 | 0.084 | 2.829 | 0.000 | 0.475 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 280 | 285 | 67 | 362 | 0 | 933 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.24 | 1.29 | 0.00 | 3.33 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.459 | 0.042 | 0.394 | 0.000 | 0.457 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 37 | 35 | 0 | 42 | 0 | 0 | 50 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.00 | 1.14 | 0.00 | 0.00 | 1.35 |
time (sec) |
N/A | 0.230 | 0.060 | 0.226 | 0.000 | 0.309 | 0.000 | 0.000 | 0.767 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 57 | 54 | 0 | 54 | 0 | 0 | 95 |
N.S. |
1 | 1.00 | 0.76 | 0.72 | 0.00 | 0.72 | 0.00 | 0.00 | 1.27 |
time (sec) |
N/A | 0.352 | 0.168 | 0.229 | 0.000 | 0.329 | 0.000 | 0.000 | 1.916 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 120 | 67 | 65 | 0 | 64 | 0 | 0 | 216 |
N.S. |
1 | 1.07 | 0.60 | 0.58 | 0.00 | 0.57 | 0.00 | 0.00 | 1.93 |
time (sec) |
N/A | 0.486 | 0.169 | 0.340 | 0.000 | 0.379 | 0.000 | 0.000 | 6.247 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 131 | 135 | 71 | 1744 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.54 | 13.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.578 | 0.089 | 1.474 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 67 | 211 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.72 | 2.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.389 | 0.058 | 1.343 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 67 | 213 | 0 | 108 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.68 | 2.17 | 0.00 | 1.10 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.409 | 0.113 | 0.193 | 0.000 | 0.113 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 133 | 143 | 70 | 227 | 0 | 121 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 0.53 | 1.71 | 0.00 | 0.91 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.553 | 0.101 | 0.237 | 0.000 | 0.110 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 320 | 325 | 67 | 433 | 0 | 1015 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.21 | 1.35 | 0.00 | 3.17 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.586 | 0.049 | 0.197 | 0.000 | 0.453 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 313 | 323 | 67 | 687 | 0 | 1092 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.21 | 2.19 | 0.00 | 3.49 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.593 | 0.112 | 0.250 | 0.000 | 0.520 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 40 | 38 | 0 | 50 | 0 | 0 | 64 |
N.S. |
1 | 1.00 | 1.08 | 1.03 | 0.00 | 1.35 | 0.00 | 0.00 | 1.73 |
time (sec) |
N/A | 0.212 | 0.077 | 0.202 | 0.000 | 0.328 | 0.000 | 0.000 | 1.332 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 106 | 121 | 57 | 59 | 0 | 61 | 0 | 0 | 207 |
N.S. |
1 | 1.14 | 0.54 | 0.56 | 0.00 | 0.58 | 0.00 | 0.00 | 1.95 |
time (sec) |
N/A | 0.490 | 0.210 | 0.155 | 0.000 | 0.376 | 0.000 | 0.000 | 6.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 141 | 166 | 67 | 68 | 0 | 73 | 0 | 0 | 193 |
N.S. |
1 | 1.18 | 0.48 | 0.48 | 0.00 | 0.52 | 0.00 | 0.00 | 1.37 |
time (sec) |
N/A | 0.626 | 0.217 | 0.310 | 0.000 | 0.446 | 0.000 | 0.000 | 6.656 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 166 | 181 | 72 | 439 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 0.43 | 2.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.742 | 0.122 | 1.700 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 131 | 138 | 70 | 426 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.53 | 3.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.556 | 0.123 | 1.421 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 95 | 95 | 67 | 410 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.71 | 4.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.396 | 0.065 | 0.263 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 67 | 398 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.71 | 4.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.402 | 0.084 | 0.217 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 133 | 139 | 70 | 416 | 0 | 212 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.53 | 3.13 | 0.00 | 1.59 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.558 | 0.124 | 0.227 | 0.000 | 0.140 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 168 | 184 | 72 | 442 | 0 | 224 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 0.43 | 2.63 | 0.00 | 1.33 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.724 | 0.119 | 0.238 | 0.000 | 0.119 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 320 | 325 | 67 | 447 | 0 | 1028 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.21 | 1.40 | 0.00 | 3.21 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.558 | 0.081 | 0.421 | 0.000 | 0.527 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 315 | 325 | 67 | 492 | 0 | 1164 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.21 | 1.56 | 0.00 | 3.70 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.581 | 0.084 | 0.260 | 0.000 | 0.498 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 40 | 40 | 0 | 60 | 0 | 0 | 89 |
N.S. |
1 | 1.00 | 1.08 | 1.08 | 0.00 | 1.62 | 0.00 | 0.00 | 2.41 |
time (sec) |
N/A | 0.219 | 0.101 | 0.193 | 0.000 | 0.365 | 0.000 | 0.000 | 1.769 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 106 | 121 | 57 | 61 | 0 | 74 | 0 | 0 | 176 |
N.S. |
1 | 1.14 | 0.54 | 0.58 | 0.00 | 0.70 | 0.00 | 0.00 | 1.66 |
time (sec) |
N/A | 0.462 | 0.220 | 0.145 | 0.000 | 0.429 | 0.000 | 0.000 | 6.541 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 141 | 166 | 67 | 70 | 0 | 87 | 0 | 0 | 207 |
N.S. |
1 | 1.18 | 0.48 | 0.50 | 0.00 | 0.62 | 0.00 | 0.00 | 1.47 |
time (sec) |
N/A | 0.625 | 0.318 | 0.309 | 0.000 | 0.594 | 0.000 | 0.000 | 6.508 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 226 | 230 | 57 | 892 | 0 | 766 | 0 | 0 | 44 |
N.S. |
1 | 1.02 | 0.25 | 3.95 | 0.00 | 3.39 | 0.00 | 0.00 | 0.19 |
time (sec) |
N/A | 0.548 | 0.037 | 2.293 | 0.000 | 0.476 | 0.000 | 0.000 | 1.949 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 11 | 0 | 16 | 0 | 0 | 53 |
N.S. |
1 | 1.00 | 1.00 | 0.69 | 0.00 | 1.00 | 0.00 | 0.00 | 3.31 |
time (sec) |
N/A | 0.172 | 0.014 | 0.408 | 0.000 | 0.311 | 0.000 | 0.000 | 0.652 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 122 | 134 | 38 | 195 | 0 | 305 | 0 | 0 | 25 |
N.S. |
1 | 1.10 | 0.31 | 1.60 | 0.00 | 2.50 | 0.00 | 0.00 | 0.20 |
time (sec) |
N/A | 0.327 | 0.012 | 2.773 | 0.000 | 0.422 | 0.000 | 0.000 | 0.460 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 143 | 153 | 38 | 388 | 0 | 315 | 0 | 0 | 25 |
N.S. |
1 | 1.07 | 0.27 | 2.71 | 0.00 | 2.20 | 0.00 | 0.00 | 0.17 |
time (sec) |
N/A | 0.392 | 0.010 | 0.292 | 0.000 | 0.377 | 0.000 | 0.000 | 0.552 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 132 | 135 | 70 | 1727 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.53 | 13.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.558 | 0.083 | 0.511 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 68 | 203 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.74 | 2.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.391 | 0.079 | 0.259 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 65 | 113 | 0 | 62 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.23 | 2.13 | 0.00 | 1.17 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.258 | 0.043 | 0.220 | 0.000 | 0.110 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 65 | 207 | 0 | 108 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.67 | 2.13 | 0.00 | 1.11 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.406 | 0.071 | 0.235 | 0.000 | 0.109 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 134 | 142 | 70 | 226 | 0 | 122 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.52 | 1.69 | 0.00 | 0.91 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.533 | 0.092 | 0.276 | 0.000 | 0.114 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 280 | 285 | 65 | 362 | 0 | 911 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.23 | 1.29 | 0.00 | 3.25 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.439 | 0.042 | 0.885 | 0.000 | 0.436 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 36 | 35 | 0 | 39 | 0 | 0 | 31 |
N.S. |
1 | 1.00 | 1.03 | 1.00 | 0.00 | 1.11 | 0.00 | 0.00 | 0.89 |
time (sec) |
N/A | 0.208 | 0.044 | 0.214 | 0.000 | 0.310 | 0.000 | 0.000 | 0.605 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 52 | 51 | 0 | 51 | 0 | 0 | 77 |
N.S. |
1 | 1.00 | 0.69 | 0.68 | 0.00 | 0.68 | 0.00 | 0.00 | 1.03 |
time (sec) |
N/A | 0.326 | 0.117 | 0.174 | 0.000 | 0.338 | 0.000 | 0.000 | 1.332 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 120 | 67 | 65 | 0 | 61 | 0 | 0 | 123 |
N.S. |
1 | 1.07 | 0.60 | 0.58 | 0.00 | 0.54 | 0.00 | 0.00 | 1.10 |
time (sec) |
N/A | 0.448 | 0.171 | 0.188 | 0.000 | 0.339 | 0.000 | 0.000 | 3.676 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 174 | 177 | 55 | 343 | 0 | 651 | 0 | 0 | 44 |
N.S. |
1 | 1.02 | 0.32 | 1.97 | 0.00 | 3.74 | 0.00 | 0.00 | 0.25 |
time (sec) |
N/A | 0.323 | 0.021 | 0.317 | 0.000 | 0.406 | 0.000 | 0.000 | 1.396 |