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 | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 22 | 22 | 17 | 22 | 81 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 0.85 | 1.10 | 4.05 | 1.10 |
time (sec) |
N/A | 0.185 | 1.065 | 0.175 | 0.505 | 0.072 | 0.412 | 0.173 | 0.165 | 42.285 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 2505 | 48 | 19 | 22 | 226 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 125.25 | 2.40 | 0.95 | 1.10 | 11.30 | 1.10 |
time (sec) |
N/A | 0.183 | 2.055 | 0.816 | 3.957 | 0.085 | 1.427 | 0.184 | 0.171 | 40.562 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 76 | 70 | 73 | 86 | 66 | 0 | 400 | 16 | 0 |
N.S. |
1 | 0.97 | 0.90 | 0.94 | 1.10 | 0.85 | 0.00 | 5.13 | 0.21 | 0.00 |
time (sec) |
N/A | 0.620 | 0.124 | 1.810 | 0.080 | 0.085 | 0.000 | 0.119 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 55 | 52 | 57 | 76 | 56 | 0 | 251 | 51 | 0 |
N.S. |
1 | 0.92 | 0.87 | 0.95 | 1.27 | 0.93 | 0.00 | 4.18 | 0.85 | 0.00 |
time (sec) |
N/A | 0.529 | 0.074 | 1.402 | 0.078 | 0.078 | 0.000 | 0.117 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 34 | 32 | 38 | 58 | 34 | 0 | 132 | 12 | 0 |
N.S. |
1 | 1.06 | 1.00 | 1.19 | 1.81 | 1.06 | 0.00 | 4.12 | 0.38 | 0.00 |
time (sec) |
N/A | 0.414 | 0.033 | 0.800 | 0.076 | 0.075 | 0.000 | 0.141 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 22 | 43 | 21 | 17 | 42 | 16 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.05 | 2.05 | 1.00 | 0.81 | 2.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.243 | 0.060 | 0.829 | 0.075 | 0.072 | 0.400 | 0.116 | 0.168 | 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 | 12 | 12 | 12 | 13 | 12 | 14 | 14 | 14 | 14 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.00 | 1.17 | 1.17 | 1.17 | 1.17 | 1.00 |
time (sec) |
N/A | 0.208 | 0.022 | 0.480 | 0.031 | 0.066 | 0.264 | 0.111 | 0.154 | 40.616 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 34 | 50 | 33 | 29 | 48 | 33 | 29 |
N.S. |
1 | 1.00 | 1.00 | 1.17 | 1.72 | 1.14 | 1.00 | 1.66 | 1.14 | 1.00 |
time (sec) |
N/A | 0.267 | 0.007 | 0.833 | 0.127 | 0.071 | 0.368 | 0.117 | 0.152 | 40.916 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 49 | 38 | 46 | 51 | 44 | 46 | 106 | 56 | 46 |
N.S. |
1 | 1.09 | 0.84 | 1.02 | 1.13 | 0.98 | 1.02 | 2.36 | 1.24 | 1.02 |
time (sec) |
N/A | 0.356 | 0.065 | 0.858 | 0.079 | 0.070 | 0.489 | 0.138 | 0.162 | 41.288 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 71 | 61 | 52 | 50 | 52 | 61 | 191 | 75 | 64 |
N.S. |
1 | 1.16 | 1.00 | 0.85 | 0.82 | 0.85 | 1.00 | 3.13 | 1.23 | 1.05 |
time (sec) |
N/A | 0.453 | 0.010 | 0.909 | 0.074 | 0.071 | 0.678 | 0.143 | 0.151 | 41.793 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 97 | 86 | 96 | 99 | 96 | 0 | 442 | 811 | 0 |
N.S. |
1 | 0.97 | 0.86 | 0.96 | 0.99 | 0.96 | 0.00 | 4.42 | 8.11 | 0.00 |
time (sec) |
N/A | 0.384 | 0.206 | 1.232 | 0.083 | 0.078 | 0.000 | 0.120 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 67 | 65 | 76 | 87 | 77 | 0 | 283 | 763 | 0 |
N.S. |
1 | 1.02 | 0.98 | 1.15 | 1.32 | 1.17 | 0.00 | 4.29 | 11.56 | 0.00 |
time (sec) |
N/A | 0.600 | 0.185 | 1.114 | 0.082 | 0.081 | 0.000 | 0.114 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 41 | 52 | 66 | 45 | 0 | 153 | 14 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.27 | 1.61 | 1.10 | 0.00 | 3.73 | 0.34 | 0.00 |
time (sec) |
N/A | 0.448 | 0.098 | 1.020 | 0.076 | 0.084 | 0.000 | 0.118 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 32 | 36 | 51 | 31 | 31 | 65 | 18 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.97 | 1.38 | 0.84 | 0.84 | 1.76 | 0.49 | 0.00 |
time (sec) |
N/A | 0.222 | 0.092 | 1.044 | 0.074 | 0.096 | 0.994 | 0.129 | 0.157 | 0.000 |
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 | 31 | 31 | 32 | 23 | 25 | 34 | 262 | 29 | 38 | 22 |
N.S. |
1 | 1.00 | 1.03 | 0.74 | 0.81 | 1.10 | 8.45 | 0.94 | 1.23 | 0.71 |
time (sec) |
N/A | 0.228 | 0.079 | 0.821 | 0.033 | 0.073 | 0.953 | 0.111 | 0.159 | 41.907 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 43 | 42 | 68 | 60 | 391 | 77 | 18 | 41 |
N.S. |
1 | 1.00 | 0.84 | 0.82 | 1.33 | 1.18 | 7.67 | 1.51 | 0.35 | 0.80 |
time (sec) |
N/A | 0.252 | 0.091 | 1.063 | 0.075 | 0.081 | 1.289 | 0.164 | 0.156 | 42.667 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 92 | 54 | 56 | 69 | 72 | 654 | 153 | 18 | 64 |
N.S. |
1 | 1.06 | 0.62 | 0.64 | 0.79 | 0.83 | 7.52 | 1.76 | 0.21 | 0.74 |
time (sec) |
N/A | 0.341 | 0.146 | 1.299 | 0.078 | 0.075 | 1.732 | 0.135 | 0.159 | 42.892 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 112 | 65 | 67 | 68 | 90 | 726 | 255 | 18 | 84 |
N.S. |
1 | 1.05 | 0.61 | 0.63 | 0.64 | 0.84 | 6.79 | 2.38 | 0.17 | 0.79 |
time (sec) |
N/A | 0.362 | 0.217 | 1.447 | 0.075 | 0.078 | 2.425 | 0.120 | 0.159 | 43.200 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 88 | 81 | 59 | 127 | 74 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.10 | 1.01 | 0.74 | 1.59 | 0.92 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.337 | 0.153 | 0.635 | 0.079 | 0.082 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 22 | 43 | 21 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 1.72 | 0.84 | 0.00 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.246 | 0.060 | 0.652 | 0.076 | 0.075 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 61 | 47 | 98 | 64 | 0 | 0 | 18 | 55 |
N.S. |
1 | 1.00 | 0.81 | 0.63 | 1.31 | 0.85 | 0.00 | 0.00 | 0.24 | 0.73 |
time (sec) |
N/A | 0.278 | 0.120 | 0.629 | 0.146 | 0.110 | 0.000 | 0.000 | 0.161 | 42.448 |
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 | 15 | 15 | 15 | 14 | 13 | 17 | 20 | 17 | 17 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 1.13 | 1.33 | 1.13 | 1.13 | 0.87 |
time (sec) |
N/A | 0.203 | 0.020 | 0.546 | 0.026 | 0.067 | 0.468 | 0.104 | 0.152 | 43.345 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 100 | 89 | 65 | 74 | 85 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.03 | 0.92 | 0.67 | 0.76 | 0.88 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.342 | 0.187 | 0.762 | 0.081 | 0.080 | 0.000 | 0.000 | 0.157 | 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 | 8 | 8 | 8 | 7 | 6 | 6 | 8 | 6 | 5 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.75 | 0.75 | 1.00 | 0.75 | 0.62 | 0.75 |
time (sec) |
N/A | 0.192 | 0.020 | 0.191 | 0.027 | 0.071 | 0.097 | 0.107 | 0.162 | 42.308 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 18 | 23 | 15 | 15 | 15 | 29 | 15 | 17 | 14 |
N.S. |
1 | 0.86 | 1.10 | 0.71 | 0.71 | 0.71 | 1.38 | 0.71 | 0.81 | 0.67 |
time (sec) |
N/A | 0.216 | 0.034 | 0.792 | 0.049 | 0.076 | 0.159 | 0.125 | 0.153 | 42.072 |
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 | 22 | 22 | 22 | 17 | 16 | 16 | 20 | 16 | 13 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.73 | 0.73 | 0.91 | 0.73 | 0.59 | 0.73 |
time (sec) |
N/A | 0.232 | 0.030 | 0.237 | 0.029 | 0.075 | 0.088 | 0.131 | 0.164 | 40.526 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 76 | 41 | 19 | 30 | 37 | 379 | 30 | 43 | 34 |
N.S. |
1 | 1.10 | 0.59 | 0.28 | 0.43 | 0.54 | 5.49 | 0.43 | 0.62 | 0.49 |
time (sec) |
N/A | 0.284 | 0.058 | 0.394 | 0.029 | 0.082 | 0.407 | 0.110 | 0.163 | 41.814 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 98 | 62 | 59 | 47 | 51 | 71 | 47 | 64 | 58 |
N.S. |
1 | 1.13 | 0.71 | 0.68 | 0.54 | 0.59 | 0.82 | 0.54 | 0.74 | 0.67 |
time (sec) |
N/A | 0.490 | 0.066 | 0.829 | 0.030 | 0.080 | 2.893 | 0.110 | 0.158 | 43.414 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 20 | 20 | 17 | 20 | 23 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.11 | 0.94 | 1.11 | 1.28 | 1.11 |
time (sec) |
N/A | 0.186 | 1.846 | 0.227 | 1.559 | 0.092 | 10.721 | 0.857 | 0.168 | 42.126 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 22 | 22 | 19 | 22 | 24 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 0.95 | 1.10 | 1.20 | 1.10 |
time (sec) |
N/A | 0.195 | 1.892 | 0.224 | 1.337 | 0.089 | 33.273 | 4.547 | 0.168 | 42.761 |
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 | 92 | 92 | 88 | 0 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.333 | 0.204 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 24 | 24 | 20 | 24 | 33 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.91 | 1.09 | 1.50 | 1.09 |
time (sec) |
N/A | 0.254 | 1.967 | 0.279 | 1.265 | 0.082 | 9.103 | 0.892 | 0.181 | 43.120 |
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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 132 | 148 | 0 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.424 | 0.948 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 26 | 26 | 22 | 26 | 34 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.08 | 0.92 | 1.08 | 1.42 | 1.08 |
time (sec) |
N/A | 0.259 | 2.118 | 0.250 | 1.337 | 0.089 | 26.100 | 4.325 | 0.174 | 42.721 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 23 | 24 | 91 | 23 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.96 | 3.64 | 0.92 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.255 | 0.079 | 0.676 | 0.166 | 0.078 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 37 | 40 | 100 | 36 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.93 | 2.33 | 0.84 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.236 | 0.103 | 0.872 | 0.249 | 0.085 | 0.000 | 0.000 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 54 | 52 | 181 | 50 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.00 | 0.81 | 0.78 | 2.70 | 0.75 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.283 | 0.129 | 0.983 | 0.267 | 0.077 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 66 | 66 | 189 | 62 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.84 | 2.39 | 0.78 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.287 | 0.124 | 2.474 | 0.266 | 0.079 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 95 | 74 | 0 | 0 | 0 | 0 | 10 | 0 |
N.S. |
1 | 1.00 | 1.09 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.225 | 0.105 | 0.340 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 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 | 100 | 94 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.271 | 0.312 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 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 | 187 | 187 | 177 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.312 | 0.419 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 118 | 110 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 1.08 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.278 | 0.223 | 0.465 | 0.000 | 0.000 | 0.000 | 0.000 | 0.152 | 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 | 139 | 139 | 129 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.356 | 0.590 | 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 | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 237 | 237 | 225 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.452 | 0.640 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 33 | 30 | 36 | 32 | 32 | 56 | 0 | 30 | 0 |
N.S. |
1 | 0.94 | 0.86 | 1.03 | 0.91 | 0.91 | 1.60 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.280 | 0.079 | 0.799 | 0.038 | 0.090 | 3.288 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 32 | 29 | 35 | 29 | 29 | 56 | 0 | 29 | 0 |
N.S. |
1 | 0.94 | 0.85 | 1.03 | 0.85 | 0.85 | 1.65 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.281 | 0.071 | 1.006 | 0.049 | 0.075 | 3.310 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 42 | 47 | 44 | 0 | 47 | 0 | 0 | 19 | 0 |
N.S. |
1 | 0.91 | 1.02 | 0.96 | 0.00 | 1.02 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.444 | 0.086 | 0.867 | 0.000 | 0.080 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 67 | 58 | 66 | 0 | 53 | 0 | 0 | 54 | 0 |
N.S. |
1 | 0.99 | 0.85 | 0.97 | 0.00 | 0.78 | 0.00 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.314 | 0.151 | 1.368 | 0.000 | 0.114 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 113 | 95 | 99 | 0 | 95 | 0 | 0 | 746 | 0 |
N.S. |
1 | 0.99 | 0.83 | 0.87 | 0.00 | 0.83 | 0.00 | 0.00 | 6.54 | 0.00 |
time (sec) |
N/A | 0.411 | 0.214 | 5.130 | 0.000 | 0.095 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 65 | 68 | 65 | 0 | 68 | 0 | 0 | 62 | 0 |
N.S. |
1 | 0.83 | 0.87 | 0.83 | 0.00 | 0.87 | 0.00 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.527 | 0.149 | 0.842 | 0.000 | 0.079 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 95 | 82 | 89 | 0 | 88 | 0 | 0 | 816 | 0 |
N.S. |
1 | 0.98 | 0.85 | 0.92 | 0.00 | 0.91 | 0.00 | 0.00 | 8.41 | 0.00 |
time (sec) |
N/A | 0.350 | 0.198 | 1.376 | 0.000 | 0.092 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 165 | 141 | 144 | 0 | 143 | 0 | 0 | 803 | 0 |
N.S. |
1 | 0.99 | 0.84 | 0.86 | 0.00 | 0.86 | 0.00 | 0.00 | 4.81 | 0.00 |
time (sec) |
N/A | 0.494 | 0.437 | 5.293 | 0.000 | 0.092 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | C | A | F | C | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 209 | 173 | 586 | 974 | 255 | 0 | 509 | 1101 | 231 |
N.S. |
1 | 0.94 | 0.78 | 2.63 | 4.37 | 1.14 | 0.00 | 2.28 | 4.94 | 1.04 |
time (sec) |
N/A | 0.427 | 1.067 | 1.766 | 1.008 | 0.086 | 0.000 | 0.182 | 0.215 | 39.761 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | C | A | F | C | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 142 | 117 | 291 | 564 | 162 | 0 | 331 | 683 | 136 |
N.S. |
1 | 0.95 | 0.78 | 1.94 | 3.76 | 1.08 | 0.00 | 2.21 | 4.55 | 0.91 |
time (sec) |
N/A | 0.315 | 0.653 | 1.431 | 0.633 | 0.087 | 0.000 | 0.169 | 0.206 | 0.213 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | C | A | F | C | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 67 | 66 | 120 | 271 | 80 | 0 | 233 | 53 | 58 |
N.S. |
1 | 0.97 | 0.96 | 1.74 | 3.93 | 1.16 | 0.00 | 3.38 | 0.77 | 0.84 |
time (sec) |
N/A | 0.244 | 0.243 | 1.287 | 0.354 | 0.091 | 0.000 | 0.190 | 0.172 | 0.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 39 | 42 | 53 | 45 | 0 | 143 | 23 | 41 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.36 | 1.15 | 0.00 | 3.67 | 0.59 | 1.05 |
time (sec) |
N/A | 0.179 | 0.019 | 0.464 | 0.043 | 0.077 | 0.000 | 0.127 | 0.165 | 0.087 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 20 | 31 | 29 | 20 | 31 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.72 | 1.61 | 1.11 | 1.72 | 1.11 |
time (sec) |
N/A | 0.184 | 4.061 | 0.337 | 0.235 | 0.072 | 0.847 | 0.236 | 0.164 | 39.743 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 20 | 42 | 31 | 20 | 42 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 2.33 | 1.72 | 1.11 | 2.33 | 1.11 |
time (sec) |
N/A | 0.180 | 7.375 | 0.329 | 0.246 | 0.080 | 2.333 | 2.437 | 0.191 | 40.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 337 | 311 | 440 | 277 | 0 | 398 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.92 | 1.31 | 0.82 | 0.00 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.542 | 6.700 | 2.181 | 0.000 | 0.110 | 0.000 | 0.000 | 14.624 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 216 | 265 | 196 | 0 | 262 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 1.14 | 0.84 | 0.00 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.413 | 1.566 | 1.756 | 0.000 | 0.093 | 0.000 | 0.000 | 0.676 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 112 | 95 | 101 | 0 | 130 | 0 | 0 | 53 | 0 |
N.S. |
1 | 0.93 | 0.79 | 0.84 | 0.00 | 1.08 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.299 | 0.523 | 1.300 | 0.000 | 0.089 | 0.000 | 0.000 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 59 | 60 | 52 | 0 | 73 | 0 | 0 | 23 | 52 |
N.S. |
1 | 0.98 | 1.00 | 0.87 | 0.00 | 1.22 | 0.00 | 0.00 | 0.38 | 0.87 |
time (sec) |
N/A | 0.245 | 0.041 | 0.668 | 0.000 | 0.081 | 0.000 | 0.000 | 0.187 | 40.376 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 20 | 31 | 26 | 20 | 31 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.72 | 1.44 | 1.11 | 1.72 | 1.11 |
time (sec) |
N/A | 0.176 | 1.674 | 0.390 | 0.209 | 0.073 | 19.665 | 0.141 | 0.185 | 40.799 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 20 | 42 | 0 | 20 | 42 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 2.33 | 0.00 | 1.11 | 2.33 | 1.11 |
time (sec) |
N/A | 0.176 | 25.849 | 0.407 | 0.218 | 0.084 | 0.000 | 0.280 | 0.200 | 46.432 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 341 | 321 | 218 | 690 | 1824 | 328 | 0 | 523 | 1146 | 0 |
N.S. |
1 | 0.94 | 0.64 | 2.02 | 5.35 | 0.96 | 0.00 | 1.53 | 3.36 | 0.00 |
time (sec) |
N/A | 0.561 | 3.142 | 2.375 | 1.673 | 0.124 | 0.000 | 0.299 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 256 | 242 | 151 | 438 | 1038 | 208 | 0 | 345 | 713 | 0 |
N.S. |
1 | 0.95 | 0.59 | 1.71 | 4.05 | 0.81 | 0.00 | 1.35 | 2.79 | 0.00 |
time (sec) |
N/A | 0.414 | 1.973 | 1.964 | 0.868 | 0.086 | 0.000 | 0.293 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 117 | 114 | 209 | 483 | 131 | 0 | 247 | 55 | 0 |
N.S. |
1 | 0.96 | 0.93 | 1.71 | 3.96 | 1.07 | 0.00 | 2.02 | 0.45 | 0.00 |
time (sec) |
N/A | 0.301 | 0.705 | 1.289 | 0.441 | 0.084 | 0.000 | 0.254 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | F | C | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 67 | 87 | 69 | 89 | 0 | 151 | 24 | 95 |
N.S. |
1 | 1.00 | 0.81 | 1.05 | 0.83 | 1.07 | 0.00 | 1.82 | 0.29 | 1.14 |
time (sec) |
N/A | 0.261 | 0.061 | 0.655 | 0.045 | 0.081 | 0.000 | 0.184 | 0.194 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 22 | 32 | 31 | 22 | 32 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.60 | 1.55 | 1.10 | 1.60 | 1.10 |
time (sec) |
N/A | 0.176 | 9.115 | 0.396 | 0.266 | 0.079 | 0.844 | 0.376 | 0.179 | 39.889 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 22 | 43 | 32 | 22 | 43 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 2.15 | 1.60 | 1.10 | 2.15 | 1.10 |
time (sec) |
N/A | 0.179 | 10.117 | 0.401 | 0.370 | 0.078 | 2.335 | 6.543 | 0.182 | 40.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 434 | 414 | 353 | 0 | 0 | 591 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.81 | 0.00 | 0.00 | 1.36 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.499 | 18.073 | 0.000 | 0.000 | 0.104 | 0.000 | 0.000 | 0.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 280 | 269 | 300 | 0 | 0 | 409 | 0 | 0 | 127 | 0 |
N.S. |
1 | 0.96 | 1.07 | 0.00 | 0.00 | 1.46 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.389 | 12.587 | 0.000 | 0.000 | 0.099 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 227 | 381 | 0 | 0 | 263 | 0 | 0 | 79 | 0 |
N.S. |
1 | 0.97 | 1.62 | 0.00 | 0.00 | 1.12 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.323 | 10.849 | 0.000 | 0.000 | 0.093 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 115 | 0 | 0 | 113 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 1.07 | 0.00 | 0.00 | 1.06 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.235 | 0.152 | 0.000 | 0.000 | 0.082 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 22 | 44 | 44 | 22 | 44 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 2.20 | 2.20 | 1.10 | 2.20 | 1.10 |
time (sec) |
N/A | 0.184 | 24.597 | 0.450 | 0.329 | 0.075 | 0.988 | 2.689 | 0.206 | 39.389 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 22 | 55 | 46 | 22 | 55 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 2.75 | 2.30 | 1.10 | 2.75 | 1.10 |
time (sec) |
N/A | 0.183 | 56.975 | 0.444 | 0.346 | 0.077 | 2.593 | 3.793 | 0.184 | 39.941 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 371 | 345 | 467 | 274 | 0 | 392 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 1.26 | 0.74 | 0.00 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.623 | 2.864 | 2.743 | 0.000 | 0.126 | 0.000 | 0.000 | 0.976 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 184 | 242 | 150 | 0 | 233 | 0 | 0 | 93 | 0 |
N.S. |
1 | 0.93 | 1.22 | 0.76 | 0.00 | 1.18 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.421 | 1.111 | 1.748 | 0.000 | 0.101 | 0.000 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 110 | 100 | 80 | 0 | 137 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.05 | 0.95 | 0.76 | 0.00 | 1.30 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.343 | 0.189 | 0.892 | 0.000 | 0.088 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 22 | 51 | 27 | 22 | 51 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 2.55 | 1.35 | 1.10 | 2.55 | 1.10 |
time (sec) |
N/A | 0.180 | 3.971 | 0.523 | 0.412 | 0.079 | 18.976 | 0.759 | 0.193 | 40.413 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 22 | 62 | 0 | 22 | 62 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 3.10 | 0.00 | 1.10 | 3.10 | 1.10 |
time (sec) |
N/A | 0.180 | 32.520 | 0.521 | 0.441 | 0.083 | 0.000 | 1.080 | 0.201 | 42.982 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 330 | 313 | 620 | 0 | 0 | 576 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 1.88 | 0.00 | 0.00 | 1.75 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.471 | 4.272 | 0.000 | 0.000 | 0.100 | 0.000 | 0.000 | 0.450 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 227 | 705 | 0 | 0 | 367 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 3.00 | 0.00 | 0.00 | 1.56 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.310 | 2.462 | 0.000 | 0.000 | 0.095 | 0.000 | 0.000 | 1.453 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 203 | 0 | 0 | 185 | 0 | 0 | 66 | 0 |
N.S. |
1 | 1.00 | 1.90 | 0.00 | 0.00 | 1.73 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.231 | 0.484 | 0.000 | 0.000 | 0.087 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 22 | 74 | 39 | 22 | 74 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 3.70 | 1.95 | 1.10 | 3.70 | 1.10 |
time (sec) |
N/A | 0.178 | 5.370 | 0.530 | 0.555 | 0.070 | 70.163 | 4.906 | 0.221 | 41.342 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 22 | 85 | 0 | 22 | 85 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 4.25 | 0.00 | 1.10 | 4.25 | 1.10 |
time (sec) |
N/A | 0.180 | 36.467 | 0.549 | 0.562 | 0.091 | 0.000 | 6.895 | 0.248 | 46.578 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 410 | 414 | 138 | 1161 | 1101 | 196 | 529 | 698 | 383 | 0 |
N.S. |
1 | 1.01 | 0.34 | 2.83 | 2.69 | 0.48 | 1.29 | 1.70 | 0.93 | 0.00 |
time (sec) |
N/A | 0.578 | 1.846 | 1.234 | 0.091 | 0.088 | 0.371 | 0.129 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 189 | 85 | 347 | 348 | 86 | 221 | 218 | 147 | 0 |
N.S. |
1 | 1.02 | 0.46 | 1.88 | 1.88 | 0.46 | 1.19 | 1.18 | 0.79 | 0.00 |
time (sec) |
N/A | 0.343 | 0.664 | 1.148 | 0.050 | 0.080 | 0.238 | 0.116 | 0.176 | 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 | 54 | 52 | 50 | 61 | 62 | 44 | 65 | 44 | 40 | 43 |
N.S. |
1 | 0.96 | 0.93 | 1.13 | 1.15 | 0.81 | 1.20 | 0.81 | 0.74 | 0.80 |
time (sec) |
N/A | 0.272 | 0.066 | 0.520 | 0.039 | 0.075 | 0.195 | 0.134 | 0.176 | 39.230 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 238 | 258 | 238 | 793 | 0 | 250 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.08 | 1.00 | 3.33 | 0.00 | 1.05 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.886 | 2.375 | 0.849 | 0.000 | 0.088 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 339 | 355 | 397 | 1831 | 0 | 416 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.05 | 1.17 | 5.40 | 0.00 | 1.23 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 1.030 | 3.965 | 0.947 | 0.000 | 0.105 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 382 | 366 | 419 | 0 | 694 | 366 | 0 | 0 | 91 | 0 |
N.S. |
1 | 0.96 | 1.10 | 0.00 | 1.82 | 0.96 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.438 | 3.584 | 0.000 | 0.525 | 0.100 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 291 | 281 | 705 | 0 | 375 | 223 | 0 | 0 | 55 | 0 |
N.S. |
1 | 0.97 | 2.42 | 0.00 | 1.29 | 0.77 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.351 | 3.121 | 0.000 | 0.381 | 0.097 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 114 | 123 | 0 | 112 | 75 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.99 | 1.07 | 0.00 | 0.97 | 0.65 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.273 | 0.175 | 0.000 | 0.217 | 0.084 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 22 | 29 | 34 | 22 | 32 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.32 | 1.55 | 1.00 | 1.45 | 1.00 |
time (sec) |
N/A | 0.179 | 22.463 | 0.415 | 0.558 | 0.081 | 5.511 | 0.241 | 0.164 | 38.754 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 22 | 40 | 36 | 22 | 43 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.82 | 1.64 | 1.00 | 1.95 | 1.00 |
time (sec) |
N/A | 0.180 | 30.838 | 0.415 | 0.729 | 0.081 | 36.385 | 0.286 | 0.197 | 39.637 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 611 | 631 | 557 | 696 | 877 | 393 | 0 | 6587 | 85 | 0 |
N.S. |
1 | 1.03 | 0.91 | 1.14 | 1.44 | 0.64 | 0.00 | 10.78 | 0.14 | 0.00 |
time (sec) |
N/A | 0.915 | 2.445 | 4.397 | 0.663 | 0.098 | 0.000 | 3.409 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 301 | 318 | 367 | 295 | 407 | 203 | 0 | 2158 | 51 | 0 |
N.S. |
1 | 1.06 | 1.22 | 0.98 | 1.35 | 0.67 | 0.00 | 7.17 | 0.17 | 0.00 |
time (sec) |
N/A | 0.538 | 0.967 | 2.915 | 0.279 | 0.100 | 0.000 | 0.470 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 99 | 84 | 124 | 104 | 0 | 413 | 22 | 0 |
N.S. |
1 | 1.00 | 1.05 | 0.89 | 1.32 | 1.11 | 0.00 | 4.39 | 0.23 | 0.00 |
time (sec) |
N/A | 0.532 | 0.090 | 1.773 | 0.130 | 0.093 | 0.000 | 0.163 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 276 | 296 | 0 | 441 | 0 | 308 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.07 | 0.00 | 1.60 | 0.00 | 1.12 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 1.125 | 0.000 | 2.250 | 0.000 | 0.114 | 0.000 | 0.000 | 0.189 | 0.000 |