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 | B | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 53 | 20 | 18 | 85 | 20 | 22 | 23 | 62 | 24 |
N.S. |
1 | 2.41 | 0.91 | 0.82 | 3.86 | 0.91 | 1.00 | 1.05 | 2.82 | 1.09 |
time (sec) |
N/A | 0.472 | 0.039 | 0.326 | 0.166 | 0.076 | 0.128 | 0.112 | 0.146 | 3.036 |
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 | 23 | 29 | 19 | 26 | 24 | 24 | 24 | 24 | 25 | 16 |
N.S. |
1 | 1.26 | 0.83 | 1.13 | 1.04 | 1.04 | 1.04 | 1.04 | 1.09 | 0.70 |
time (sec) |
N/A | 0.271 | 0.110 | 0.142 | 0.035 | 0.077 | 0.058 | 0.118 | 0.152 | 0.031 |
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 | 28 | 19 | 21 | 20 | 1341 | 244 | 245 | 739 | 471 | 8176 |
N.S. |
1 | 0.68 | 0.75 | 0.71 | 47.89 | 8.71 | 8.75 | 26.39 | 16.82 | 292.00 |
time (sec) |
N/A | 1.968 | 5.040 | 0.692 | 7.002 | 0.074 | 0.617 | 0.295 | 0.162 | 9.258 |
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 | 18 | 34 | 18 | 17 | 16 | 16 | 15 | 16 | 17 | 16 |
N.S. |
1 | 1.89 | 1.00 | 0.94 | 0.89 | 0.89 | 0.83 | 0.89 | 0.94 | 0.89 |
time (sec) |
N/A | 0.484 | 0.058 | 0.220 | 0.077 | 0.086 | 0.072 | 0.119 | 0.141 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 64 | 0 | 45 | 60 | 64 | 63 | 57 |
N.S. |
1 | 1.00 | 1.00 | 3.37 | 0.00 | 2.37 | 3.16 | 3.37 | 3.32 | 3.00 |
time (sec) |
N/A | 0.466 | 0.014 | 1.914 | 0.000 | 0.076 | 0.181 | 0.148 | 0.141 | 3.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 16 | 17 | 32 | 38 | 29 | 16 | 18 | 16 |
N.S. |
1 | 0.00 | 0.76 | 0.81 | 1.52 | 1.81 | 1.38 | 0.76 | 0.86 | 0.76 |
time (sec) |
N/A | 0.000 | 0.044 | 0.312 | 0.132 | 0.080 | 0.216 | 0.113 | 0.148 | 3.191 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 90 | 100 | 103 | 131 | 131 | 114 | 0 | 166 | 103 |
N.S. |
1 | 2.90 | 3.23 | 3.32 | 4.23 | 4.23 | 3.68 | 0.00 | 5.35 | 3.32 |
time (sec) |
N/A | 2.003 | 0.133 | 13.023 | 0.050 | 0.092 | 0.241 | 0.000 | 0.147 | 3.266 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 28 | 12 | 48 | 11 | 14 | 22 | 29 | 11 |
N.S. |
1 | 0.00 | 1.40 | 0.60 | 2.40 | 0.55 | 0.70 | 1.10 | 1.45 | 0.55 |
time (sec) |
N/A | 0.000 | 0.104 | 0.095 | 0.024 | 0.078 | 0.075 | 0.111 | 0.141 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 0 | 20 | 18 | 22 | 20 | 19 | 19 | 18 | 19 |
N.S. |
1 | 0.00 | 1.43 | 1.29 | 1.57 | 1.43 | 1.36 | 1.36 | 1.29 | 1.36 |
time (sec) |
N/A | 0.000 | 0.363 | 0.183 | 0.061 | 0.078 | 0.110 | 0.112 | 0.146 | 0.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 59 | 29 | 82 | 95 | 81 | 83 | 95 | 217 | 104 |
N.S. |
1 | 1.90 | 0.94 | 2.65 | 3.06 | 2.61 | 2.68 | 3.06 | 7.00 | 3.35 |
time (sec) |
N/A | 5.487 | 0.143 | 6.788 | 0.373 | 0.099 | 0.414 | 0.630 | 200.024 | 3.559 |
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 | 8 | 8 | 9 | 8 | 8 | 7 | 8 | 8 | 8 |
N.S. |
1 | 0.67 | 0.67 | 0.75 | 0.67 | 0.67 | 0.58 | 0.67 | 0.67 | 0.67 |
time (sec) |
N/A | 0.133 | 0.000 | 0.033 | 0.031 | 0.062 | 0.024 | 0.118 | 0.156 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 26 | 30 | 26 | 29 | 26 | 59 | 38 | 31 |
N.S. |
1 | 0.00 | 0.93 | 1.07 | 0.93 | 1.04 | 0.93 | 2.11 | 1.36 | 1.11 |
time (sec) |
N/A | 0.000 | 1.133 | 0.342 | 0.169 | 0.080 | 0.124 | 0.123 | 0.158 | 3.171 |
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 | 31 | 39 | 33 | 31 | 33 | 53 | 26 | 45 | 82 | 32 |
N.S. |
1 | 1.26 | 1.06 | 1.00 | 1.06 | 1.71 | 0.84 | 1.45 | 2.65 | 1.03 |
time (sec) |
N/A | 2.582 | 5.049 | 2.365 | 0.080 | 0.086 | 0.248 | 0.117 | 0.178 | 3.234 |
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 | 35 | 33 | 26 | 27 | 32 | 17 | 34 | 34 | 29 |
N.S. |
1 | 1.21 | 1.14 | 0.90 | 0.93 | 1.10 | 0.59 | 1.17 | 1.17 | 1.00 |
time (sec) |
N/A | 0.706 | 0.030 | 0.306 | 0.058 | 0.088 | 0.064 | 0.122 | 0.180 | 3.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 60 | 48 | 64 | 139 | 75 | 85 | 89 | 60 | 15 |
N.S. |
1 | 3.53 | 2.82 | 3.76 | 8.18 | 4.41 | 5.00 | 5.24 | 3.53 | 0.88 |
time (sec) |
N/A | 0.272 | 0.016 | 0.342 | 0.108 | 0.087 | 0.139 | 0.118 | 0.165 | 2.847 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | F(-2) | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 77 | 23 | 21 | 0 | 25 | 0 | 25 | 26 | 20 |
N.S. |
1 | 3.08 | 0.92 | 0.84 | 0.00 | 1.00 | 0.00 | 1.00 | 1.04 | 0.80 |
time (sec) |
N/A | 0.749 | 0.111 | 0.434 | 0.000 | 0.088 | 0.000 | 0.255 | 0.187 | 3.491 |
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 | 18 | 12 | 18 | 13 | 12 | 12 | 10 | 13 | 12 | 12 |
N.S. |
1 | 0.67 | 1.00 | 0.72 | 0.67 | 0.67 | 0.56 | 0.72 | 0.67 | 0.67 |
time (sec) |
N/A | 0.158 | 0.004 | 0.151 | 0.027 | 0.076 | 0.050 | 0.108 | 0.167 | 2.876 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 0 | 34 | 33 | 36 | 36 | 39 | 46 | 54 | 30 |
N.S. |
1 | 0.00 | 0.81 | 0.79 | 0.86 | 0.86 | 0.93 | 1.10 | 1.29 | 0.71 |
time (sec) |
N/A | 0.000 | 0.044 | 0.489 | 0.109 | 0.108 | 0.163 | 0.139 | 0.168 | 3.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 31 | 16 | 12 | 38 | 11 | 14 | 38 | 15 | 7 |
N.S. |
1 | 1.48 | 0.76 | 0.57 | 1.81 | 0.52 | 0.67 | 1.81 | 0.71 | 0.33 |
time (sec) |
N/A | 0.169 | 0.002 | 0.097 | 0.024 | 0.096 | 0.024 | 0.104 | 0.164 | 2.923 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 38 | 39 | 45 | 41 | 39 | 67 | 73 | 36 |
N.S. |
1 | 0.00 | 1.27 | 1.30 | 1.50 | 1.37 | 1.30 | 2.23 | 2.43 | 1.20 |
time (sec) |
N/A | 0.000 | 0.090 | 15.585 | 0.406 | 0.111 | 0.480 | 1.775 | 0.178 | 3.751 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | B | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 128 | 60 | 53 | 0 | 57 | 100 | 56 | 54 | 58 |
N.S. |
1 | 4.13 | 1.94 | 1.71 | 0.00 | 1.84 | 3.23 | 1.81 | 1.74 | 1.87 |
time (sec) |
N/A | 1.350 | 0.209 | 0.507 | 0.000 | 0.090 | 0.194 | 0.131 | 0.167 | 2.974 |
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 | 26 | 20 | 20 | 25 | 19 | 24 | 17 | 24 | 30 | 20 |
N.S. |
1 | 0.77 | 0.77 | 0.96 | 0.73 | 0.92 | 0.65 | 0.92 | 1.15 | 0.77 |
time (sec) |
N/A | 0.272 | 0.141 | 0.266 | 0.084 | 0.080 | 0.067 | 0.113 | 0.690 | 2.925 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 0 | 12 | 13 | 26 | 26 | 26 | 53 | 48 | 12 |
N.S. |
1 | 0.00 | 1.00 | 1.08 | 2.17 | 2.17 | 2.17 | 4.42 | 4.00 | 1.00 |
time (sec) |
N/A | 0.000 | 0.037 | 0.212 | 0.064 | 0.084 | 0.079 | 0.114 | 0.159 | 3.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | A | A | F | B | F(-1) |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 0 | 0 | 50 | 104 | 60 | 46 | 0 | 50 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.32 | 2.74 | 1.58 | 1.21 | 0.00 | 1.32 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 30.694 | 0.204 | 0.100 | 3.855 | 0.000 | 0.198 | 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 | 17 | 14 | 16 | 15 | 15 | 12 | 16 | 15 | 15 |
N.S. |
1 | 1.06 | 0.88 | 1.00 | 0.94 | 0.94 | 0.75 | 1.00 | 0.94 | 0.94 |
time (sec) |
N/A | 0.169 | 0.003 | 0.106 | 0.035 | 0.094 | 0.033 | 0.109 | 0.160 | 2.904 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 25 | 26 | 38 | 29 | 20 | 29 | 33 | 28 |
N.S. |
1 | 0.00 | 1.04 | 1.08 | 1.58 | 1.21 | 0.83 | 1.21 | 1.38 | 1.17 |
time (sec) |
N/A | 0.000 | 3.669 | 0.157 | 0.076 | 0.098 | 0.094 | 0.121 | 0.191 | 0.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 27 | 44 | 42 | 48 | 49 | 0 | 59 | 46 |
N.S. |
1 | 0.00 | 1.29 | 2.10 | 2.00 | 2.29 | 2.33 | 0.00 | 2.81 | 2.19 |
time (sec) |
N/A | 0.000 | 0.090 | 0.589 | 0.244 | 0.104 | 0.229 | 0.000 | 0.771 | 3.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 28 | 33 | 491 | 46 | 42 | 46 | 45 | 33 |
N.S. |
1 | 0.00 | 1.33 | 1.57 | 23.38 | 2.19 | 2.00 | 2.19 | 2.14 | 1.57 |
time (sec) |
N/A | 0.000 | 0.044 | 11.530 | 0.125 | 0.085 | 0.135 | 4.206 | 0.166 | 3.493 |
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 | 26 | 40 | 25 | 24 | 30 | 24 | 22 | 30 | 26 | 21 |
N.S. |
1 | 1.54 | 0.96 | 0.92 | 1.15 | 0.92 | 0.85 | 1.15 | 1.00 | 0.81 |
time (sec) |
N/A | 0.232 | 0.435 | 0.210 | 0.183 | 0.090 | 0.124 | 0.116 | 0.227 | 0.070 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 28 | 32 | 24 | 0 | 23 | 24 | 23 | 24 | 23 |
N.S. |
1 | 0.97 | 1.10 | 0.83 | 0.00 | 0.79 | 0.83 | 0.79 | 0.83 | 0.79 |
time (sec) |
N/A | 0.651 | 0.018 | 0.526 | 0.000 | 0.095 | 0.131 | 0.115 | 0.163 | 2.965 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 84 | 36 | 27 | 95 | 24 | 26 | 35 | 19 | 20 |
N.S. |
1 | 4.42 | 1.89 | 1.42 | 5.00 | 1.26 | 1.37 | 1.84 | 1.00 | 1.05 |
time (sec) |
N/A | 0.256 | 0.017 | 0.391 | 0.105 | 0.084 | 0.079 | 0.115 | 0.152 | 2.927 |
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 | 27 | 47 | 31 | 24 | 46 | 37 | 22 | 33 | 34 | 28 |
N.S. |
1 | 1.74 | 1.15 | 0.89 | 1.70 | 1.37 | 0.81 | 1.22 | 1.26 | 1.04 |
time (sec) |
N/A | 0.525 | 0.071 | 0.224 | 0.069 | 0.091 | 0.067 | 0.113 | 0.150 | 2.959 |
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 | 25 | 37 | 23 | 24 | 21 | 38 | 17 | 22 | 39 | 21 |
N.S. |
1 | 1.48 | 0.92 | 0.96 | 0.84 | 1.52 | 0.68 | 0.88 | 1.56 | 0.84 |
time (sec) |
N/A | 0.324 | 0.019 | 0.126 | 0.030 | 0.076 | 0.084 | 0.116 | 0.162 | 2.937 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 54 | 28 | 41 | 28 | 28 | 29 | 30 | 35 | 28 |
N.S. |
1 | 2.45 | 1.27 | 1.86 | 1.27 | 1.27 | 1.32 | 1.36 | 1.59 | 1.27 |
time (sec) |
N/A | 2.114 | 0.184 | 40.944 | 0.150 | 0.080 | 0.118 | 0.137 | 0.150 | 3.164 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 53 | 28 | 26 | 49 | 25 | 32 | 33 | 29 | 25 |
N.S. |
1 | 2.21 | 1.17 | 1.08 | 2.04 | 1.04 | 1.33 | 1.38 | 1.21 | 1.04 |
time (sec) |
N/A | 0.375 | 0.066 | 11.983 | 0.161 | 0.089 | 0.126 | 0.123 | 0.148 | 2.986 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 24 | 34 | 26 | 30 | 39 | 42 | 30 | 87 |
N.S. |
1 | 0.00 | 1.00 | 1.42 | 1.08 | 1.25 | 1.62 | 1.75 | 1.25 | 3.62 |
time (sec) |
N/A | 0.000 | 0.138 | 0.839 | 0.160 | 0.094 | 0.142 | 0.125 | 0.150 | 3.334 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 46 | 32 | 69 | 203 | 34 | 1417 | 54 | 37 |
N.S. |
1 | 0.00 | 1.35 | 0.94 | 2.03 | 5.97 | 1.00 | 41.68 | 1.59 | 1.09 |
time (sec) |
N/A | 0.000 | 0.097 | 92.948 | 0.125 | 0.094 | 0.203 | 0.204 | 0.152 | 3.125 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 51 | 42 | 36 | 0 | 37 | 31 | 54 | 57 | 39 |
N.S. |
1 | 2.04 | 1.68 | 1.44 | 0.00 | 1.48 | 1.24 | 2.16 | 2.28 | 1.56 |
time (sec) |
N/A | 0.471 | 0.088 | 0.494 | 0.000 | 0.083 | 0.143 | 0.122 | 0.148 | 0.092 |
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 | 24 | 6 | 6 | 5 | 4 | 4 | 5 | 5 | 4 | 4 |
N.S. |
1 | 0.25 | 0.25 | 0.21 | 0.17 | 0.17 | 0.21 | 0.21 | 0.17 | 0.17 |
time (sec) |
N/A | 0.125 | 0.000 | 0.022 | 0.024 | 0.083 | 0.022 | 0.112 | 0.151 | 0.038 |
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 | 16 | 14 | 14 | 14 | 14 | 13 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 0.93 | 0.93 | 0.93 | 0.93 | 0.87 | 1.00 |
time (sec) |
N/A | 0.136 | 0.001 | 0.141 | 0.031 | 0.085 | 0.023 | 0.113 | 0.153 | 2.912 |
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 | 27 | 10 | 12 | 9 | 9 | 9 | 8 | 9 | 8 | 8 |
N.S. |
1 | 0.37 | 0.44 | 0.33 | 0.33 | 0.33 | 0.30 | 0.33 | 0.30 | 0.30 |
time (sec) |
N/A | 0.133 | 0.000 | 0.033 | 0.031 | 0.088 | 0.016 | 0.110 | 0.157 | 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 | 11 | 14 | 19 | 17 | 16 | 16 | 15 | 16 | 19 | 16 |
N.S. |
1 | 1.27 | 1.73 | 1.55 | 1.45 | 1.45 | 1.36 | 1.45 | 1.73 | 1.45 |
time (sec) |
N/A | 0.146 | 0.000 | 0.050 | 0.027 | 0.106 | 0.018 | 0.110 | 0.152 | 0.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 24 | 25 | 35 | 27 | 22 | 41 | 47 | 0 |
N.S. |
1 | 0.00 | 0.96 | 1.00 | 1.40 | 1.08 | 0.88 | 1.64 | 1.88 | 0.00 |
time (sec) |
N/A | 0.000 | 0.082 | 9.704 | 0.125 | 0.088 | 0.653 | 0.279 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 23 | 80 | 31 | 27 | 261 | 271 | 76 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 3.20 | 1.24 | 1.08 | 10.44 | 10.84 | 3.04 |
time (sec) |
N/A | 1.045 | 0.100 | 114.962 | 0.265 | 0.092 | 0.111 | 0.128 | 0.172 | 3.054 |
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 | 18 | 14 | 17 | 15 | 17 | 30 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.12 | 0.88 | 1.06 | 0.94 | 1.06 | 1.88 | 1.06 |
time (sec) |
N/A | 0.295 | 0.006 | 0.162 | 0.106 | 0.088 | 0.056 | 0.120 | 0.148 | 0.136 |
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 | 19 | 15 | 15 | 14 | 15 | 15 | 15 | 17 | 15 | 13 |
N.S. |
1 | 0.79 | 0.79 | 0.74 | 0.79 | 0.79 | 0.79 | 0.89 | 0.79 | 0.68 |
time (sec) |
N/A | 0.219 | 0.005 | 0.100 | 0.034 | 0.110 | 0.048 | 0.114 | 0.154 | 0.029 |
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 | 29 | 28 | 24 | 21 | 19 | 25 | 19 | 20 | 29 | 23 |
N.S. |
1 | 0.97 | 0.83 | 0.72 | 0.66 | 0.86 | 0.66 | 0.69 | 1.00 | 0.79 |
time (sec) |
N/A | 0.199 | 0.002 | 0.077 | 0.025 | 0.089 | 0.050 | 0.113 | 0.147 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 48 | 30 | 115 | 35 | 37 | 35 | 60 | 86 |
N.S. |
1 | 0.00 | 1.50 | 0.94 | 3.59 | 1.09 | 1.16 | 1.09 | 1.88 | 2.69 |
time (sec) |
N/A | 0.000 | 0.103 | 0.848 | 0.541 | 0.086 | 0.389 | 0.376 | 0.150 | 3.502 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 30 | 25 | 27 | 35 | 26 | 24 | 41 | 27 |
N.S. |
1 | 0.00 | 1.11 | 0.93 | 1.00 | 1.30 | 0.96 | 0.89 | 1.52 | 1.00 |
time (sec) |
N/A | 0.000 | 0.170 | 0.210 | 0.151 | 0.100 | 0.067 | 0.147 | 0.147 | 2.966 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 27 | 30 | 69 | 57 | 27 | 89 | 130 | 51 |
N.S. |
1 | 0.00 | 0.90 | 1.00 | 2.30 | 1.90 | 0.90 | 2.97 | 4.33 | 1.70 |
time (sec) |
N/A | 0.000 | 0.059 | 23.135 | 0.162 | 0.100 | 0.098 | 0.157 | 0.153 | 3.117 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 24 | 32 | 0 | 31 | 26 | 0 | 33 | 32 |
N.S. |
1 | 0.00 | 1.04 | 1.39 | 0.00 | 1.35 | 1.13 | 0.00 | 1.43 | 1.39 |
time (sec) |
N/A | 0.000 | 0.301 | 14.284 | 0.000 | 0.105 | 0.888 | 0.000 | 0.153 | 3.770 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 22 | 19 | 18 | 36 | 22 | 17 | 22 | 21 | 22 |
N.S. |
1 | 1.16 | 1.00 | 0.95 | 1.89 | 1.16 | 0.89 | 1.16 | 1.11 | 1.16 |
time (sec) |
N/A | 0.186 | 0.004 | 0.213 | 0.036 | 0.100 | 0.085 | 0.113 | 0.152 | 3.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 30 | 37 | 32 | 52 | 27 | 0 | 40 | 49 |
N.S. |
1 | 0.00 | 0.94 | 1.16 | 1.00 | 1.62 | 0.84 | 0.00 | 1.25 | 1.53 |
time (sec) |
N/A | 0.000 | 5.214 | 72.263 | 0.214 | 0.084 | 0.431 | 0.000 | 0.154 | 3.165 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 60 | 81 | 71 | 75 | 81 | 158 | 90 |
N.S. |
1 | 1.00 | 1.00 | 2.50 | 3.38 | 2.96 | 3.12 | 3.38 | 6.58 | 3.75 |
time (sec) |
N/A | 7.795 | 0.104 | 1.272 | 0.316 | 0.099 | 0.246 | 0.425 | 200.025 | 3.268 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 48 | 31 | 28 | 83 | 33 | 87 | 35 | 54 | 82 |
N.S. |
1 | 2.82 | 1.82 | 1.65 | 4.88 | 1.94 | 5.12 | 2.06 | 3.18 | 4.82 |
time (sec) |
N/A | 0.317 | 0.056 | 0.415 | 0.220 | 0.091 | 0.237 | 0.164 | 0.169 | 3.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | A | B | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 53 | 18 | 48 | 67 | 39 | 42 | 0 | 48 | 47 |
N.S. |
1 | 2.41 | 0.82 | 2.18 | 3.05 | 1.77 | 1.91 | 0.00 | 2.18 | 2.14 |
time (sec) |
N/A | 0.337 | 0.028 | 0.369 | 0.026 | 0.093 | 0.114 | 0.000 | 0.162 | 2.960 |
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 | 34 | 23 | 21 | 19 | 18 | 18 | 15 | 18 | 19 | 18 |
N.S. |
1 | 0.68 | 0.62 | 0.56 | 0.53 | 0.53 | 0.44 | 0.53 | 0.56 | 0.53 |
time (sec) |
N/A | 0.187 | 0.006 | 0.852 | 0.029 | 0.094 | 0.071 | 0.103 | 0.163 | 2.982 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 46 | 53 | 3 | 55 | 56 | 61 | 67 | 53 |
N.S. |
1 | 0.00 | 1.59 | 1.83 | 0.10 | 1.90 | 1.93 | 2.10 | 2.31 | 1.83 |
time (sec) |
N/A | 0.000 | 4.541 | 0.402 | 0.099 | 0.090 | 0.121 | 0.131 | 0.151 | 3.134 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | B | B | B | B | F | B | F(-1) |
verified | N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 0 | 87 | 82 | 69 | 68 | 0 | 86 | 0 |
N.S. |
1 | 1.00 | 0.00 | 3.35 | 3.15 | 2.65 | 2.62 | 0.00 | 3.31 | 0.00 |
time (sec) |
N/A | 0.762 | 0.000 | 19.969 | 0.148 | 0.083 | 0.410 | 0.000 | 0.163 | 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 | 20 | 14 | 14 | 14 | 11 | 14 | 12 | 12 | 14 | 11 |
N.S. |
1 | 0.70 | 0.70 | 0.70 | 0.55 | 0.70 | 0.60 | 0.60 | 0.70 | 0.55 |
time (sec) |
N/A | 0.174 | 0.001 | 0.076 | 0.023 | 0.083 | 0.022 | 0.113 | 0.151 | 0.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | C | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 38 | 33 | 55 | 33 | 32 | 36 | 36 | 28 |
N.S. |
1 | 0.00 | 1.31 | 1.14 | 1.90 | 1.14 | 1.10 | 1.24 | 1.24 | 0.97 |
time (sec) |
N/A | 0.000 | 0.128 | 0.340 | 0.068 | 0.088 | 0.060 | 0.113 | 0.152 | 2.982 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | F(-1) | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 46 | 46 | 39 | 38 | 58 | 39 | 0 | 46 | 0 |
N.S. |
1 | 1.59 | 1.59 | 1.34 | 1.31 | 2.00 | 1.34 | 0.00 | 1.59 | 0.00 |
time (sec) |
N/A | 0.891 | 0.029 | 2.140 | 0.424 | 0.085 | 0.188 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | F | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 22 | 28 | 19 | 27 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.27 | 0.86 | 1.23 | 0.00 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.000 | 1.189 | 0.746 | 0.083 | 0.087 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 14 | 21 | 82 | 20 | 15 | 0 | 20 | 14 |
N.S. |
1 | 0.00 | 0.74 | 1.11 | 4.32 | 1.05 | 0.79 | 0.00 | 1.05 | 0.74 |
time (sec) |
N/A | 0.000 | 0.055 | 0.214 | 0.026 | 0.099 | 0.062 | 0.000 | 0.198 | 3.293 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 43 | 43 | 36 | 27 | 34 | 55 | 60 | 39 |
N.S. |
1 | 0.00 | 1.54 | 1.54 | 1.29 | 0.96 | 1.21 | 1.96 | 2.14 | 1.39 |
time (sec) |
N/A | 0.000 | 0.443 | 0.484 | 0.144 | 0.088 | 0.230 | 0.135 | 0.158 | 3.247 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 62 | 20 | 25 | 34 | 26 | 24 | 46 | 26 | 25 |
N.S. |
1 | 2.95 | 0.95 | 1.19 | 1.62 | 1.24 | 1.14 | 2.19 | 1.24 | 1.19 |
time (sec) |
N/A | 0.314 | 0.569 | 0.351 | 0.113 | 0.084 | 0.536 | 0.130 | 0.166 | 0.085 |
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 | 21 | 21 | 21 | 20 | 26 | 19 | 14 | 21 | 27 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 1.24 | 0.90 | 0.67 | 1.00 | 1.29 | 1.00 |
time (sec) |
N/A | 0.539 | 142.203 | 0.167 | 0.062 | 0.090 | 0.117 | 0.133 | 0.166 | 3.149 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 16 | 14 | 24 | 14 | 17 | 21 | 230 | 14 |
N.S. |
1 | 0.00 | 0.67 | 0.58 | 1.00 | 0.58 | 0.71 | 0.88 | 9.58 | 0.58 |
time (sec) |
N/A | 0.000 | 1.153 | 0.244 | 0.150 | 0.091 | 0.225 | 0.217 | 0.177 | 3.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 35 | 61 | 83 | 83 | 78 | 84 | 88 | 0 |
N.S. |
1 | 0.00 | 1.09 | 1.91 | 2.59 | 2.59 | 2.44 | 2.62 | 2.75 | 0.00 |
time (sec) |
N/A | 0.000 | 8.812 | 0.817 | 0.094 | 0.099 | 0.117 | 0.139 | 0.150 | 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 | 20 | 35 | 20 | 17 | 24 | 19 | 19 | 16 | 24 | 16 |
N.S. |
1 | 1.75 | 1.00 | 0.85 | 1.20 | 0.95 | 0.95 | 0.80 | 1.20 | 0.80 |
time (sec) |
N/A | 0.178 | 0.042 | 0.079 | 0.025 | 0.083 | 0.129 | 0.115 | 0.146 | 3.010 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 27 | 26 | 34 | 59 | 22 | 48 | 39 | 29 |
N.S. |
1 | 0.00 | 1.00 | 0.96 | 1.26 | 2.19 | 0.81 | 1.78 | 1.44 | 1.07 |
time (sec) |
N/A | 0.000 | 6.363 | 0.514 | 0.071 | 0.126 | 0.110 | 0.116 | 0.166 | 0.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 222 | 18 | 17 | 0 | 26 | 27 | 26 | 28 | 16 |
N.S. |
1 | 12.33 | 1.00 | 0.94 | 0.00 | 1.44 | 1.50 | 1.44 | 1.56 | 0.89 |
time (sec) |
N/A | 0.986 | 0.071 | 0.273 | 0.000 | 0.078 | 0.057 | 0.122 | 0.151 | 3.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | F(-1) | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 28 | 29 | 0 | 28 | 0 | 0 | 72 | 25 |
N.S. |
1 | 0.00 | 0.93 | 0.97 | 0.00 | 0.93 | 0.00 | 0.00 | 2.40 | 0.83 |
time (sec) |
N/A | 0.000 | 0.197 | 63.303 | 0.000 | 0.093 | 0.000 | 0.000 | 87.287 | 3.054 |
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 | 13 | 24 | 7 | 7 | 18 | 6 | 5 | 6 | 9 | 6 |
N.S. |
1 | 1.85 | 0.54 | 0.54 | 1.38 | 0.46 | 0.38 | 0.46 | 0.69 | 0.46 |
time (sec) |
N/A | 0.182 | 0.001 | 0.039 | 0.029 | 0.072 | 0.037 | 0.114 | 0.165 | 0.013 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | C | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 150 | 23 | 91 | 124 | 131 | 97 | 109 | 122 | 88 |
N.S. |
1 | 6.00 | 0.92 | 3.64 | 4.96 | 5.24 | 3.88 | 4.36 | 4.88 | 3.52 |
time (sec) |
N/A | 11.469 | 4.592 | 5.185 | 0.118 | 0.092 | 0.150 | 0.119 | 0.160 | 3.130 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 20 | 24 | 106 | 106 | 110 | 147 | 304 | 0 |
N.S. |
1 | 0.00 | 0.87 | 1.04 | 4.61 | 4.61 | 4.78 | 6.39 | 13.22 | 0.00 |
time (sec) |
N/A | 0.000 | 3.292 | 2.139 | 0.327 | 0.096 | 0.208 | 1.102 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | C | C | C | C | B | B | B |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 72 | 21 | 38 | 57 | 48 | 36 | 675 | 28 | 21 |
N.S. |
1 | 2.88 | 0.84 | 1.52 | 2.28 | 1.92 | 1.44 | 27.00 | 1.12 | 0.84 |
time (sec) |
N/A | 0.370 | 0.036 | 0.711 | 0.201 | 0.103 | 0.397 | 0.170 | 0.154 | 3.419 |
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 | 26 | 36 | 27 | 24 | 23 | 23 | 26 | 23 | 19 | 16 |
N.S. |
1 | 1.38 | 1.04 | 0.92 | 0.88 | 0.88 | 1.00 | 0.88 | 0.73 | 0.62 |
time (sec) |
N/A | 0.171 | 0.009 | 0.165 | 0.031 | 0.092 | 0.074 | 0.108 | 0.161 | 3.262 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | B | F(-2) | A | B | F(-1) |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 0 | 40 | 68 | 54 | 0 | 43 | 86 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.54 | 2.62 | 2.08 | 0.00 | 1.65 | 3.31 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.691 | 0.157 | 0.092 | 0.000 | 0.250 | 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 | 20 | 13 | 11 | 12 | 13 | 15 | 10 | 13 | 13 | 13 |
N.S. |
1 | 0.65 | 0.55 | 0.60 | 0.65 | 0.75 | 0.50 | 0.65 | 0.65 | 0.65 |
time (sec) |
N/A | 0.140 | 0.000 | 0.024 | 0.024 | 0.085 | 0.014 | 0.108 | 0.165 | 0.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | A | B | F(-1) | B | B |
verified | N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 29 | 0 | 0 | 47 | 92 | 0 | 52 | 3644 |
N.S. |
1 | 0.00 | 0.97 | 0.00 | 0.00 | 1.57 | 3.07 | 0.00 | 1.73 | 121.47 |
time (sec) |
N/A | 0.000 | 0.089 | 0.000 | 0.000 | 0.092 | 7.785 | 0.000 | 0.192 | 4.030 |
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 | 32 | 34 | 38 | 27 | 24 | 43 | 27 | 26 | 37 | 28 |
N.S. |
1 | 1.06 | 1.19 | 0.84 | 0.75 | 1.34 | 0.84 | 0.81 | 1.16 | 0.88 |
time (sec) |
N/A | 0.224 | 0.015 | 0.263 | 0.025 | 0.080 | 0.067 | 0.175 | 0.159 | 3.255 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 18 | 18 | 24 | 23 | 17 | 0 | 18 | 17 |
N.S. |
1 | 0.00 | 0.78 | 0.78 | 1.04 | 1.00 | 0.74 | 0.00 | 0.78 | 0.74 |
time (sec) |
N/A | 0.000 | 0.101 | 0.163 | 0.139 | 0.090 | 0.071 | 0.000 | 0.163 | 3.336 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 0 | 17 | 17 | 16 | 16 | 15 | 16 | 19 | 16 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 0.94 | 0.94 | 0.88 | 0.94 | 1.12 | 0.94 |
time (sec) |
N/A | 0.000 | 0.055 | 0.471 | 0.058 | 0.079 | 0.055 | 0.183 | 0.165 | 3.577 |
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 | 26 | 21 | 21 | 19 | 18 | 18 | 19 | 18 | 19 | 18 |
N.S. |
1 | 0.81 | 0.81 | 0.73 | 0.69 | 0.69 | 0.73 | 0.69 | 0.73 | 0.69 |
time (sec) |
N/A | 0.921 | 0.044 | 0.122 | 0.080 | 0.107 | 0.083 | 0.169 | 0.243 | 3.383 |
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 | 33 | 42 | 32 | 25 | 34 | 24 | 29 | 34 | 24 | 29 |
N.S. |
1 | 1.27 | 0.97 | 0.76 | 1.03 | 0.73 | 0.88 | 1.03 | 0.73 | 0.88 |
time (sec) |
N/A | 0.172 | 0.007 | 0.152 | 0.030 | 0.077 | 0.076 | 0.197 | 0.217 | 3.265 |
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 | 13 | 12 | 12 | 13 | 12 | 11 | 12 | 12 | 12 | 15 |
N.S. |
1 | 0.92 | 0.92 | 1.00 | 0.92 | 0.85 | 0.92 | 0.92 | 0.92 | 1.15 |
time (sec) |
N/A | 0.169 | 0.004 | 0.100 | 0.029 | 0.083 | 0.038 | 0.188 | 0.205 | 3.277 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | F | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 87 | 99 | 0 | 99 | 85 | 123 | 138 | 0 |
N.S. |
1 | 0.00 | 3.48 | 3.96 | 0.00 | 3.96 | 3.40 | 4.92 | 5.52 | 0.00 |
time (sec) |
N/A | 0.000 | 1.094 | 0.845 | 0.000 | 0.096 | 0.291 | 0.230 | 0.195 | 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 | 5 | 5 | 6 | 5 | 5 | 3 | 5 | 5 | 5 |
N.S. |
1 | 0.31 | 0.31 | 0.38 | 0.31 | 0.31 | 0.19 | 0.31 | 0.31 | 0.31 |
time (sec) |
N/A | 0.131 | 0.000 | 0.018 | 0.026 | 0.064 | 0.016 | 0.172 | 0.217 | 0.013 |
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 | 26 | 40 | 42 | 35 | 34 | 34 | 56 | 34 | 24 | 46 |
N.S. |
1 | 1.54 | 1.62 | 1.35 | 1.31 | 1.31 | 2.15 | 1.31 | 0.92 | 1.77 |
time (sec) |
N/A | 0.184 | 0.005 | 0.346 | 0.026 | 0.077 | 0.136 | 0.119 | 0.224 | 0.116 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | B | B | A | B | F(-1) |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 0 | 32 | 43 | 45 | 39 | 33 | 34 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.60 | 2.15 | 2.25 | 1.95 | 1.65 | 1.70 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 36.188 | 0.157 | 0.094 | 0.240 | 0.131 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 35 | 20 | 20 | 19 | 19 | 17 | 19 | 16 | 14 |
N.S. |
1 | 2.19 | 1.25 | 1.25 | 1.19 | 1.19 | 1.06 | 1.19 | 1.00 | 0.88 |
time (sec) |
N/A | 0.171 | 0.017 | 0.167 | 0.033 | 0.092 | 0.063 | 0.115 | 0.154 | 3.256 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | A | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 44 | 43 | 67 | 67 | 32 | 42 | 0 | 0 |
N.S. |
1 | 0.00 | 1.76 | 1.72 | 2.68 | 2.68 | 1.28 | 1.68 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.067 | 7.908 | 0.083 | 0.090 | 0.112 | 0.206 | 0.191 | 0.000 |
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 | 19 | 37 | 36 | 37 | 33 | 33 | 58 | 33 | 32 | 43 |
N.S. |
1 | 1.95 | 1.89 | 1.95 | 1.74 | 1.74 | 3.05 | 1.74 | 1.68 | 2.26 |
time (sec) |
N/A | 0.174 | 0.004 | 0.095 | 0.027 | 0.078 | 0.020 | 0.111 | 0.160 | 0.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 179 | 17 | 18 | 0 | 17 | 15 | 17 | 17 | 17 |
N.S. |
1 | 7.78 | 0.74 | 0.78 | 0.00 | 0.74 | 0.65 | 0.74 | 0.74 | 0.74 |
time (sec) |
N/A | 1.578 | 0.077 | 0.315 | 0.000 | 0.082 | 0.074 | 0.129 | 0.154 | 3.393 |
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 | 23 | 39 | 16 | 16 | 34 | 20 | 15 | 17 | 19 | 19 |
N.S. |
1 | 1.70 | 0.70 | 0.70 | 1.48 | 0.87 | 0.65 | 0.74 | 0.83 | 0.83 |
time (sec) |
N/A | 0.295 | 0.010 | 0.115 | 0.034 | 0.075 | 0.056 | 0.112 | 0.172 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 29 | 33 | 34 | 30 | 0 | 0 | 0 | 30 |
N.S. |
1 | 0.00 | 1.38 | 1.57 | 1.62 | 1.43 | 0.00 | 0.00 | 0.00 | 1.43 |
time (sec) |
N/A | 0.000 | 0.082 | 21.991 | 0.113 | 0.094 | 0.000 | 0.000 | 0.255 | 3.605 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 70 | 30 | 57 | 81 | 48 | 48 | 64 | 52 | 57 |
N.S. |
1 | 2.19 | 0.94 | 1.78 | 2.53 | 1.50 | 1.50 | 2.00 | 1.62 | 1.78 |
time (sec) |
N/A | 1.322 | 0.159 | 0.498 | 0.148 | 0.091 | 2.493 | 0.144 | 0.153 | 3.369 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 32 | 32 | 43 | 43 | 26 | 43 | 56 | 169 |
N.S. |
1 | 0.00 | 0.94 | 0.94 | 1.26 | 1.26 | 0.76 | 1.26 | 1.65 | 4.97 |
time (sec) |
N/A | 0.000 | 0.061 | 0.431 | 0.077 | 0.094 | 0.091 | 0.171 | 0.160 | 3.350 |
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 | 13 | 15 | 13 | 12 | 11 | 11 | 12 | 11 | 12 | 11 |
N.S. |
1 | 1.15 | 1.00 | 0.92 | 0.85 | 0.85 | 0.92 | 0.85 | 0.92 | 0.85 |
time (sec) |
N/A | 0.161 | 0.001 | 0.050 | 0.030 | 0.070 | 0.016 | 0.104 | 0.154 | 0.014 |