Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 79 | 51 | 72 | 71 | 50 | 75 | 67 | 69 | 0 |
N.S. |
1 | 1.05 | 0.68 | 0.96 | 0.95 | 0.67 | 1.00 | 0.89 | 0.92 | 0.00 |
time (sec) |
N/A | 0.236 | 0.023 | 0.111 | 0.124 | 0.144 | 0.323 | 0.123 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 83 | 54 | 60 | 61 | 48 | 66 | 57 | 58 | 0 |
N.S. |
1 | 1.20 | 0.78 | 0.87 | 0.88 | 0.70 | 0.96 | 0.83 | 0.84 | 0.00 |
time (sec) |
N/A | 0.224 | 0.022 | 0.078 | 0.114 | 0.149 | 0.246 | 0.130 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 58 | 42 | 52 | 50 | 41 | 53 | 47 | 50 | 0 |
N.S. |
1 | 1.07 | 0.78 | 0.96 | 0.93 | 0.76 | 0.98 | 0.87 | 0.93 | 0.00 |
time (sec) |
N/A | 0.214 | 0.018 | 0.078 | 0.149 | 0.106 | 0.191 | 0.125 | 0.218 | 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 | 45 | 51 | 42 | 40 | 40 | 37 | 42 | 37 | 37 | 38 |
N.S. |
1 | 1.13 | 0.93 | 0.89 | 0.89 | 0.82 | 0.93 | 0.82 | 0.82 | 0.84 |
time (sec) |
N/A | 0.191 | 0.009 | 0.072 | 0.123 | 0.121 | 0.153 | 0.127 | 0.221 | 0.297 |
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 | 26 | 26 | 25 | 26 | 26 | 24 | 26 | 25 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 1.00 | 1.00 | 0.92 | 1.00 | 0.96 | 0.92 |
time (sec) |
N/A | 0.168 | 0.003 | 0.043 | 0.110 | 0.116 | 0.066 | 0.126 | 0.223 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 59 | 51 | 68 | 0 | 0 | 0 | 0 | 10 | 0 |
N.S. |
1 | 1.16 | 1.00 | 1.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.326 | 0.011 | 0.156 | 0.000 | 0.000 | 0.000 | 0.000 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 34 | 26 | 38 | 82 | 34 | 48 | 23 | 25 |
N.S. |
1 | 1.00 | 1.26 | 0.96 | 1.41 | 3.04 | 1.26 | 1.78 | 0.85 | 0.93 |
time (sec) |
N/A | 0.198 | 0.009 | 0.074 | 0.128 | 0.120 | 0.813 | 0.123 | 0.225 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 31 | 29 | 28 | 27 | 53 | 68 | 26 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.85 | 0.82 | 0.79 | 1.56 | 2.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.200 | 0.011 | 0.079 | 0.120 | 0.132 | 0.624 | 0.137 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 57 | 67 | 50 | 60 | 110 | 109 | 70 | 42 | 0 |
N.S. |
1 | 1.02 | 1.20 | 0.89 | 1.07 | 1.96 | 1.95 | 1.25 | 0.75 | 0.00 |
time (sec) |
N/A | 0.233 | 0.018 | 0.078 | 0.120 | 0.163 | 1.430 | 0.121 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 63 | 41 | 52 | 50 | 37 | 102 | 130 | 45 | 0 |
N.S. |
1 | 1.09 | 0.71 | 0.90 | 0.86 | 0.64 | 1.76 | 2.24 | 0.78 | 0.00 |
time (sec) |
N/A | 0.208 | 0.017 | 0.083 | 0.122 | 0.138 | 0.915 | 0.133 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 86 | 72 | 73 | 82 | 122 | 184 | 101 | 62 | 0 |
N.S. |
1 | 1.08 | 0.90 | 0.91 | 1.02 | 1.52 | 2.30 | 1.26 | 0.78 | 0.00 |
time (sec) |
N/A | 0.221 | 0.044 | 0.080 | 0.130 | 0.150 | 2.803 | 0.124 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 141 | 82 | 76 | 102 | 76 | 121 | 100 | 12 | 0 |
N.S. |
1 | 1.18 | 0.68 | 0.63 | 0.85 | 0.63 | 1.01 | 0.83 | 0.10 | 0.00 |
time (sec) |
N/A | 0.556 | 0.038 | 0.287 | 0.125 | 0.129 | 0.438 | 0.132 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 115 | 74 | 91 | 0 | 70 | 97 | 87 | 12 | 0 |
N.S. |
1 | 1.17 | 0.76 | 0.93 | 0.00 | 0.71 | 0.99 | 0.89 | 0.12 | 0.00 |
time (sec) |
N/A | 0.536 | 0.029 | 0.252 | 0.000 | 0.119 | 0.361 | 0.131 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 95 | 63 | 59 | 72 | 59 | 83 | 68 | 12 | 0 |
N.S. |
1 | 1.16 | 0.77 | 0.72 | 0.88 | 0.72 | 1.01 | 0.83 | 0.15 | 0.00 |
time (sec) |
N/A | 0.410 | 0.033 | 0.237 | 0.126 | 0.114 | 0.256 | 0.131 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 66 | 57 | 43 | 0 | 51 | 58 | 55 | 55 | 0 |
N.S. |
1 | 1.10 | 0.95 | 0.72 | 0.00 | 0.85 | 0.97 | 0.92 | 0.92 | 0.00 |
time (sec) |
N/A | 0.351 | 0.020 | 0.178 | 0.000 | 0.141 | 0.187 | 0.118 | 0.264 | 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 | 35 | 42 | 35 | 37 | 33 | 36 | 37 | 33 | 35 | 45 |
N.S. |
1 | 1.20 | 1.00 | 1.06 | 0.94 | 1.03 | 1.06 | 0.94 | 1.00 | 1.29 |
time (sec) |
N/A | 0.257 | 0.012 | 0.108 | 0.127 | 0.117 | 0.082 | 0.125 | 0.212 | 0.368 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 90 | 73 | 101 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.23 | 1.00 | 1.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.463 | 0.016 | 0.188 | 0.000 | 0.000 | 0.000 | 0.000 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 75 | 98 | 136 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.01 | 1.32 | 1.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.411 | 0.095 | 0.168 | 0.000 | 0.000 | 0.000 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 46 | 43 | 47 | 39 | 44 | 0 | 82 | 12 | 0 |
N.S. |
1 | 1.07 | 1.00 | 1.09 | 0.91 | 1.02 | 0.00 | 1.91 | 0.28 | 0.00 |
time (sec) |
N/A | 0.295 | 0.020 | 0.166 | 0.131 | 0.114 | 0.000 | 0.159 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 120 | 152 | 166 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 0.97 | 1.23 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.587 | 0.428 | 0.307 | 0.000 | 0.000 | 0.000 | 0.000 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 89 | 69 | 82 | 74 | 62 | 0 | 171 | 12 | 0 |
N.S. |
1 | 1.02 | 0.79 | 0.94 | 0.85 | 0.71 | 0.00 | 1.97 | 0.14 | 0.00 |
time (sec) |
N/A | 0.505 | 0.028 | 0.173 | 0.119 | 0.144 | 0.000 | 0.175 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 303 | 122 | 159 | 171 | 104 | 202 | 175 | 12 | 0 |
N.S. |
1 | 1.51 | 0.61 | 0.79 | 0.85 | 0.52 | 1.00 | 0.87 | 0.06 | 0.00 |
time (sec) |
N/A | 1.520 | 0.042 | 0.324 | 0.136 | 0.153 | 0.588 | 0.139 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 245 | 115 | 151 | 0 | 96 | 167 | 141 | 12 | 0 |
N.S. |
1 | 1.47 | 0.69 | 0.90 | 0.00 | 0.57 | 1.00 | 0.84 | 0.07 | 0.00 |
time (sec) |
N/A | 1.166 | 0.046 | 0.349 | 0.000 | 0.138 | 0.460 | 0.132 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 176 | 95 | 106 | 120 | 78 | 134 | 117 | 12 | 0 |
N.S. |
1 | 1.29 | 0.70 | 0.78 | 0.88 | 0.57 | 0.99 | 0.86 | 0.09 | 0.00 |
time (sec) |
N/A | 0.876 | 0.035 | 0.303 | 0.130 | 0.121 | 0.317 | 0.137 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 117 | 85 | 58 | 0 | 69 | 99 | 83 | 82 | 0 |
N.S. |
1 | 1.18 | 0.86 | 0.59 | 0.00 | 0.70 | 1.00 | 0.84 | 0.83 | 0.00 |
time (sec) |
N/A | 0.550 | 0.028 | 0.290 | 0.000 | 0.103 | 0.246 | 0.129 | 0.208 | 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 | 60 | 69 | 60 | 57 | 59 | 44 | 60 | 56 | 54 | 59 |
N.S. |
1 | 1.15 | 1.00 | 0.95 | 0.98 | 0.73 | 1.00 | 0.93 | 0.90 | 0.98 |
time (sec) |
N/A | 0.326 | 0.013 | 0.197 | 0.114 | 0.138 | 0.127 | 0.127 | 0.224 | 0.374 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 123 | 101 | 135 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.22 | 1.00 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.571 | 0.017 | 0.296 | 0.000 | 0.000 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 127 | 139 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.04 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.600 | 0.078 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 107 | 92 | 117 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.05 | 0.90 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.587 | 0.144 | 0.333 | 0.000 | 0.000 | 0.000 | 0.000 | 0.241 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 194 | 165 | 256 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.01 | 0.86 | 1.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.103 | 0.579 | 0.418 | 0.000 | 0.000 | 0.000 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 181 | 151 | 190 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.07 | 0.89 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 1.030 | 0.234 | 0.401 | 0.000 | 0.000 | 0.000 | 0.000 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 282 | 500 | 167 | 332 | 0 | 153 | 275 | 245 | 12 | 0 |
N.S. |
1 | 1.77 | 0.59 | 1.18 | 0.00 | 0.54 | 0.98 | 0.87 | 0.04 | 0.00 |
time (sec) |
N/A | 2.623 | 0.057 | 0.632 | 0.000 | 0.173 | 1.082 | 0.133 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 416 | 150 | 197 | 206 | 134 | 248 | 212 | 12 | 0 |
N.S. |
1 | 1.66 | 0.60 | 0.79 | 0.82 | 0.54 | 0.99 | 0.85 | 0.05 | 0.00 |
time (sec) |
N/A | 2.343 | 0.052 | 0.498 | 0.160 | 0.120 | 0.785 | 0.139 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 291 | 135 | 213 | 0 | 121 | 197 | 173 | 12 | 0 |
N.S. |
1 | 1.47 | 0.68 | 1.08 | 0.00 | 0.61 | 0.99 | 0.87 | 0.06 | 0.00 |
time (sec) |
N/A | 1.812 | 0.046 | 0.514 | 0.000 | 0.139 | 0.577 | 0.138 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 230 | 114 | 130 | 146 | 99 | 165 | 140 | 12 | 0 |
N.S. |
1 | 1.39 | 0.69 | 0.78 | 0.88 | 0.60 | 0.99 | 0.84 | 0.07 | 0.00 |
time (sec) |
N/A | 1.450 | 0.048 | 0.482 | 0.126 | 0.132 | 0.431 | 0.135 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 132 | 96 | 73 | 0 | 82 | 110 | 101 | 98 | 0 |
N.S. |
1 | 1.18 | 0.86 | 0.65 | 0.00 | 0.73 | 0.98 | 0.90 | 0.88 | 0.00 |
time (sec) |
N/A | 0.886 | 0.028 | 0.457 | 0.000 | 0.124 | 0.311 | 0.131 | 0.245 | 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 | 69 | 85 | 69 | 67 | 74 | 55 | 70 | 65 | 64 | 63 |
N.S. |
1 | 1.23 | 1.00 | 0.97 | 1.07 | 0.80 | 1.01 | 0.94 | 0.93 | 0.91 |
time (sec) |
N/A | 0.458 | 0.017 | 0.343 | 0.121 | 0.126 | 0.156 | 0.129 | 0.207 | 0.353 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 154 | 119 | 168 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.29 | 1.00 | 1.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.682 | 0.017 | 0.467 | 0.000 | 0.000 | 0.000 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 185 | 549 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.05 | 3.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.768 | 0.707 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 136 | 115 | 150 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.12 | 0.95 | 1.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.738 | 0.251 | 0.513 | 0.000 | 0.000 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 304 | 304 | 1475 | 419 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.00 | 4.85 | 1.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.520 | 12.051 | 0.610 | 0.000 | 0.000 | 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 | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 48 | 40 | 40 | 0 | 0 | 0 | 47 | 12 | 0 |
N.S. |
1 | 0.87 | 0.73 | 0.73 | 0.00 | 0.00 | 0.00 | 0.85 | 0.22 | 0.00 |
time (sec) |
N/A | 0.306 | 0.064 | 0.103 | 0.000 | 0.000 | 0.000 | 0.134 | 0.262 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 39 | 33 | 33 | 0 | 0 | 0 | 37 | 12 | 0 |
N.S. |
1 | 0.91 | 0.77 | 0.77 | 0.00 | 0.00 | 0.00 | 0.86 | 0.28 | 0.00 |
time (sec) |
N/A | 0.295 | 0.056 | 0.087 | 0.000 | 0.000 | 0.000 | 0.126 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 37 | 31 | 31 | 0 | 0 | 0 | 35 | 12 | 0 |
N.S. |
1 | 0.90 | 0.76 | 0.76 | 0.00 | 0.00 | 0.00 | 0.85 | 0.29 | 0.00 |
time (sec) |
N/A | 0.290 | 0.048 | 0.060 | 0.000 | 0.000 | 0.000 | 0.138 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 28 | 24 | 24 | 0 | 0 | 0 | 25 | 12 | 0 |
N.S. |
1 | 0.97 | 0.83 | 0.83 | 0.00 | 0.00 | 0.00 | 0.86 | 0.41 | 0.00 |
time (sec) |
N/A | 0.272 | 0.044 | 0.057 | 0.000 | 0.000 | 0.000 | 0.130 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 26 | 20 | 22 | 0 | 0 | 0 | 23 | 12 | 0 |
N.S. |
1 | 0.96 | 0.74 | 0.81 | 0.00 | 0.00 | 0.00 | 0.85 | 0.44 | 0.00 |
time (sec) |
N/A | 0.276 | 0.034 | 0.056 | 0.000 | 0.000 | 0.000 | 0.129 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 0 | 0 | 0 | 12 | 10 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.00 | 0.00 | 0.00 | 0.86 | 0.71 | 0.00 |
time (sec) |
N/A | 0.276 | 0.015 | 0.078 | 0.000 | 0.000 | 0.000 | 0.129 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 10 | 11 | 0 | 0 | 0 | 10 | 8 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 0.00 | 0.00 | 0.00 | 1.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.214 | 0.018 | 0.044 | 0.000 | 0.000 | 0.000 | 0.121 | 0.219 | 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 | 10 | 10 | 12 | 10 | 12 | 12 | 8 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 0.80 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.186 | 0.150 | 0.068 | 0.189 | 0.093 | 0.269 | 0.145 | 0.245 | 0.299 |
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 | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.173 | 0.657 | 0.096 | 0.214 | 0.096 | 0.304 | 0.171 | 0.218 | 0.268 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 75 | 86 | 105 | 0 | 0 | 0 | 72 | 12 | 0 |
N.S. |
1 | 0.91 | 1.05 | 1.28 | 0.00 | 0.00 | 0.00 | 0.88 | 0.15 | 0.00 |
time (sec) |
N/A | 0.282 | 0.114 | 0.112 | 0.000 | 0.000 | 0.000 | 0.139 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 66 | 63 | 78 | 0 | 0 | 0 | 62 | 12 | 0 |
N.S. |
1 | 0.94 | 0.90 | 1.11 | 0.00 | 0.00 | 0.00 | 0.89 | 0.17 | 0.00 |
time (sec) |
N/A | 0.271 | 0.116 | 0.085 | 0.000 | 0.000 | 0.000 | 0.137 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 64 | 61 | 81 | 0 | 0 | 0 | 60 | 12 | 0 |
N.S. |
1 | 0.94 | 0.90 | 1.19 | 0.00 | 0.00 | 0.00 | 0.88 | 0.18 | 0.00 |
time (sec) |
N/A | 0.287 | 0.114 | 0.070 | 0.000 | 0.000 | 0.000 | 0.150 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 55 | 50 | 54 | 0 | 0 | 0 | 50 | 12 | 0 |
N.S. |
1 | 0.98 | 0.89 | 0.96 | 0.00 | 0.00 | 0.00 | 0.89 | 0.21 | 0.00 |
time (sec) |
N/A | 0.265 | 0.102 | 0.057 | 0.000 | 0.000 | 0.000 | 0.139 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 53 | 50 | 57 | 0 | 0 | 0 | 48 | 12 | 0 |
N.S. |
1 | 0.98 | 0.93 | 1.06 | 0.00 | 0.00 | 0.00 | 0.89 | 0.22 | 0.00 |
time (sec) |
N/A | 0.278 | 0.091 | 0.068 | 0.000 | 0.000 | 0.000 | 0.141 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 37 | 30 | 0 | 0 | 0 | 36 | 10 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.79 | 0.00 | 0.00 | 0.00 | 0.95 | 0.26 | 0.00 |
time (sec) |
N/A | 0.282 | 0.065 | 0.088 | 0.000 | 0.000 | 0.000 | 0.129 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 35 | 32 | 0 | 0 | 0 | 33 | 8 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.00 | 0.00 | 0.00 | 0.94 | 0.23 | 0.00 |
time (sec) |
N/A | 0.378 | 0.014 | 0.047 | 0.000 | 0.000 | 0.000 | 0.124 | 0.201 | 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 | 10 | 10 | 12 | 10 | 127 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 12.70 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.191 | 0.884 | 0.072 | 0.410 | 0.092 | 0.345 | 0.165 | 0.206 | 0.278 |
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 | 10 | 10 | 12 | 10 | 136 | 12 | 12 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 13.60 | 1.20 | 1.20 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.196 | 12.683 | 0.123 | 0.521 | 0.094 | 0.365 | 0.221 | 0.202 | 0.278 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 132 | 103 | 121 | 0 | 0 | 0 | 86 | 12 | 0 |
N.S. |
1 | 1.35 | 1.05 | 1.23 | 0.00 | 0.00 | 0.00 | 0.88 | 0.12 | 0.00 |
time (sec) |
N/A | 0.817 | 0.081 | 0.100 | 0.000 | 0.000 | 0.000 | 0.146 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 108 | 70 | 82 | 0 | 0 | 0 | 75 | 12 | 0 |
N.S. |
1 | 1.30 | 0.84 | 0.99 | 0.00 | 0.00 | 0.00 | 0.90 | 0.14 | 0.00 |
time (sec) |
N/A | 0.865 | 0.100 | 0.094 | 0.000 | 0.000 | 0.000 | 0.143 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 102 | 65 | 82 | 0 | 0 | 0 | 72 | 12 | 0 |
N.S. |
1 | 1.24 | 0.79 | 1.00 | 0.00 | 0.00 | 0.00 | 0.88 | 0.15 | 0.00 |
time (sec) |
N/A | 0.843 | 0.085 | 0.066 | 0.000 | 0.000 | 0.000 | 0.147 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 69 | 63 | 43 | 0 | 0 | 0 | 57 | 10 | 0 |
N.S. |
1 | 1.10 | 1.00 | 0.68 | 0.00 | 0.00 | 0.00 | 0.90 | 0.16 | 0.00 |
time (sec) |
N/A | 0.744 | 0.026 | 0.082 | 0.000 | 0.000 | 0.000 | 0.143 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 54 | 47 | 43 | 0 | 0 | 0 | 43 | 8 | 0 |
N.S. |
1 | 1.06 | 0.92 | 0.84 | 0.00 | 0.00 | 0.00 | 0.84 | 0.16 | 0.00 |
time (sec) |
N/A | 0.403 | 0.011 | 0.050 | 0.000 | 0.000 | 0.000 | 0.121 | 0.233 | 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 | 10 | 10 | 12 | 10 | 124 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 12.40 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.171 | 0.473 | 0.069 | 1.723 | 0.110 | 0.396 | 0.182 | 0.244 | 0.303 |
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 | 10 | 10 | 12 | 10 | 143 | 12 | 12 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 14.30 | 1.20 | 1.20 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.174 | 6.498 | 0.125 | 1.780 | 0.120 | 0.485 | 0.211 | 0.214 | 0.298 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 208 | 159 | 171 | 0 | 0 | 0 | 138 | 12 | 0 |
N.S. |
1 | 1.32 | 1.01 | 1.08 | 0.00 | 0.00 | 0.00 | 0.87 | 0.08 | 0.00 |
time (sec) |
N/A | 0.674 | 0.123 | 0.113 | 0.000 | 0.000 | 0.000 | 0.138 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 178 | 107 | 114 | 0 | 0 | 0 | 125 | 12 | 0 |
N.S. |
1 | 1.24 | 0.75 | 0.80 | 0.00 | 0.00 | 0.00 | 0.87 | 0.08 | 0.00 |
time (sec) |
N/A | 0.772 | 0.176 | 0.082 | 0.000 | 0.000 | 0.000 | 0.139 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 174 | 112 | 117 | 0 | 0 | 0 | 121 | 12 | 0 |
N.S. |
1 | 1.23 | 0.79 | 0.83 | 0.00 | 0.00 | 0.00 | 0.86 | 0.09 | 0.00 |
time (sec) |
N/A | 1.020 | 0.108 | 0.072 | 0.000 | 0.000 | 0.000 | 0.142 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 107 | 86 | 60 | 0 | 0 | 0 | 83 | 10 | 0 |
N.S. |
1 | 1.10 | 0.89 | 0.62 | 0.00 | 0.00 | 0.00 | 0.86 | 0.10 | 0.00 |
time (sec) |
N/A | 0.675 | 0.075 | 0.083 | 0.000 | 0.000 | 0.000 | 0.134 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 90 | 71 | 63 | 0 | 0 | 0 | 66 | 8 | 0 |
N.S. |
1 | 1.15 | 0.91 | 0.81 | 0.00 | 0.00 | 0.00 | 0.85 | 0.10 | 0.00 |
time (sec) |
N/A | 0.548 | 0.037 | 0.052 | 0.000 | 0.000 | 0.000 | 0.125 | 0.220 | 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 | 10 | 10 | 12 | 10 | 200 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 20.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.166 | 2.917 | 0.076 | 5.216 | 0.118 | 0.512 | 0.179 | 0.222 | 0.276 |
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 | 10 | 10 | 12 | 10 | 229 | 12 | 12 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 22.90 | 1.20 | 1.20 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.178 | 14.938 | 0.135 | 6.483 | 0.114 | 0.677 | 0.289 | 0.208 | 0.276 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 120 | 194 | 143 | 0 | 0 | 0 | 247 | 11 | 0 |
N.S. |
1 | 0.99 | 1.60 | 1.18 | 0.00 | 0.00 | 0.00 | 2.04 | 0.09 | 0.00 |
time (sec) |
N/A | 0.500 | 0.078 | 0.194 | 0.000 | 0.000 | 0.000 | 0.189 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 94 | 131 | 91 | 0 | 0 | 0 | 153 | 11 | 0 |
N.S. |
1 | 0.99 | 1.38 | 0.96 | 0.00 | 0.00 | 0.00 | 1.61 | 0.12 | 0.00 |
time (sec) |
N/A | 0.473 | 0.053 | 0.136 | 0.000 | 0.000 | 0.000 | 0.185 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 88 | 128 | 96 | 0 | 0 | 0 | 165 | 11 | 0 |
N.S. |
1 | 1.02 | 1.49 | 1.12 | 0.00 | 0.00 | 0.00 | 1.92 | 0.13 | 0.00 |
time (sec) |
N/A | 0.469 | 0.062 | 0.106 | 0.000 | 0.000 | 0.000 | 0.187 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 57 | 49 | 42 | 0 | 0 | 0 | 71 | 9 | 0 |
N.S. |
1 | 0.97 | 0.83 | 0.71 | 0.00 | 0.00 | 0.00 | 1.20 | 0.15 | 0.00 |
time (sec) |
N/A | 0.422 | 0.026 | 0.074 | 0.000 | 0.000 | 0.000 | 0.169 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 69 | 49 | 0 | 0 | 0 | 83 | 7 | 0 |
N.S. |
1 | 1.00 | 1.57 | 1.11 | 0.00 | 0.00 | 0.00 | 1.89 | 0.16 | 0.00 |
time (sec) |
N/A | 0.384 | 0.019 | 0.070 | 0.000 | 0.000 | 0.000 | 0.152 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 10 | 0 | 0 | 10 | 12 | 11 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 0.00 | 0.00 | 0.83 | 1.00 | 0.92 | 1.00 |
time (sec) |
N/A | 0.181 | 0.172 | 0.126 | 0.000 | 0.000 | 0.338 | 0.335 | 0.213 | 0.293 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 282 | 337 | 185 | 193 | 0 | 0 | 0 | 355 | 15 | 0 |
N.S. |
1 | 1.20 | 0.66 | 0.68 | 0.00 | 0.00 | 0.00 | 1.26 | 0.05 | 0.00 |
time (sec) |
N/A | 2.060 | 0.086 | 0.179 | 0.000 | 0.000 | 0.000 | 0.192 | 0.253 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 201 | 128 | 121 | 0 | 0 | 0 | 225 | 15 | 0 |
N.S. |
1 | 1.28 | 0.82 | 0.77 | 0.00 | 0.00 | 0.00 | 1.43 | 0.10 | 0.00 |
time (sec) |
N/A | 1.528 | 0.051 | 0.141 | 0.000 | 0.000 | 0.000 | 0.185 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 193 | 125 | 130 | 0 | 0 | 0 | 237 | 15 | 0 |
N.S. |
1 | 1.31 | 0.85 | 0.88 | 0.00 | 0.00 | 0.00 | 1.61 | 0.10 | 0.00 |
time (sec) |
N/A | 1.226 | 0.061 | 0.115 | 0.000 | 0.000 | 0.000 | 0.191 | 0.243 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 95 | 64 | 64 | 0 | 0 | 0 | 107 | 13 | 0 |
N.S. |
1 | 1.07 | 0.72 | 0.72 | 0.00 | 0.00 | 0.00 | 1.20 | 0.15 | 0.00 |
time (sec) |
N/A | 0.977 | 0.045 | 0.081 | 0.000 | 0.000 | 0.000 | 0.175 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 76 | 66 | 72 | 0 | 0 | 0 | 119 | 46 | 0 |
N.S. |
1 | 1.01 | 0.88 | 0.96 | 0.00 | 0.00 | 0.00 | 1.59 | 0.61 | 0.00 |
time (sec) |
N/A | 0.511 | 0.019 | 0.073 | 0.000 | 0.000 | 0.000 | 0.209 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 10 | 0 | 0 | 10 | 12 | 15 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 0.00 | 0.00 | 0.83 | 1.00 | 1.25 | 1.00 |
time (sec) |
N/A | 0.186 | 0.173 | 0.122 | 0.000 | 0.000 | 1.332 | 0.395 | 0.208 | 0.277 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F(-1) | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 298 | 402 | 194 | 233 | 0 | 0 | 0 | 463 | 17 | 0 |
N.S. |
1 | 1.35 | 0.65 | 0.78 | 0.00 | 0.00 | 0.00 | 1.55 | 0.06 | 0.00 |
time (sec) |
N/A | 2.641 | 0.074 | 0.202 | 0.000 | 0.000 | 0.000 | 0.205 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 272 | 131 | 154 | 0 | 0 | 0 | 297 | 17 | 0 |
N.S. |
1 | 1.33 | 0.64 | 0.75 | 0.00 | 0.00 | 0.00 | 1.45 | 0.08 | 0.00 |
time (sec) |
N/A | 1.772 | 0.051 | 0.146 | 0.000 | 0.000 | 0.000 | 0.197 | 0.254 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 235 | 128 | 156 | 0 | 0 | 0 | 309 | 17 | 0 |
N.S. |
1 | 1.32 | 0.72 | 0.88 | 0.00 | 0.00 | 0.00 | 1.74 | 0.10 | 0.00 |
time (sec) |
N/A | 1.472 | 0.060 | 0.118 | 0.000 | 0.000 | 0.000 | 0.201 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 131 | 73 | 79 | 0 | 0 | 0 | 143 | 15 | 0 |
N.S. |
1 | 1.10 | 0.61 | 0.66 | 0.00 | 0.00 | 0.00 | 1.20 | 0.13 | 0.00 |
time (sec) |
N/A | 0.867 | 0.062 | 0.084 | 0.000 | 0.000 | 0.000 | 0.178 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 95 | 69 | 88 | 0 | 0 | 0 | 155 | 14 | 0 |
N.S. |
1 | 1.08 | 0.78 | 1.00 | 0.00 | 0.00 | 0.00 | 1.76 | 0.16 | 0.00 |
time (sec) |
N/A | 0.578 | 0.018 | 0.076 | 0.000 | 0.000 | 0.000 | 0.208 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 10 | 0 | 0 | 10 | 12 | 17 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 0.00 | 0.00 | 0.83 | 1.00 | 1.42 | 1.00 |
time (sec) |
N/A | 0.172 | 0.174 | 0.121 | 0.000 | 0.000 | 16.853 | 0.413 | 0.210 | 0.285 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 102 | 192 | 72 | 0 | 0 | 0 | 139 | 227 | 0 |
N.S. |
1 | 0.96 | 1.81 | 0.68 | 0.00 | 0.00 | 0.00 | 1.31 | 2.14 | 0.00 |
time (sec) |
N/A | 0.323 | 0.069 | 0.153 | 0.000 | 0.000 | 0.000 | 0.177 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 64 | 130 | 43 | 0 | 0 | 0 | 81 | 169 | 0 |
N.S. |
1 | 0.98 | 2.00 | 0.66 | 0.00 | 0.00 | 0.00 | 1.25 | 2.60 | 0.00 |
time (sec) |
N/A | 0.284 | 0.049 | 0.122 | 0.000 | 0.000 | 0.000 | 0.170 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 70 | 126 | 50 | 0 | 0 | 0 | 93 | 98 | 0 |
N.S. |
1 | 0.99 | 1.77 | 0.70 | 0.00 | 0.00 | 0.00 | 1.31 | 1.38 | 0.00 |
time (sec) |
N/A | 0.296 | 0.059 | 0.094 | 0.000 | 0.000 | 0.000 | 0.159 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 21 | 0 | 0 | 0 | 35 | 75 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 0.00 | 0.00 | 0.00 | 1.25 | 2.68 | 0.00 |
time (sec) |
N/A | 0.341 | 0.017 | 0.066 | 0.000 | 0.000 | 0.000 | 0.156 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 68 | 26 | 0 | 0 | 0 | 47 | 59 | 0 |
N.S. |
1 | 1.00 | 2.19 | 0.84 | 0.00 | 0.00 | 0.00 | 1.52 | 1.90 | 0.00 |
time (sec) |
N/A | 0.281 | 0.017 | 0.056 | 0.000 | 0.000 | 0.000 | 0.141 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 10 | 0 | 0 | 12 | 12 | 17 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 0.00 | 0.00 | 1.00 | 1.00 | 1.42 | 1.00 |
time (sec) |
N/A | 0.184 | 0.168 | 0.123 | 0.000 | 0.000 | 0.352 | 0.235 | 0.212 | 0.289 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 10 | 0 | 0 | 14 | 12 | 17 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 0.00 | 0.00 | 1.17 | 1.00 | 1.42 | 1.00 |
time (sec) |
N/A | 0.179 | 1.761 | 0.144 | 0.000 | 0.000 | 0.473 | 0.250 | 0.232 | 0.278 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 165 | 306 | 183 | 0 | 0 | 0 | 0 | 406 | 0 |
N.S. |
1 | 0.96 | 1.79 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 2.37 | 0.00 |
time (sec) |
N/A | 0.395 | 0.201 | 0.207 | 0.000 | 0.000 | 0.000 | 0.000 | 0.351 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 126 | 226 | 121 | 0 | 0 | 0 | 0 | 195 | 0 |
N.S. |
1 | 0.99 | 1.78 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 1.54 | 0.00 |
time (sec) |
N/A | 0.350 | 0.325 | 0.174 | 0.000 | 0.000 | 0.000 | 0.000 | 0.322 | 0.000 |