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 | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 104 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.255 | 1.520 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 49 | 52 | 42 | 61 | 148 | 185 | 0 | 0 |
N.S. |
1 | 0.91 | 0.96 | 0.78 | 1.13 | 2.74 | 3.43 | 0.00 | 0.00 |
time (sec) |
N/A | 0.175 | 0.032 | 1.756 | 0.289 | 0.409 | 1.165 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 78 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.262 | 0.140 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 72 | 70 | 74 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.230 | 0.134 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 78 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.278 | 0.145 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 72 | 70 | 74 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.233 | 0.137 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 64 | 56 | 0 | 102 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.00 | 1.75 | 0.00 | 3.19 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.177 | 0.025 | 0.294 | 0.000 | 0.343 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 60 | 49 | 0 | 80 | 0 | 40 | 0 |
N.S. |
1 | 1.00 | 1.88 | 1.53 | 0.00 | 2.50 | 0.00 | 1.25 | 0.00 |
time (sec) |
N/A | 0.180 | 0.023 | 0.071 | 0.000 | 0.289 | 0.000 | 0.297 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 64 | 0 | 0 | 102 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.00 | 0.00 | 0.00 | 3.19 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.180 | 0.026 | 0.000 | 0.000 | 0.600 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 76 | 0 | 0 | 102 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.05 | 0.00 | 0.00 | 2.76 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.187 | 0.045 | 0.000 | 0.000 | 0.318 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 72 | 60 | 0 | 111 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.18 | 1.82 | 0.00 | 3.36 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.173 | 0.236 | 2.440 | 0.000 | 0.573 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 68 | 51 | 0 | 88 | 0 | 47 | 0 |
N.S. |
1 | 1.00 | 2.06 | 1.55 | 0.00 | 2.67 | 0.00 | 1.42 | 0.00 |
time (sec) |
N/A | 0.184 | 0.026 | 0.063 | 0.000 | 0.527 | 0.000 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 72 | 0 | 0 | 111 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.18 | 0.00 | 0.00 | 3.36 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.178 | 0.319 | 0.000 | 0.000 | 0.917 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 78 | 0 | 0 | 106 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.05 | 0.00 | 0.00 | 2.79 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.190 | 0.094 | 0.000 | 0.000 | 0.262 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F(-2) | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 78 | 0 | 0 | 0 | 0 | 0 | 67 |
N.S. |
1 | 1.00 | 2.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.81 |
time (sec) |
N/A | 0.186 | 0.105 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 9.269 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | A | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 78 | 0 | 0 | 109 | 0 | 0 | 67 |
N.S. |
1 | 1.00 | 2.11 | 0.00 | 0.00 | 2.95 | 0.00 | 0.00 | 1.81 |
time (sec) |
N/A | 0.178 | 0.017 | 0.000 | 0.000 | 0.281 | 0.000 | 0.000 | 9.190 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F(-2) | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 78 | 0 | 0 | 0 | 0 | 0 | 67 |
N.S. |
1 | 1.00 | 2.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.81 |
time (sec) |
N/A | 0.181 | 0.016 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 9.150 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F(-2) | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 80 | 0 | 0 | 0 | 0 | 0 | 66 |
N.S. |
1 | 1.00 | 2.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.74 |
time (sec) |
N/A | 0.183 | 0.107 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 9.221 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | A | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 80 | 0 | 0 | 109 | 0 | 0 | 66 |
N.S. |
1 | 1.00 | 2.11 | 0.00 | 0.00 | 2.87 | 0.00 | 0.00 | 1.74 |
time (sec) |
N/A | 0.184 | 0.017 | 0.000 | 0.000 | 0.442 | 0.000 | 0.000 | 9.126 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F(-2) | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 80 | 0 | 0 | 0 | 0 | 0 | 66 |
N.S. |
1 | 1.00 | 2.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.74 |
time (sec) |
N/A | 0.180 | 0.017 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 9.148 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 218 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.269 | 0.568 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 156 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.260 | 0.355 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 102 | 120 | 106 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.18 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.275 | 0.284 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 111 | 123 | 116 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.268 | 0.349 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 111 | 123 | 166 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 1.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.267 | 0.625 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 177 | 0 | 0 | 0 | 0 | 0 | 82 |
N.S. |
1 | 1.00 | 1.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.85 |
time (sec) |
N/A | 0.252 | 0.234 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 9.170 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 87 | 101 | 134 | 0 | 0 | 0 | 0 | 0 | 82 |
N.S. |
1 | 1.16 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.94 |
time (sec) |
N/A | 0.244 | 0.178 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 9.142 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 88 | 0 | 0 | 0 | 0 | 0 | 83 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.89 |
time (sec) |
N/A | 0.241 | 0.084 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 9.164 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 104 | 0 | 0 | 0 | 0 | 0 | 83 |
N.S. |
1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.82 |
time (sec) |
N/A | 0.246 | 0.124 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 9.377 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 185 | 0 | 0 | 0 | 0 | 0 | 83 |
N.S. |
1 | 1.00 | 1.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.82 |
time (sec) |
N/A | 0.249 | 0.283 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 9.510 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 19 | 16 | 0 | 16 | 0 | 50 | 15 |
N.S. |
1 | 1.00 | 1.06 | 0.89 | 0.00 | 0.89 | 0.00 | 2.78 | 0.83 |
time (sec) |
N/A | 0.164 | 0.024 | 0.058 | 0.000 | 0.731 | 0.000 | 0.296 | 9.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 18 | 0 | 19 | 0 | 11 | 27 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.00 | 0.95 | 0.00 | 0.55 | 1.35 |
time (sec) |
N/A | 0.143 | 0.043 | 2.030 | 0.000 | 0.281 | 0.000 | 0.284 | 9.155 |
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 | 8 | 8 | 8 | 7 | 6 | 6 | 7 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.75 | 0.75 | 0.88 | 0.75 | 0.75 |
time (sec) |
N/A | 0.146 | 0.002 | 1.794 | 0.286 | 0.246 | 0.085 | 0.311 | 9.125 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 29 | 14 | 28 | 0 | 27 | 22 |
N.S. |
1 | 1.00 | 1.00 | 1.16 | 0.56 | 1.12 | 0.00 | 1.08 | 0.88 |
time (sec) |
N/A | 0.162 | 0.014 | 1.893 | 0.211 | 0.248 | 0.000 | 0.294 | 9.120 |
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 | 25 | 25 | 25 | 29 | 14 | 28 | 0 | 27 | 29 |
N.S. |
1 | 1.00 | 1.00 | 1.16 | 0.56 | 1.12 | 0.00 | 1.08 | 1.16 |
time (sec) |
N/A | 0.154 | 0.002 | 1.890 | 0.207 | 0.248 | 0.000 | 0.290 | 8.945 |
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 | 25 | 25 | 25 | 29 | 14 | 28 | 0 | 14 | 22 |
N.S. |
1 | 1.00 | 1.00 | 1.16 | 0.56 | 1.12 | 0.00 | 0.56 | 0.88 |
time (sec) |
N/A | 0.167 | 0.013 | 2.412 | 0.224 | 0.244 | 0.000 | 0.284 | 8.941 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | C | F | F | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 988 | 61 | 61 | 0 | 0 | 0 | 0 | 0 | 42 |
N.S. |
1 | 0.06 | 0.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 |
time (sec) |
N/A | 0.199 | 10.024 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 9.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | C | F | F | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 487 | 61 | 61 | 0 | 0 | 0 | 0 | 0 | 42 |
N.S. |
1 | 0.13 | 0.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 |
time (sec) |
N/A | 0.199 | 10.021 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 9.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 89 | 92 | 92 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.241 | 0.157 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 73 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.220 | 0.174 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 66 | 72 | 74 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.252 | 0.142 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 82 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.222 | 0.215 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 84 | 95 | 83 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.251 | 0.183 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 43 | 0 | 0 | 64 | 0 | 0 | 76 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 1.45 | 0.00 | 0.00 | 1.73 |
time (sec) |
N/A | 0.174 | 0.076 | 0.000 | 0.000 | 0.468 | 0.000 | 0.000 | 9.155 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 43 | 0 | 0 | 61 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 1.39 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.190 | 0.002 | 0.000 | 0.000 | 0.266 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 45 | 0 | 0 | 76 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 1.65 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.212 | 0.088 | 0.000 | 0.000 | 0.255 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 45 | 0 | 0 | 79 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 1.72 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.177 | 0.004 | 0.000 | 0.000 | 0.268 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 36 | 40 | 17 | 44 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.91 | 0.39 | 1.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.190 | 0.070 | 1.808 | 0.245 | 0.359 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 36 | 40 | 17 | 44 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.91 | 0.39 | 1.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.191 | 0.069 | 1.802 | 0.239 | 0.423 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 36 | 40 | 17 | 44 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.91 | 0.39 | 1.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.193 | 0.067 | 1.829 | 0.234 | 0.690 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 47 | 0 | 0 | 47 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.82 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.206 | 0.052 | 0.000 | 0.000 | 0.253 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 45 | 0 | 0 | 54 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.74 | 0.00 | 0.00 | 0.89 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.202 | 0.031 | 0.000 | 0.000 | 0.259 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 40 | 0 | 0 | 76 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.00 | 0.00 | 1.95 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.181 | 0.144 | 0.000 | 0.000 | 0.267 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 38 | 86 | 0 | 64 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.95 | 2.15 | 0.00 | 1.60 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.224 | 0.121 | 2.915 | 0.000 | 0.453 | 0.000 | 0.000 | 0.000 |