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 | C | B | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 126 | 134 | 40 | 320 | 0 | 188 | 0 | 0 | 161 | 0 |
| N.S. |
1 | 1.06 | 0.32 | 2.54 | 0.00 | 1.49 | 0.00 | 0.00 | 1.28 | 0.00 |
| time (sec) |
N/A | 0.301 | 10.022 | 7.281 | 0.000 | 0.087 | 0.000 | 0.000 | 0.359 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 172 | 188 | 40 | 457 | 0 | 275 | 0 | 0 | 205 | 0 |
| N.S. |
1 | 1.09 | 0.23 | 2.66 | 0.00 | 1.60 | 0.00 | 0.00 | 1.19 | 0.00 |
| time (sec) |
N/A | 0.368 | 10.023 | 9.431 | 0.000 | 0.094 | 0.000 | 0.000 | 0.429 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 157 | 161 | 86 | 245 | 0 | 129 | 0 | 0 | 462 | 0 |
| N.S. |
1 | 1.03 | 0.55 | 1.56 | 0.00 | 0.82 | 0.00 | 0.00 | 2.94 | 0.00 |
| time (sec) |
N/A | 0.385 | 10.066 | 3.582 | 0.000 | 0.092 | 0.000 | 0.000 | 0.323 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 111 | 109 | 54 | 183 | 0 | 91 | 0 | 0 | 322 | 0 |
| N.S. |
1 | 0.98 | 0.49 | 1.65 | 0.00 | 0.82 | 0.00 | 0.00 | 2.90 | 0.00 |
| time (sec) |
N/A | 0.297 | 10.032 | 2.497 | 0.000 | 0.087 | 0.000 | 0.000 | 0.278 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 63 | 64 | 40 | 118 | 0 | 36 | 0 | 0 | 53 | 0 |
| N.S. |
1 | 1.02 | 0.63 | 1.87 | 0.00 | 0.57 | 0.00 | 0.00 | 0.84 | 0.00 |
| time (sec) |
N/A | 0.231 | 10.025 | 1.948 | 0.000 | 0.077 | 0.000 | 0.000 | 0.258 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 109 | 38 | 143 | 0 | 93 | 0 | 0 | 95 | 0 |
| N.S. |
1 | 1.02 | 0.36 | 1.34 | 0.00 | 0.87 | 0.00 | 0.00 | 0.89 | 0.00 |
| time (sec) |
N/A | 0.296 | 10.016 | 2.929 | 0.000 | 0.083 | 0.000 | 0.000 | 0.323 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 159 | 163 | 40 | 263 | 0 | 168 | 0 | 0 | 1204 | 0 |
| N.S. |
1 | 1.03 | 0.25 | 1.65 | 0.00 | 1.06 | 0.00 | 0.00 | 7.57 | 0.00 |
| time (sec) |
N/A | 0.373 | 10.025 | 4.832 | 0.000 | 0.108 | 0.000 | 0.000 | 0.504 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 324 | 424 | 104 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
| N.S. |
1 | 1.31 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
| time (sec) |
N/A | 0.551 | 10.104 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.032 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | B | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 44 | 44 | 50 | 44 | 0 | 194 | 0 | 0 | 26 | 0 |
| N.S. |
1 | 1.00 | 1.14 | 1.00 | 0.00 | 4.41 | 0.00 | 0.00 | 0.59 | 0.00 |
| time (sec) |
N/A | 0.167 | 5.020 | 1.035 | 0.000 | 0.141 | 0.000 | 0.000 | 200.036 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | B | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 89 | 89 | 74 | 76 | 0 | 409 | 0 | 0 | 26 | 0 |
| N.S. |
1 | 1.00 | 0.83 | 0.85 | 0.00 | 4.60 | 0.00 | 0.00 | 0.29 | 0.00 |
| time (sec) |
N/A | 0.222 | 4.998 | 1.005 | 0.000 | 0.200 | 0.000 | 0.000 | 200.032 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 133 | 151 | 122 | 139 | 783 | 687 | 0 | 0 | 26 | 0 |
| N.S. |
1 | 1.14 | 0.92 | 1.05 | 5.89 | 5.17 | 0.00 | 0.00 | 0.20 | 0.00 |
| time (sec) |
N/A | 0.279 | 5.105 | 1.054 | 0.262 | 0.315 | 0.000 | 0.000 | 200.040 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 661 | 569 | 104 | 0 | 0 | 0 | 0 | 0 | 84 | 0 |
| N.S. |
1 | 0.86 | 0.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
| time (sec) |
N/A | 0.521 | 10.058 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 31.564 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 651 | 563 | 104 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
| N.S. |
1 | 0.86 | 0.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
| time (sec) |
N/A | 0.465 | 10.054 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.034 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 643 | 557 | 112 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
| N.S. |
1 | 0.87 | 0.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
| time (sec) |
N/A | 0.450 | 10.078 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.051 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 700 | 640 | 112 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
| N.S. |
1 | 0.91 | 0.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
| time (sec) |
N/A | 0.516 | 5.126 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.053 | 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 | 100 | 141 | 104 | 0 | 0 | 0 | 0 | 0 | 135 | 0 |
| N.S. |
1 | 1.41 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.35 | 0.00 |
| time (sec) |
N/A | 0.251 | 10.051 | 0.000 | 0.000 | 0.000 | 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 | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 100 | 141 | 104 | 0 | 0 | 0 | 0 | 0 | 249 | 0 |
| N.S. |
1 | 1.41 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.49 | 0.00 |
| time (sec) |
N/A | 0.247 | 10.066 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.286 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 100 | 141 | 112 | 0 | 0 | 0 | 0 | 0 | 363 | 0 |
| N.S. |
1 | 1.41 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.63 | 0.00 |
| time (sec) |
N/A | 0.243 | 10.080 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.286 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 141 | 141 | 103 | 626 | 1299 | 691 | 9491 | 1506 | 799 | 655 |
| N.S. |
1 | 1.00 | 0.73 | 4.44 | 9.21 | 4.90 | 67.31 | 10.68 | 5.67 | 4.65 |
| time (sec) |
N/A | 0.311 | 0.247 | 0.991 | 0.092 | 0.103 | 1.904 | 0.375 | 0.214 | 6.041 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 103 | 77 | 255 | 539 | 307 | 3196 | 651 | 331 | 307 |
| N.S. |
1 | 1.00 | 0.75 | 2.48 | 5.23 | 2.98 | 31.03 | 6.32 | 3.21 | 2.98 |
| time (sec) |
N/A | 0.258 | 0.132 | 0.935 | 0.083 | 0.097 | 0.866 | 0.359 | 0.206 | 5.894 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 65 | 65 | 64 | 76 | 167 | 106 | 707 | 209 | 102 | 120 |
| N.S. |
1 | 1.00 | 0.98 | 1.17 | 2.57 | 1.63 | 10.88 | 3.22 | 1.57 | 1.85 |
| time (sec) |
N/A | 0.200 | 0.086 | 0.545 | 0.049 | 0.092 | 0.418 | 0.379 | 0.197 | 5.813 |
| 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 | 74 | 68 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
| N.S. |
1 | 1.09 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
| time (sec) |
N/A | 0.201 | 0.092 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.206 | 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 | 69 | 75 | 69 | 0 | 0 | 0 | 0 | 0 | 53 | 0 |
| N.S. |
1 | 1.09 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.77 | 0.00 |
| time (sec) |
N/A | 0.205 | 0.100 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 71 | 77 | 71 | 0 | 0 | 0 | 0 | 0 | 94 | 0 |
| N.S. |
1 | 1.08 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.32 | 0.00 |
| time (sec) |
N/A | 0.204 | 0.115 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.220 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 82 | 147 | 115 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
| N.S. |
1 | 1.79 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
| time (sec) |
N/A | 0.256 | 0.608 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.034 | 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 | 98 | 149 | 113 | 0 | 0 | 0 | 0 | 0 | 86 | 0 |
| N.S. |
1 | 1.52 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 |
| time (sec) |
N/A | 0.250 | 0.498 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 59.296 | 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 | 98 | 137 | 105 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
| N.S. |
1 | 1.40 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
| time (sec) |
N/A | 0.242 | 0.288 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.309 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 96 | 134 | 102 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
| N.S. |
1 | 1.40 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
| time (sec) |
N/A | 0.244 | 0.336 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.270 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 94 | 142 | 110 | 0 | 0 | 0 | 0 | 0 | 60 | 0 |
| N.S. |
1 | 1.51 | 1.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.64 | 0.00 |
| time (sec) |
N/A | 0.245 | 0.540 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.338 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 96 | 143 | 111 | 0 | 0 | 0 | 0 | 0 | 120 | 0 |
| N.S. |
1 | 1.49 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.25 | 0.00 |
| time (sec) |
N/A | 0.246 | 1.121 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.375 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 143 | 113 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.34 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.229 | 0.344 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.285 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 112 | 145 | 233 | 295 | 401 | 0 | 297 | 382 | 375 |
| N.S. |
1 | 0.93 | 1.20 | 1.93 | 2.44 | 3.31 | 0.00 | 2.45 | 3.16 | 3.10 |
| time (sec) |
N/A | 0.255 | 0.212 | 1.189 | 0.083 | 0.097 | 0.000 | 0.372 | 0.210 | 5.965 |
| 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 | 68 | 68 | 58 | 74 | 123 | 151 | 877 | 88 | 129 | 160 |
| N.S. |
1 | 1.00 | 0.85 | 1.09 | 1.81 | 2.22 | 12.90 | 1.29 | 1.90 | 2.35 |
| time (sec) |
N/A | 0.202 | 0.154 | 0.966 | 0.087 | 0.091 | 99.382 | 0.363 | 0.206 | 5.996 |
| 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 | 21 | 21 | 20 | 22 | 21 | 32 | 112 | 21 | 29 | 42 |
| N.S. |
1 | 1.00 | 0.95 | 1.05 | 1.00 | 1.52 | 5.33 | 1.00 | 1.38 | 2.00 |
| time (sec) |
N/A | 0.150 | 0.048 | 0.847 | 0.031 | 0.084 | 28.315 | 0.344 | 0.214 | 5.934 |
| 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 | 63 | 97 | 64 | 0 | 0 | 0 | 0 | 0 | 241 | 0 |
| N.S. |
1 | 1.54 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.83 | 0.00 |
| time (sec) |
N/A | 0.220 | 0.133 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.258 | 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 | 63 | 97 | 64 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.54 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.218 | 0.439 | 0.000 | 0.000 | 0.000 | 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 | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 63 | 97 | 64 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.54 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.217 | 0.432 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.290 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 90 | 128 | 92 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.42 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.221 | 0.169 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.218 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 90 | 128 | 92 | 0 | 0 | 0 | 0 | 0 | 928 | 0 |
| N.S. |
1 | 1.42 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 10.31 | 0.00 |
| time (sec) |
N/A | 0.218 | 0.146 | 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 | 88 | 128 | 90 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.45 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.216 | 0.430 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.235 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 90 | 128 | 92 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.42 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.219 | 0.548 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.310 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 90 | 128 | 92 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.42 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.223 | 0.631 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.346 | 0.000 |
| 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 | 16 | 16 | 16 | 13 | 12 | 12 | 14 | 12 | 12 | 11 |
| N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 0.75 | 0.88 | 0.75 | 0.75 | 0.69 |
| time (sec) |
N/A | 0.135 | 0.014 | 0.734 | 0.032 | 0.077 | 0.076 | 0.343 | 0.214 | 5.743 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 19 | 19 | 19 | 16 | 15 | 15 | 17 | 15 | 37 | 15 |
| N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.79 | 0.79 | 0.89 | 0.79 | 1.95 | 0.79 |
| time (sec) |
N/A | 0.140 | 0.025 | 0.987 | 0.030 | 0.086 | 0.106 | 1.187 | 0.282 | 5.732 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 173 | 182 | 157 | 252 | 264 | 330 | 0 | 283 | 395 | 186 |
| N.S. |
1 | 1.05 | 0.91 | 1.46 | 1.53 | 1.91 | 0.00 | 1.64 | 2.28 | 1.08 |
| time (sec) |
N/A | 0.463 | 0.097 | 1.067 | 0.042 | 0.294 | 0.000 | 0.343 | 0.205 | 6.292 |
| 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 | 105 | 114 | 99 | 150 | 160 | 211 | 0 | 163 | 246 | 109 |
| N.S. |
1 | 1.09 | 0.94 | 1.43 | 1.52 | 2.01 | 0.00 | 1.55 | 2.34 | 1.04 |
| time (sec) |
N/A | 0.316 | 0.059 | 0.993 | 0.038 | 0.140 | 0.000 | 0.938 | 0.249 | 6.082 |
| 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 | 73 | 82 | 74 | 96 | 99 | 116 | 408 | 101 | 135 | 85 |
| N.S. |
1 | 1.12 | 1.01 | 1.32 | 1.36 | 1.59 | 5.59 | 1.38 | 1.85 | 1.16 |
| time (sec) |
N/A | 0.263 | 0.036 | 0.994 | 0.055 | 0.114 | 5.139 | 0.360 | 0.204 | 0.246 |
| 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 | 58 | 67 | 50 | 58 | 58 | 53 | 226 | 60 | 60 | 59 |
| N.S. |
1 | 1.16 | 0.86 | 1.00 | 1.00 | 0.91 | 3.90 | 1.03 | 1.03 | 1.02 |
| time (sec) |
N/A | 0.234 | 0.018 | 0.951 | 0.047 | 0.092 | 0.785 | 0.361 | 0.212 | 0.148 |
| 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 | 36 | 51 | 26 | 28 | 36 | 26 | 128 | 46 | 26 | 40 |
| N.S. |
1 | 1.42 | 0.72 | 0.78 | 1.00 | 0.72 | 3.56 | 1.28 | 0.72 | 1.11 |
| time (sec) |
N/A | 0.203 | 0.009 | 0.918 | 0.039 | 0.083 | 0.156 | 0.350 | 0.224 | 0.043 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 86 | 99 | 80 | 87 | 112 | 112 | 0 | 131 | 125 | 171 |
| N.S. |
1 | 1.15 | 0.93 | 1.01 | 1.30 | 1.30 | 0.00 | 1.52 | 1.45 | 1.99 |
| time (sec) |
N/A | 0.298 | 0.037 | 1.136 | 0.053 | 2.880 | 0.000 | 0.410 | 0.218 | 6.172 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | F(-1) | C | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 136 | 153 | 123 | 136 | 308 | 590 | 0 | 546 | 789 | 303 |
| N.S. |
1 | 1.12 | 0.90 | 1.00 | 2.26 | 4.34 | 0.00 | 4.01 | 5.80 | 2.23 |
| time (sec) |
N/A | 0.407 | 0.208 | 1.210 | 0.049 | 45.759 | 0.000 | 0.349 | 0.210 | 6.631 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | F(-1) | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 220 | 247 | 214 | 222 | 771 | 0 | 0 | 749 | 2244 | 779 |
| N.S. |
1 | 1.12 | 0.97 | 1.01 | 3.50 | 0.00 | 0.00 | 3.40 | 10.20 | 3.54 |
| time (sec) |
N/A | 0.626 | 0.183 | 1.282 | 0.082 | 0.000 | 0.000 | 0.321 | 0.237 | 7.802 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | B | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 201 | 220 | 201 | 486 | 767 | 2046 | 0 | 744 | 3689 | 801 |
| N.S. |
1 | 1.09 | 1.00 | 2.42 | 3.82 | 10.18 | 0.00 | 3.70 | 18.35 | 3.99 |
| time (sec) |
N/A | 0.581 | 0.142 | 1.107 | 0.052 | 1.239 | 0.000 | 0.384 | 0.236 | 6.181 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | B | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 166 | 185 | 166 | 369 | 621 | 1479 | 0 | 577 | 2785 | 634 |
| N.S. |
1 | 1.11 | 1.00 | 2.22 | 3.74 | 8.91 | 0.00 | 3.48 | 16.78 | 3.82 |
| time (sec) |
N/A | 0.469 | 0.115 | 1.085 | 0.058 | 0.384 | 0.000 | 0.321 | 0.268 | 6.217 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 156 | 175 | 157 | 279 | 502 | 1027 | 1380 | 433 | 2052 | 478 |
| N.S. |
1 | 1.12 | 1.01 | 1.79 | 3.22 | 6.58 | 8.85 | 2.78 | 13.15 | 3.06 |
| time (sec) |
N/A | 0.426 | 0.087 | 1.046 | 0.043 | 0.150 | 117.476 | 0.348 | 0.267 | 5.969 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 133 | 158 | 119 | 174 | 351 | 666 | 872 | 313 | 1297 | 353 |
| N.S. |
1 | 1.19 | 0.89 | 1.31 | 2.64 | 5.01 | 6.56 | 2.35 | 9.75 | 2.65 |
| time (sec) |
N/A | 0.388 | 0.090 | 1.046 | 0.046 | 0.084 | 1.972 | 0.311 | 0.304 | 5.567 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 122 | 153 | 106 | 117 | 257 | 414 | 706 | 219 | 867 | 259 |
| N.S. |
1 | 1.25 | 0.87 | 0.96 | 2.11 | 3.39 | 5.79 | 1.80 | 7.11 | 2.12 |
| time (sec) |
N/A | 0.356 | 0.064 | 0.968 | 0.049 | 0.081 | 1.259 | 0.328 | 0.232 | 5.550 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 81 | 106 | 66 | 82 | 208 | 241 | 406 | 166 | 459 | 182 |
| N.S. |
1 | 1.31 | 0.81 | 1.01 | 2.57 | 2.98 | 5.01 | 2.05 | 5.67 | 2.25 |
| time (sec) |
N/A | 0.275 | 0.046 | 0.924 | 0.043 | 0.081 | 0.544 | 0.339 | 0.242 | 0.124 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | F(-1) | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 186 | 199 | 185 | 187 | 873 | 0 | 0 | 794 | 3635 | 801 |
| N.S. |
1 | 1.07 | 0.99 | 1.01 | 4.69 | 0.00 | 0.00 | 4.27 | 19.54 | 4.31 |
| time (sec) |
N/A | 0.522 | 0.191 | 1.253 | 0.093 | 0.000 | 0.000 | 0.336 | 0.211 | 7.885 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | F(-1) | F(-1) | C | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 234 | 257 | 232 | 235 | 2096 | 0 | 0 | 1644 | 8516 | 1940 |
| N.S. |
1 | 1.10 | 0.99 | 1.00 | 8.96 | 0.00 | 0.00 | 7.03 | 36.39 | 8.29 |
| time (sec) |
N/A | 0.703 | 0.361 | 1.346 | 0.118 | 0.000 | 0.000 | 0.396 | 0.248 | 9.688 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | F(-1) | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 324 | 361 | 321 | 327 | 4029 | 0 | 0 | 2843 | 18244 | 4019 |
| N.S. |
1 | 1.11 | 0.99 | 1.01 | 12.44 | 0.00 | 0.00 | 8.77 | 56.31 | 12.40 |
| time (sec) |
N/A | 1.006 | 0.494 | 1.608 | 0.488 | 0.000 | 0.000 | 0.375 | 0.289 | 13.405 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | B | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 373 | 398 | 373 | 1220 | 2742 | 6696 | 0 | 2915 | 12557 | 3170 |
| N.S. |
1 | 1.07 | 1.00 | 3.27 | 7.35 | 17.95 | 0.00 | 7.82 | 33.66 | 8.50 |
| time (sec) |
N/A | 1.186 | 0.438 | 1.154 | 0.105 | 10.772 | 0.000 | 0.383 | 26.069 | 8.603 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | B | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 339 | 364 | 339 | 1005 | 2337 | 5430 | 0 | 2387 | 10338 | 2656 |
| N.S. |
1 | 1.07 | 1.00 | 2.96 | 6.89 | 16.02 | 0.00 | 7.04 | 30.50 | 7.83 |
| time (sec) |
N/A | 1.024 | 0.402 | 1.138 | 0.118 | 4.432 | 0.000 | 0.314 | 7.827 | 7.310 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | B | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 328 | 353 | 327 | 817 | 1961 | 4299 | 0 | 1915 | 8298 | 2161 |
| N.S. |
1 | 1.08 | 1.00 | 2.49 | 5.98 | 13.11 | 0.00 | 5.84 | 25.30 | 6.59 |
| time (sec) |
N/A | 0.918 | 0.246 | 1.112 | 0.103 | 1.219 | 0.000 | 0.294 | 0.843 | 8.008 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 237 | 268 | 237 | 612 | 1558 | 3352 | 2864 | 1599 | 6415 | 1677 |
| N.S. |
1 | 1.13 | 1.00 | 2.58 | 6.57 | 14.14 | 12.08 | 6.75 | 27.07 | 7.08 |
| time (sec) |
N/A | 0.673 | 0.167 | 1.039 | 0.069 | 0.149 | 52.716 | 0.320 | 0.247 | 7.343 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 243 | 280 | 239 | 474 | 1243 | 2669 | 2564 | 1179 | 5214 | 1312 |
| N.S. |
1 | 1.15 | 0.98 | 1.95 | 5.12 | 10.98 | 10.55 | 4.85 | 21.46 | 5.40 |
| time (sec) |
N/A | 0.670 | 0.195 | 1.087 | 0.074 | 0.126 | 12.007 | 0.367 | 0.201 | 6.807 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 286 | 329 | 272 | 353 | 958 | 1913 | 2638 | 813 | 3731 | 1021 |
| N.S. |
1 | 1.15 | 0.95 | 1.23 | 3.35 | 6.69 | 9.22 | 2.84 | 13.05 | 3.57 |
| time (sec) |
N/A | 0.771 | 0.135 | 1.043 | 0.063 | 0.122 | 5.001 | 0.353 | 0.220 | 6.367 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 203 | 238 | 185 | 196 | 766 | 1285 | 1431 | 540 | 2239 | 733 |
| N.S. |
1 | 1.17 | 0.91 | 0.97 | 3.77 | 6.33 | 7.05 | 2.66 | 11.03 | 3.61 |
| time (sec) |
N/A | 0.515 | 0.094 | 1.055 | 0.062 | 0.128 | 2.697 | 0.360 | 0.214 | 5.993 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 143 | 160 | 128 | 140 | 594 | 760 | 881 | 345 | 1202 | 542 |
| N.S. |
1 | 1.12 | 0.90 | 0.98 | 4.15 | 5.31 | 6.16 | 2.41 | 8.41 | 3.79 |
| time (sec) |
N/A | 0.366 | 0.075 | 1.059 | 0.049 | 0.097 | 1.174 | 1.532 | 0.225 | 0.206 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | F(-1) | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 356 | 369 | 355 | 371 | 3790 | 0 | 0 | 2839 | 14564 | 3770 |
| N.S. |
1 | 1.04 | 1.00 | 1.04 | 10.65 | 0.00 | 0.00 | 7.97 | 40.91 | 10.59 |
| time (sec) |
N/A | 1.052 | 0.316 | 1.474 | 0.346 | 0.000 | 0.000 | 0.376 | 0.312 | 12.842 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | F(-1) | F(-1) | C | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 409 | 434 | 407 | 420 | 7156 | 0 | 0 | 4279 | 31106 | 57828 |
| N.S. |
1 | 1.06 | 1.00 | 1.03 | 17.50 | 0.00 | 0.00 | 10.46 | 76.05 | 141.39 |
| time (sec) |
N/A | 1.401 | 0.498 | 1.729 | 0.685 | 0.000 | 0.000 | 0.590 | 0.606 | 15.451 |
| 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 | 150 | 162 | 86 | 89 | 102 | 111 | 309 | 104 | 242 | 147 |
| N.S. |
1 | 1.08 | 0.57 | 0.59 | 0.68 | 0.74 | 2.06 | 0.69 | 1.61 | 0.98 |
| time (sec) |
N/A | 0.407 | 0.055 | 0.816 | 0.106 | 0.185 | 0.397 | 0.389 | 0.203 | 0.096 |
| 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 | 110 | 110 | 63 | 57 | 69 | 79 | 204 | 72 | 152 | 92 |
| N.S. |
1 | 1.00 | 0.57 | 0.52 | 0.63 | 0.72 | 1.85 | 0.65 | 1.38 | 0.84 |
| time (sec) |
N/A | 0.304 | 0.026 | 0.806 | 0.130 | 0.134 | 0.274 | 0.392 | 0.223 | 5.724 |
| 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 | 72 | 73 | 41 | 35 | 47 | 56 | 97 | 50 | 81 | 53 |
| N.S. |
1 | 1.01 | 0.57 | 0.49 | 0.65 | 0.78 | 1.35 | 0.69 | 1.12 | 0.74 |
| time (sec) |
N/A | 0.235 | 0.012 | 0.704 | 0.110 | 0.155 | 0.140 | 0.367 | 0.215 | 0.068 |
| 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 | 38 | 31 | 17 | 27 | 37 | 39 | 29 | 25 | 16 |
| N.S. |
1 | 2.00 | 1.63 | 0.89 | 1.42 | 1.95 | 2.05 | 1.53 | 1.32 | 0.84 |
| time (sec) |
N/A | 0.180 | 0.009 | 0.667 | 0.113 | 0.091 | 0.039 | 0.405 | 0.220 | 0.109 |
| 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 | 94 | 94 | 67 | 71 | 94 | 79 | 1812 | 104 | 108 | 89 |
| N.S. |
1 | 1.00 | 0.71 | 0.76 | 1.00 | 0.84 | 19.28 | 1.11 | 1.15 | 0.95 |
| time (sec) |
N/A | 0.297 | 0.026 | 0.995 | 0.122 | 0.110 | 5.582 | 0.376 | 0.215 | 0.139 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 124 | 124 | 107 | 118 | 205 | 234 | 4780 | 304 | 499 | 193 |
| N.S. |
1 | 1.00 | 0.86 | 0.95 | 1.65 | 1.89 | 38.55 | 2.45 | 4.02 | 1.56 |
| time (sec) |
N/A | 0.358 | 0.108 | 0.916 | 0.120 | 0.125 | 22.371 | 0.408 | 0.230 | 0.202 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 164 | 164 | 162 | 172 | 383 | 517 | 9041 | 335 | 1187 | 352 |
| N.S. |
1 | 1.00 | 0.99 | 1.05 | 2.34 | 3.15 | 55.13 | 2.04 | 7.24 | 2.15 |
| time (sec) |
N/A | 0.451 | 0.121 | 0.966 | 0.113 | 0.162 | 109.963 | 0.375 | 0.209 | 0.261 |
| 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 | 66 | 66 | 69 | 42 | 52 | 62 | 66 | 55 | 62 | 49 |
| N.S. |
1 | 1.00 | 1.05 | 0.64 | 0.79 | 0.94 | 1.00 | 0.83 | 0.94 | 0.74 |
| time (sec) |
N/A | 0.242 | 0.058 | 0.858 | 0.126 | 0.074 | 0.057 | 0.352 | 0.212 | 5.790 |
| 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 | 57 | 57 | 60 | 37 | 47 | 56 | 53 | 50 | 57 | 44 |
| N.S. |
1 | 1.00 | 1.05 | 0.65 | 0.82 | 0.98 | 0.93 | 0.88 | 1.00 | 0.77 |
| time (sec) |
N/A | 0.232 | 0.052 | 0.792 | 0.113 | 0.081 | 0.054 | 0.358 | 0.226 | 0.048 |
| 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 | 54 | 54 | 59 | 32 | 42 | 52 | 54 | 45 | 52 | 39 |
| N.S. |
1 | 1.00 | 1.09 | 0.59 | 0.78 | 0.96 | 1.00 | 0.83 | 0.96 | 0.72 |
| time (sec) |
N/A | 0.219 | 0.026 | 0.779 | 0.114 | 0.103 | 0.050 | 0.383 | 0.234 | 6.051 |
| 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 | 49 | 49 | 44 | 28 | 39 | 48 | 46 | 42 | 49 | 36 |
| N.S. |
1 | 1.00 | 0.90 | 0.57 | 0.80 | 0.98 | 0.94 | 0.86 | 1.00 | 0.73 |
| time (sec) |
N/A | 0.207 | 0.012 | 0.721 | 0.112 | 0.094 | 0.044 | 0.330 | 0.222 | 0.064 |
| 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 | 38 | 31 | 17 | 27 | 37 | 39 | 29 | 25 | 16 |
| N.S. |
1 | 2.00 | 1.63 | 0.89 | 1.42 | 1.95 | 2.05 | 1.53 | 1.32 | 0.84 |
| time (sec) |
N/A | 0.177 | 0.005 | 0.684 | 0.118 | 0.082 | 0.040 | 0.346 | 0.220 | 0.001 |
| 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 | 59 | 79 | 52 | 37 | 47 | 57 | 90 | 51 | 57 | 42 |
| N.S. |
1 | 1.34 | 0.88 | 0.63 | 0.80 | 0.97 | 1.53 | 0.86 | 0.97 | 0.71 |
| time (sec) |
N/A | 0.239 | 0.013 | 0.780 | 0.119 | 0.077 | 0.263 | 0.375 | 0.213 | 0.149 |
| 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 | 82 | 82 | 69 | 46 | 56 | 82 | 104 | 77 | 129 | 49 |
| N.S. |
1 | 1.00 | 0.84 | 0.56 | 0.68 | 1.00 | 1.27 | 0.94 | 1.57 | 0.60 |
| time (sec) |
N/A | 0.258 | 0.043 | 0.760 | 0.129 | 0.086 | 0.285 | 0.326 | 0.256 | 5.685 |
| 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 | 93 | 93 | 87 | 55 | 66 | 105 | 112 | 65 | 208 | 58 |
| N.S. |
1 | 1.00 | 0.94 | 0.59 | 0.71 | 1.13 | 1.20 | 0.70 | 2.24 | 0.62 |
| time (sec) |
N/A | 0.280 | 0.051 | 0.789 | 0.110 | 0.099 | 0.301 | 0.348 | 0.215 | 5.656 |
| 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 | 17 | 17 | 17 | 14 | 13 | 13 | 14 | 15 | 13 | 13 |
| N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 0.76 | 0.82 | 0.88 | 0.76 | 0.76 |
| time (sec) |
N/A | 0.162 | 0.004 | 0.678 | 0.038 | 0.085 | 0.040 | 0.343 | 0.227 | 0.027 |
| 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 | 51 | 51 | 49 | 29 | 39 | 49 | 49 | 42 | 49 | 36 |
| N.S. |
1 | 1.00 | 0.96 | 0.57 | 0.76 | 0.96 | 0.96 | 0.82 | 0.96 | 0.71 |
| time (sec) |
N/A | 0.213 | 0.017 | 0.685 | 0.108 | 0.083 | 0.046 | 0.699 | 0.204 | 0.063 |
| 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 | 49 | 51 | 44 | 31 | 41 | 51 | 42 | 46 | 49 | 36 |
| N.S. |
1 | 1.04 | 0.90 | 0.63 | 0.84 | 1.04 | 0.86 | 0.94 | 1.00 | 0.73 |
| time (sec) |
N/A | 0.206 | 0.017 | 0.693 | 0.131 | 0.089 | 0.049 | 0.322 | 0.311 | 0.107 |
| 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 | 47 | 47 | 47 | 29 | 35 | 45 | 44 | 44 | 41 | 34 |
| N.S. |
1 | 1.00 | 1.00 | 0.62 | 0.74 | 0.96 | 0.94 | 0.94 | 0.87 | 0.72 |
| time (sec) |
N/A | 0.234 | 0.026 | 0.724 | 0.134 | 0.101 | 0.046 | 0.320 | 0.273 | 0.079 |
| 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 | 133 | 150 | 143 | 165 | 0 | 680 | 294 | 161 | 212 | 4619 |
| N.S. |
1 | 1.13 | 1.08 | 1.24 | 0.00 | 5.11 | 2.21 | 1.21 | 1.59 | 34.73 |
| time (sec) |
N/A | 0.453 | 0.439 | 3.195 | 0.000 | 0.311 | 4.529 | 0.352 | 0.316 | 6.538 |
| 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 | 115 | 123 | 106 | 101 | 0 | 508 | 270 | 113 | 94 | 631 |
| N.S. |
1 | 1.07 | 0.92 | 0.88 | 0.00 | 4.42 | 2.35 | 0.98 | 0.82 | 5.49 |
| time (sec) |
N/A | 0.272 | 0.171 | 1.260 | 0.000 | 0.145 | 4.347 | 0.312 | 0.238 | 6.084 |
| 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 | 115 | 123 | 106 | 87 | 0 | 488 | 253 | 99 | 217 | 222 |
| N.S. |
1 | 1.07 | 0.92 | 0.76 | 0.00 | 4.24 | 2.20 | 0.86 | 1.89 | 1.93 |
| time (sec) |
N/A | 0.240 | 0.221 | 1.310 | 0.000 | 0.150 | 5.857 | 0.406 | 0.257 | 6.517 |
| 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 | 147 | 192 | 147 | 150 | 0 | 1243 | 298 | 174 | 528 | 26252 |
| N.S. |
1 | 1.31 | 1.00 | 1.02 | 0.00 | 8.46 | 2.03 | 1.18 | 3.59 | 178.59 |
| time (sec) |
N/A | 0.437 | 0.403 | 1.263 | 0.000 | 0.733 | 4.366 | 0.362 | 0.252 | 8.182 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 343 | 371 | 348 | 402 | 0 | 5115 | 0 | 870 | 3219 | 28140 |
| N.S. |
1 | 1.08 | 1.01 | 1.17 | 0.00 | 14.91 | 0.00 | 2.54 | 9.38 | 82.04 |
| time (sec) |
N/A | 1.333 | 2.737 | 2.186 | 0.000 | 56.607 | 0.000 | 0.522 | 0.261 | 9.234 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 261 | 285 | 260 | 243 | 0 | 3442 | 0 | 632 | 2167 | 15161 |
| N.S. |
1 | 1.09 | 1.00 | 0.93 | 0.00 | 13.19 | 0.00 | 2.42 | 8.30 | 58.09 |
| time (sec) |
N/A | 0.856 | 1.375 | 1.919 | 0.000 | 3.340 | 0.000 | 0.401 | 0.244 | 8.040 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 220 | 240 | 211 | 228 | 0 | 2116 | 0 | 425 | 1273 | 11194 |
| N.S. |
1 | 1.09 | 0.96 | 1.04 | 0.00 | 9.62 | 0.00 | 1.93 | 5.79 | 50.88 |
| time (sec) |
N/A | 0.504 | 1.395 | 1.443 | 0.000 | 0.257 | 0.000 | 0.416 | 0.294 | 7.568 |
| 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 | 200 | 220 | 194 | 214 | 0 | 1928 | 0 | 336 | 2508 | 13100 |
| N.S. |
1 | 1.10 | 0.97 | 1.07 | 0.00 | 9.64 | 0.00 | 1.68 | 12.54 | 65.50 |
| time (sec) |
N/A | 0.466 | 1.253 | 1.484 | 0.000 | 0.261 | 0.000 | 0.965 | 0.241 | 8.733 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 256 | 311 | 246 | 256 | 0 | 4502 | 0 | 619 | 4120 | 36222 |
| N.S. |
1 | 1.21 | 0.96 | 1.00 | 0.00 | 17.59 | 0.00 | 2.42 | 16.09 | 141.49 |
| time (sec) |
N/A | 0.758 | 2.140 | 1.601 | 0.000 | 4.913 | 0.000 | 0.408 | 0.264 | 10.359 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 353 | 428 | 412 | 270 | 0 | 11596 | 0 | 1245 | 6383 | 172959 |
| N.S. |
1 | 1.21 | 1.17 | 0.76 | 0.00 | 32.85 | 0.00 | 3.53 | 18.08 | 489.97 |
| time (sec) |
N/A | 1.223 | 3.263 | 1.678 | 0.000 | 75.957 | 0.000 | 0.416 | 0.300 | 32.864 |