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 | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 201 | 239 | 203 | 219 | 925 | 20020 | 0 | 750 | 3685 |
N.S. |
1 | 1.19 | 1.01 | 1.09 | 4.60 | 99.60 | 0.00 | 3.73 | 18.33 |
time (sec) |
N/A | 0.436 | 0.684 | 0.447 | 0.499 | 0.513 | 0.000 | 0.363 | 1.258 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 3 | 3 | 14 | 4 | 5 | 8 | 0 | 5 | 3 |
N.S. |
1 | 1.00 | 4.67 | 1.33 | 1.67 | 2.67 | 0.00 | 1.67 | 1.00 |
time (sec) |
N/A | 0.233 | 0.010 | 0.136 | 0.338 | 0.238 | 0.000 | 0.259 | 1.773 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 15 | 5 | 96 | 0 | 1 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.31 | 6.00 | 0.00 | 0.06 | 0.88 |
time (sec) |
N/A | 0.244 | 0.009 | 0.086 | 0.313 | 0.255 | 0.000 | 0.276 | 0.222 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 26 | 23 | 21 | 28 | 140 | 0 | 45 | 20 |
N.S. |
1 | 1.18 | 1.05 | 0.95 | 1.27 | 6.36 | 0.00 | 2.05 | 0.91 |
time (sec) |
N/A | 0.232 | 0.023 | 0.062 | 0.312 | 0.258 | 0.000 | 0.269 | 0.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 23 | 28 | 32 | 385 | 0 | 41 | 27 |
N.S. |
1 | 1.00 | 0.66 | 0.80 | 0.91 | 11.00 | 0.00 | 1.17 | 0.77 |
time (sec) |
N/A | 0.247 | 0.023 | 0.083 | 0.314 | 0.303 | 0.000 | 0.281 | 1.819 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 15 | 11 | 14 | 11 | 2 | 0 | 11 | 2 |
N.S. |
1 | 1.36 | 1.00 | 1.27 | 1.00 | 0.18 | 0.00 | 1.00 | 0.18 |
time (sec) |
N/A | 0.238 | 0.037 | 0.078 | 0.283 | 0.262 | 0.000 | 0.267 | 0.132 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 25 | 36 | 12 | 21 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 1.92 | 2.77 | 0.92 | 1.62 | 1.08 |
time (sec) |
N/A | 0.227 | 0.035 | 0.044 | 0.279 | 0.251 | 0.224 | 0.267 | 1.848 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 92 | 85 | 288 | 0 | 4529 | 126 | 980 | 119 |
N.S. |
1 | 1.06 | 0.98 | 3.31 | 0.00 | 52.06 | 1.45 | 11.26 | 1.37 |
time (sec) |
N/A | 0.331 | 0.579 | 0.175 | 0.000 | 0.493 | 2.355 | 1.132 | 9.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 133 | 580 | 337 | 0 | 9360 | 0 | 938 | 0 |
N.S. |
1 | 1.10 | 4.79 | 2.79 | 0.00 | 77.36 | 0.00 | 7.75 | 0.00 |
time (sec) |
N/A | 0.395 | 6.212 | 0.104 | 0.000 | 0.577 | 0.000 | 0.986 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 68 | 60 | 253 | 0 | 2329 | 94 | 630 | 66 |
N.S. |
1 | 1.08 | 0.95 | 4.02 | 0.00 | 36.97 | 1.49 | 10.00 | 1.05 |
time (sec) |
N/A | 0.289 | 0.189 | 0.087 | 0.000 | 0.343 | 1.587 | 0.769 | 3.682 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 89 | 193 | 276 | 0 | 4825 | 0 | 554 | 0 |
N.S. |
1 | 1.05 | 2.27 | 3.25 | 0.00 | 56.76 | 0.00 | 6.52 | 0.00 |
time (sec) |
N/A | 0.318 | 3.739 | 0.088 | 0.000 | 0.402 | 0.000 | 0.737 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 44 | 49 | 44 | 238 | 0 | 1543 | 68 | 349 | 51 |
N.S. |
1 | 1.11 | 1.00 | 5.41 | 0.00 | 35.07 | 1.55 | 7.93 | 1.16 |
time (sec) |
N/A | 0.261 | 0.038 | 0.072 | 0.000 | 0.298 | 0.985 | 0.565 | 2.227 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 81 | 238 | 0 | 3443 | 0 | 253 | 0 |
N.S. |
1 | 1.00 | 1.35 | 3.97 | 0.00 | 57.38 | 0.00 | 4.22 | 0.00 |
time (sec) |
N/A | 0.234 | 0.370 | 0.109 | 0.000 | 0.357 | 0.000 | 0.494 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 56 | 61 | 56 | 0 | 0 | 3467 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 1.00 | 0.00 | 0.00 | 61.91 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.301 | 0.038 | 0.000 | 0.000 | 0.358 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 42 | 0 | 0 | 1539 | 0 | 348 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.00 | 32.06 | 0.00 | 7.25 | 0.00 |
time (sec) |
N/A | 0.283 | 0.141 | 0.000 | 0.000 | 0.303 | 0.000 | 0.557 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | B | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 83 | 87 | 83 | 0 | 0 | 4891 | 0 | 557 | 0 |
N.S. |
1 | 1.05 | 1.00 | 0.00 | 0.00 | 58.93 | 0.00 | 6.71 | 0.00 |
time (sec) |
N/A | 0.325 | 0.243 | 0.000 | 0.000 | 0.406 | 0.000 | 0.717 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | B | F | B | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 78 | 82 | 161 | 0 | 0 | 2355 | 0 | 629 | 0 |
N.S. |
1 | 1.05 | 2.06 | 0.00 | 0.00 | 30.19 | 0.00 | 8.06 | 0.00 |
time (sec) |
N/A | 0.332 | 2.162 | 0.000 | 0.000 | 0.354 | 0.000 | 0.831 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | B | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 121 | 134 | 111 | 0 | 0 | 9642 | 0 | 947 | 0 |
N.S. |
1 | 1.11 | 0.92 | 0.00 | 0.00 | 79.69 | 0.00 | 7.83 | 0.00 |
time (sec) |
N/A | 0.372 | 0.737 | 0.000 | 0.000 | 0.573 | 0.000 | 1.008 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 89 | 86 | 488 | 0 | 4941 | 223 | 1063 | 112 |
N.S. |
1 | 1.09 | 1.05 | 5.95 | 0.00 | 60.26 | 2.72 | 12.96 | 1.37 |
time (sec) |
N/A | 0.321 | 0.472 | 0.079 | 0.000 | 0.493 | 10.257 | 1.457 | 9.969 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 123 | 132 | 584 | 529 | 0 | 10046 | 0 | 949 | 0 |
N.S. |
1 | 1.07 | 4.75 | 4.30 | 0.00 | 81.67 | 0.00 | 7.72 | 0.00 |
time (sec) |
N/A | 0.425 | 6.252 | 0.083 | 0.000 | 0.587 | 0.000 | 1.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 70 | 59 | 473 | 0 | 2385 | 165 | 662 | 64 |
N.S. |
1 | 1.11 | 0.94 | 7.51 | 0.00 | 37.86 | 2.62 | 10.51 | 1.02 |
time (sec) |
N/A | 0.275 | 0.190 | 0.058 | 0.000 | 0.372 | 6.974 | 1.018 | 4.103 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 92 | 110 | 473 | 0 | 4841 | 0 | 584 | 0 |
N.S. |
1 | 1.05 | 1.25 | 5.38 | 0.00 | 55.01 | 0.00 | 6.64 | 0.00 |
time (sec) |
N/A | 0.295 | 0.729 | 0.101 | 0.000 | 0.428 | 0.000 | 0.806 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 71 | 76 | 71 | 0 | 0 | 4039 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 1.00 | 0.00 | 0.00 | 56.89 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.326 | 0.081 | 0.000 | 0.000 | 0.416 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 197 | 0 | 0 | 3913 | 0 | 430 | 0 |
N.S. |
1 | 1.00 | 2.56 | 0.00 | 0.00 | 50.82 | 0.00 | 5.58 | 0.00 |
time (sec) |
N/A | 0.331 | 3.360 | 0.000 | 0.000 | 0.403 | 0.000 | 0.957 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 51 | 97 | 0 | 679 | 0 | 104 | 68 |
N.S. |
1 | 1.00 | 1.65 | 3.13 | 0.00 | 21.90 | 0.00 | 3.35 | 2.19 |
time (sec) |
N/A | 0.209 | 0.096 | 0.194 | 0.000 | 0.268 | 0.000 | 0.279 | 0.194 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | C | F | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 53 | 142 | 0 | 226 | 0 | 104 | 43 |
N.S. |
1 | 1.00 | 1.18 | 3.16 | 0.00 | 5.02 | 0.00 | 2.31 | 0.96 |
time (sec) |
N/A | 0.220 | 0.057 | 0.160 | 0.000 | 0.245 | 0.000 | 0.290 | 1.938 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 53 | 74 | 158 | 0 | 1027 | 0 | 202 | 78 |
N.S. |
1 | 1.06 | 1.48 | 3.16 | 0.00 | 20.54 | 0.00 | 4.04 | 1.56 |
time (sec) |
N/A | 0.226 | 0.180 | 0.081 | 0.000 | 0.272 | 0.000 | 0.278 | 0.255 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | C | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 70 | 76 | 211 | 0 | 361 | 0 | 204 | 0 |
N.S. |
1 | 1.04 | 1.13 | 3.15 | 0.00 | 5.39 | 0.00 | 3.04 | 0.00 |
time (sec) |
N/A | 0.241 | 0.092 | 0.075 | 0.000 | 0.263 | 0.000 | 0.281 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 76 | 68 | 164 | 0 | 2827 | 0 | 592 | 65 |
N.S. |
1 | 1.09 | 0.97 | 2.34 | 0.00 | 40.39 | 0.00 | 8.46 | 0.93 |
time (sec) |
N/A | 0.316 | 0.573 | 0.117 | 0.000 | 0.426 | 0.000 | 0.667 | 2.676 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 95 | 208 | 178 | 0 | 5494 | 0 | 559 | 0 |
N.S. |
1 | 1.08 | 2.36 | 2.02 | 0.00 | 62.43 | 0.00 | 6.35 | 0.00 |
time (sec) |
N/A | 0.313 | 5.081 | 0.113 | 0.000 | 0.484 | 0.000 | 0.567 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 52 | 47 | 129 | 0 | 1625 | 0 | 345 | 39 |
N.S. |
1 | 1.11 | 1.00 | 2.74 | 0.00 | 34.57 | 0.00 | 7.34 | 0.83 |
time (sec) |
N/A | 0.277 | 0.127 | 0.091 | 0.000 | 0.382 | 0.000 | 0.492 | 2.208 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 101 | 137 | 0 | 3361 | 0 | 252 | 0 |
N.S. |
1 | 1.00 | 1.68 | 2.28 | 0.00 | 56.02 | 0.00 | 4.20 | 0.00 |
time (sec) |
N/A | 0.287 | 0.448 | 0.100 | 0.000 | 0.439 | 0.000 | 0.523 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 114 | 0 | 1361 | 68 | 188 | 23 |
N.S. |
1 | 1.00 | 1.00 | 3.93 | 0.00 | 46.93 | 2.34 | 6.48 | 0.79 |
time (sec) |
N/A | 0.244 | 0.021 | 0.129 | 0.000 | 0.307 | 1.044 | 0.408 | 2.182 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 31 | 114 | 0 | 1287 | 0 | 188 | 25 |
N.S. |
1 | 1.00 | 1.00 | 3.68 | 0.00 | 41.52 | 0.00 | 6.06 | 0.81 |
time (sec) |
N/A | 0.204 | 0.029 | 0.115 | 0.000 | 0.301 | 0.000 | 0.391 | 2.122 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 56 | 61 | 56 | 0 | 0 | 3527 | 0 | 254 | 0 |
N.S. |
1 | 1.09 | 1.00 | 0.00 | 0.00 | 62.98 | 0.00 | 4.54 | 0.00 |
time (sec) |
N/A | 0.285 | 0.056 | 0.000 | 0.000 | 0.382 | 0.000 | 0.515 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | B | F | B | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 130 | 0 | 0 | 1565 | 0 | 343 | 0 |
N.S. |
1 | 1.00 | 2.55 | 0.00 | 0.00 | 30.69 | 0.00 | 6.73 | 0.00 |
time (sec) |
N/A | 0.285 | 0.854 | 0.000 | 0.000 | 0.321 | 0.000 | 0.484 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | B | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 88 | 96 | 107 | 0 | 0 | 5711 | 0 | 565 | 0 |
N.S. |
1 | 1.09 | 1.22 | 0.00 | 0.00 | 64.90 | 0.00 | 6.42 | 0.00 |
time (sec) |
N/A | 0.336 | 0.465 | 0.000 | 0.000 | 0.494 | 0.000 | 0.615 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 77 | 67 | 322 | 0 | 3991 | 0 | 460 | 70 |
N.S. |
1 | 1.07 | 0.93 | 4.47 | 0.00 | 55.43 | 0.00 | 6.39 | 0.97 |
time (sec) |
N/A | 0.364 | 0.130 | 0.101 | 0.000 | 0.493 | 0.000 | 0.571 | 3.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 84 | 99 | 188 | 328 | 0 | 6973 | 0 | 371 | 0 |
N.S. |
1 | 1.18 | 2.24 | 3.90 | 0.00 | 83.01 | 0.00 | 4.42 | 0.00 |
time (sec) |
N/A | 0.350 | 2.971 | 0.096 | 0.000 | 0.540 | 0.000 | 0.566 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 52 | 58 | 52 | 287 | 0 | 2525 | 0 | 287 | 45 |
N.S. |
1 | 1.12 | 1.00 | 5.52 | 0.00 | 48.56 | 0.00 | 5.52 | 0.87 |
time (sec) |
N/A | 0.295 | 0.147 | 0.079 | 0.000 | 0.348 | 0.000 | 0.443 | 2.778 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 112 | 289 | 0 | 2281 | 0 | 293 | 0 |
N.S. |
1 | 1.00 | 2.11 | 5.45 | 0.00 | 43.04 | 0.00 | 5.53 | 0.00 |
time (sec) |
N/A | 0.295 | 1.690 | 0.078 | 0.000 | 0.351 | 0.000 | 0.458 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 54 | 41 | 273 | 0 | 2277 | 92 | 292 | 41 |
N.S. |
1 | 1.10 | 0.84 | 5.57 | 0.00 | 46.47 | 1.88 | 5.96 | 0.84 |
time (sec) |
N/A | 0.269 | 0.041 | 0.068 | 0.000 | 0.356 | 10.708 | 0.449 | 2.509 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 223 | 272 | 0 | 2509 | 0 | 288 | 0 |
N.S. |
1 | 1.00 | 3.98 | 4.86 | 0.00 | 44.80 | 0.00 | 5.14 | 0.00 |
time (sec) |
N/A | 0.244 | 4.778 | 0.090 | 0.000 | 0.357 | 0.000 | 0.438 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 78 | 98 | 70 | 0 | 0 | 6955 | 0 | 372 | 0 |
N.S. |
1 | 1.26 | 0.90 | 0.00 | 0.00 | 89.17 | 0.00 | 4.77 | 0.00 |
time (sec) |
N/A | 0.337 | 0.098 | 0.000 | 0.000 | 0.543 | 0.000 | 0.512 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | B | F | B | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 85 | 91 | 263 | 0 | 0 | 3929 | 0 | 459 | 0 |
N.S. |
1 | 1.07 | 3.09 | 0.00 | 0.00 | 46.22 | 0.00 | 5.40 | 0.00 |
time (sec) |
N/A | 0.361 | 8.093 | 0.000 | 0.000 | 0.492 | 0.000 | 0.569 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 118 | 148 | 231 | 549 | 0 | 19265 | 0 | 805 | 0 |
N.S. |
1 | 1.25 | 1.96 | 4.65 | 0.00 | 163.26 | 0.00 | 6.82 | 0.00 |
time (sec) |
N/A | 0.422 | 2.145 | 0.110 | 0.000 | 1.230 | 0.000 | 0.637 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 84 | 90 | 68 | 469 | 0 | 7033 | 0 | 711 | 92 |
N.S. |
1 | 1.07 | 0.81 | 5.58 | 0.00 | 83.73 | 0.00 | 8.46 | 1.10 |
time (sec) |
N/A | 0.357 | 0.125 | 0.098 | 0.000 | 0.675 | 0.000 | 0.526 | 4.406 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 99 | 132 | 491 | 0 | 5719 | 0 | 684 | 0 |
N.S. |
1 | 1.10 | 1.47 | 5.46 | 0.00 | 63.54 | 0.00 | 7.60 | 0.00 |
time (sec) |
N/A | 0.330 | 2.840 | 0.103 | 0.000 | 0.635 | 0.000 | 0.527 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 86 | 63 | 435 | 0 | 6621 | 0 | 725 | 82 |
N.S. |
1 | 1.16 | 0.85 | 5.88 | 0.00 | 89.47 | 0.00 | 9.80 | 1.11 |
time (sec) |
N/A | 0.313 | 0.096 | 0.085 | 0.000 | 0.665 | 0.000 | 0.533 | 4.162 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 97 | 216 | 454 | 0 | 6507 | 0 | 728 | 0 |
N.S. |
1 | 1.10 | 2.45 | 5.16 | 0.00 | 73.94 | 0.00 | 8.27 | 0.00 |
time (sec) |
N/A | 0.336 | 7.114 | 0.077 | 0.000 | 0.664 | 0.000 | 0.524 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 82 | 43 | 420 | 0 | 5779 | 114 | 683 | 76 |
N.S. |
1 | 1.17 | 0.61 | 6.00 | 0.00 | 82.56 | 1.63 | 9.76 | 1.09 |
time (sec) |
N/A | 0.284 | 0.052 | 0.054 | 0.000 | 0.637 | 12.557 | 0.510 | 4.280 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 93 | 106 | 976 | 420 | 0 | 6933 | 0 | 714 | 0 |
N.S. |
1 | 1.14 | 10.49 | 4.52 | 0.00 | 74.55 | 0.00 | 7.68 | 0.00 |
time (sec) |
N/A | 0.284 | 7.819 | 0.098 | 0.000 | 0.681 | 0.000 | 0.524 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 108 | 142 | 73 | 0 | 0 | 19305 | 0 | 808 | 0 |
N.S. |
1 | 1.31 | 0.68 | 0.00 | 0.00 | 178.75 | 0.00 | 7.48 | 0.00 |
time (sec) |
N/A | 0.386 | 0.101 | 0.000 | 0.000 | 1.280 | 0.000 | 0.650 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | B | F | B | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 131 | 148 | 1375 | 0 | 0 | 10671 | 0 | 898 | 0 |
N.S. |
1 | 1.13 | 10.50 | 0.00 | 0.00 | 81.46 | 0.00 | 6.85 | 0.00 |
time (sec) |
N/A | 0.441 | 8.660 | 0.000 | 0.000 | 1.342 | 0.000 | 0.744 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 35 | 62 | 0 | 543 | 0 | 58 | 63 |
N.S. |
1 | 1.00 | 1.40 | 2.48 | 0.00 | 21.72 | 0.00 | 2.32 | 2.52 |
time (sec) |
N/A | 0.195 | 0.027 | 0.169 | 0.000 | 0.259 | 0.000 | 0.274 | 0.185 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | C | F | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 37 | 66 | 0 | 175 | 0 | 58 | 22 |
N.S. |
1 | 1.00 | 1.37 | 2.44 | 0.00 | 6.48 | 0.00 | 2.15 | 0.81 |
time (sec) |
N/A | 0.202 | 0.025 | 0.167 | 0.000 | 0.250 | 0.000 | 0.282 | 1.867 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 90 | 95 | 91 | 194 | 2074 | 100 | 142 | 91 |
N.S. |
1 | 1.01 | 1.07 | 1.02 | 2.18 | 23.30 | 1.12 | 1.60 | 1.02 |
time (sec) |
N/A | 0.292 | 0.750 | 0.088 | 0.273 | 0.289 | 0.147 | 0.298 | 1.869 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 40 | 40 | 41 | 73 | 95 | 102 | 25 | 38 |
N.S. |
1 | 1.05 | 1.05 | 1.08 | 1.92 | 2.50 | 2.68 | 0.66 | 1.00 |
time (sec) |
N/A | 0.317 | 0.085 | 0.084 | 0.285 | 0.265 | 0.254 | 0.272 | 0.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 132 | 166 | 620 | 0 | 11528 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 1.34 | 5.00 | 0.00 | 92.97 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.399 | 4.547 | 0.898 | 0.000 | 0.547 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 90 | 86 | 116 | 0 | 5136 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.97 | 1.30 | 0.00 | 57.71 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.328 | 0.078 | 0.714 | 0.000 | 0.435 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 43 | 40 | 37 | 0 | 1286 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 1.00 | 0.92 | 0.00 | 32.15 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.261 | 0.022 | 0.562 | 0.000 | 0.406 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 77 | 73 | 431 | 0 | 3914 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.99 | 5.82 | 0.00 | 52.89 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.304 | 0.543 | 0.681 | 0.000 | 0.482 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 118 | 135 | 113 | 637 | 0 | 16463 | 0 | 0 | 0 |
N.S. |
1 | 1.14 | 0.96 | 5.40 | 0.00 | 139.52 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.375 | 0.877 | 0.711 | 0.000 | 2.040 | 0.000 | 0.000 | 0.000 |