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 | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 51 | 47 | 47 | 51 | 65 | 128 | 57 | 53 |
N.S. |
1 | 1.00 | 0.89 | 0.82 | 0.82 | 0.89 | 1.14 | 2.25 | 1.00 | 0.93 |
time (sec) |
N/A | 0.239 | 0.156 | 0.835 | 0.040 | 0.086 | 0.393 | 0.115 | 0.274 | 0.447 |
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 | 44 | 44 | 44 | 39 | 37 | 40 | 49 | 75 | 40 | 38 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.84 | 0.91 | 1.11 | 1.70 | 0.91 | 0.86 |
time (sec) |
N/A | 0.206 | 0.009 | 0.690 | 0.047 | 0.078 | 0.221 | 0.128 | 0.270 | 0.128 |
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 | 25 | 41 | 22 | 21 | 23 | 31 | 26 | 23 | 21 |
N.S. |
1 | 1.00 | 1.64 | 0.88 | 0.84 | 0.92 | 1.24 | 1.04 | 0.92 | 0.84 |
time (sec) |
N/A | 0.183 | 0.054 | 0.727 | 0.035 | 0.078 | 0.085 | 0.113 | 0.264 | 42.401 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 29 | 29 | 50 | 27 | 0 | 32 | 21 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.94 | 1.61 | 0.87 | 0.00 | 1.03 | 0.68 | 0.00 |
time (sec) |
N/A | 0.198 | 0.110 | 0.678 | 0.106 | 0.081 | 0.000 | 0.137 | 0.232 | 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 | 53 | 53 | 48 | 47 | 57 | 49 | 0 | 99 | 29 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.89 | 1.08 | 0.92 | 0.00 | 1.87 | 0.55 | 0.00 |
time (sec) |
N/A | 0.254 | 0.147 | 0.727 | 0.108 | 0.078 | 0.000 | 0.112 | 0.197 | 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 | 74 | 74 | 86 | 65 | 58 | 63 | 0 | 204 | 58 | 0 |
N.S. |
1 | 1.00 | 1.16 | 0.88 | 0.78 | 0.85 | 0.00 | 2.76 | 0.78 | 0.00 |
time (sec) |
N/A | 0.293 | 0.176 | 0.725 | 0.134 | 0.101 | 0.000 | 0.119 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | B | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 125 | 89 | 92 | 103 | 488 | 165 | 55 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.74 | 0.76 | 0.85 | 4.03 | 1.36 | 0.45 | 0.00 |
time (sec) |
N/A | 0.302 | 0.316 | 0.774 | 0.059 | 0.096 | 2.287 | 0.117 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | B | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 104 | 68 | 75 | 86 | 223 | 145 | 23 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.67 | 0.74 | 0.84 | 2.19 | 1.42 | 0.23 | 0.00 |
time (sec) |
N/A | 0.241 | 0.246 | 0.695 | 0.042 | 0.083 | 1.735 | 0.136 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | C | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 61 | 48 | 53 | 67 | 66 | 102 | 16 | 56 |
N.S. |
1 | 1.00 | 0.82 | 0.65 | 0.72 | 0.91 | 0.89 | 1.38 | 0.22 | 0.76 |
time (sec) |
N/A | 0.198 | 0.187 | 0.564 | 0.042 | 0.081 | 0.182 | 0.132 | 0.211 | 38.673 |
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 | 88 | 88 | 91 | 66 | 81 | 78 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.75 | 0.92 | 0.89 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.247 | 0.351 | 0.714 | 0.188 | 0.086 | 0.000 | 0.000 | 0.209 | 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 | 114 | 114 | 119 | 83 | 82 | 98 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 1.04 | 0.73 | 0.72 | 0.86 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.274 | 0.288 | 0.757 | 0.197 | 0.084 | 0.000 | 0.000 | 0.228 | 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 | 163 | 167 | 122 | 111 | 106 | 121 | 209 | 284 | 156 | 149 |
N.S. |
1 | 1.02 | 0.75 | 0.68 | 0.65 | 0.74 | 1.28 | 1.74 | 0.96 | 0.91 |
time (sec) |
N/A | 0.440 | 0.405 | 1.993 | 0.046 | 0.081 | 0.542 | 0.133 | 0.195 | 0.855 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 107 | 92 | 89 | 87 | 84 | 136 | 165 | 68 | 95 |
N.S. |
1 | 1.05 | 0.90 | 0.87 | 0.85 | 0.82 | 1.33 | 1.62 | 0.67 | 0.93 |
time (sec) |
N/A | 0.325 | 0.239 | 1.800 | 0.059 | 0.082 | 0.321 | 0.114 | 0.178 | 38.701 |
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 | 58 | 62 | 52 | 52 | 52 | 53 | 95 | 57 | 60 | 51 |
N.S. |
1 | 1.07 | 0.90 | 0.90 | 0.90 | 0.91 | 1.64 | 0.98 | 1.03 | 0.88 |
time (sec) |
N/A | 0.240 | 0.279 | 1.839 | 0.038 | 0.086 | 0.125 | 0.132 | 0.172 | 38.746 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 71 | 157 | 108 | 68 | 0 | 77 | 45 | 0 |
N.S. |
1 | 1.00 | 0.96 | 2.12 | 1.46 | 0.92 | 0.00 | 1.04 | 0.61 | 0.00 |
time (sec) |
N/A | 0.292 | 0.187 | 2.940 | 0.153 | 0.075 | 0.000 | 0.146 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 115 | 116 | 217 | 124 | 112 | 0 | 226 | 883 | 0 |
N.S. |
1 | 1.00 | 1.01 | 1.89 | 1.08 | 0.97 | 0.00 | 1.97 | 7.68 | 0.00 |
time (sec) |
N/A | 0.426 | 0.276 | 3.006 | 0.151 | 0.082 | 0.000 | 0.125 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 169 | 158 | 270 | 128 | 156 | 0 | 448 | 1358 | 0 |
N.S. |
1 | 1.00 | 0.93 | 1.60 | 0.76 | 0.92 | 0.00 | 2.65 | 8.04 | 0.00 |
time (sec) |
N/A | 0.509 | 0.495 | 3.150 | 0.147 | 0.085 | 0.000 | 0.144 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 247 | 247 | 234 | 185 | 207 | 216 | 0 | 329 | 84 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.75 | 0.84 | 0.87 | 0.00 | 1.33 | 0.34 | 0.00 |
time (sec) |
N/A | 0.450 | 0.603 | 1.985 | 0.148 | 0.089 | 0.000 | 0.129 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 198 | 191 | 138 | 171 | 176 | 0 | 283 | 47 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.70 | 0.86 | 0.89 | 0.00 | 1.43 | 0.24 | 0.00 |
time (sec) |
N/A | 0.362 | 0.553 | 1.818 | 0.148 | 0.126 | 0.000 | 0.150 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 153 | 147 | 98 | 129 | 134 | 0 | 195 | 36 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.64 | 0.84 | 0.88 | 0.00 | 1.27 | 0.24 | 0.00 |
time (sec) |
N/A | 0.296 | 0.355 | 1.632 | 0.192 | 0.081 | 0.000 | 0.142 | 0.167 | 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 | 187 | 187 | 184 | 134 | 170 | 159 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.72 | 0.91 | 0.85 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.350 | 0.633 | 1.805 | 0.243 | 0.097 | 0.000 | 0.000 | 0.178 | 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 | 239 | 239 | 226 | 173 | 176 | 206 | 0 | 0 | 56 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.72 | 0.74 | 0.86 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.419 | 0.732 | 1.895 | 0.243 | 0.101 | 0.000 | 0.000 | 0.187 | 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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 130 | 75 | 85 | 79 | 79 | 143 | 138 | 109 | 94 |
N.S. |
1 | 1.11 | 0.64 | 0.73 | 0.68 | 0.68 | 1.22 | 1.18 | 0.93 | 0.80 |
time (sec) |
N/A | 0.626 | 0.312 | 1.384 | 0.073 | 0.084 | 0.749 | 0.124 | 0.178 | 38.978 |
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 | 79 | 83 | 58 | 66 | 60 | 58 | 92 | 94 | 67 | 66 |
N.S. |
1 | 1.05 | 0.73 | 0.84 | 0.76 | 0.73 | 1.16 | 1.19 | 0.85 | 0.84 |
time (sec) |
N/A | 0.399 | 0.180 | 1.665 | 0.039 | 0.080 | 0.385 | 0.116 | 0.181 | 0.416 |
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 | 33 | 23 | 33 | 26 | 27 | 26 | 46 | 26 | 37 | 28 |
N.S. |
1 | 0.70 | 1.00 | 0.79 | 0.82 | 0.79 | 1.39 | 0.79 | 1.12 | 0.85 |
time (sec) |
N/A | 0.227 | 0.035 | 1.673 | 0.036 | 0.086 | 0.155 | 0.106 | 0.175 | 38.596 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 51 | 125 | 89 | 47 | 0 | 47 | 16 | 0 |
N.S. |
1 | 1.00 | 0.93 | 2.27 | 1.62 | 0.85 | 0.00 | 0.85 | 0.29 | 0.00 |
time (sec) |
N/A | 0.267 | 0.088 | 2.832 | 0.153 | 0.120 | 0.000 | 0.131 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 90 | 185 | 97 | 90 | 0 | 186 | 717 | 0 |
N.S. |
1 | 1.00 | 0.99 | 2.03 | 1.07 | 0.99 | 0.00 | 2.04 | 7.88 | 0.00 |
time (sec) |
N/A | 0.389 | 0.157 | 2.836 | 0.166 | 0.083 | 0.000 | 0.117 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | B | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 188 | 159 | 132 | 143 | 147 | 439 | 259 | 16 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.70 | 0.76 | 0.78 | 2.34 | 1.38 | 0.09 | 0.00 |
time (sec) |
N/A | 0.401 | 0.488 | 1.309 | 0.127 | 0.082 | 1.930 | 0.129 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 153 | 117 | 99 | 112 | 120 | 129 | 185 | 12 | 0 |
N.S. |
1 | 1.00 | 0.76 | 0.65 | 0.73 | 0.78 | 0.84 | 1.21 | 0.08 | 0.00 |
time (sec) |
N/A | 0.269 | 0.263 | 1.145 | 0.121 | 0.076 | 0.516 | 0.145 | 0.172 | 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 | 168 | 172 | 167 | 130 | 152 | 147 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.02 | 0.99 | 0.77 | 0.90 | 0.88 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.345 | 0.488 | 1.316 | 0.326 | 0.088 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 63 | 58 | 97 | 51 | 116 | 97 | 12 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.82 | 1.37 | 0.72 | 1.63 | 1.37 | 0.17 | 0.00 |
time (sec) |
N/A | 0.229 | 0.083 | 1.521 | 0.118 | 0.077 | 2.078 | 0.113 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | B | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 89 | 75 | 78 | 117 | 73 | 291 | 125 | 73 | 0 |
N.S. |
1 | 1.06 | 0.89 | 0.93 | 1.39 | 0.87 | 3.46 | 1.49 | 0.87 | 0.00 |
time (sec) |
N/A | 0.281 | 0.176 | 1.742 | 0.126 | 0.078 | 1.990 | 0.135 | 0.182 | 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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 35 | 67 | 50 | 55 | 52 | 95 | 52 | 77 | 55 |
N.S. |
1 | 0.52 | 1.00 | 0.75 | 0.82 | 0.78 | 1.42 | 0.78 | 1.15 | 0.82 |
time (sec) |
N/A | 0.239 | 0.051 | 7.118 | 0.040 | 0.090 | 0.639 | 0.136 | 0.156 | 39.172 |
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 | 44 | 44 | 41 | 39 | 54 | 38 | 51 | 39 | 49 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.89 | 1.23 | 0.86 | 1.16 | 0.89 | 1.11 | 0.00 |
time (sec) |
N/A | 0.272 | 0.138 | 2.220 | 0.073 | 0.077 | 2.128 | 0.124 | 0.155 | 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 | 362 | 341 | 289 | 0 | 0 | 1435 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.94 | 0.80 | 0.00 | 0.00 | 3.96 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.411 | 0.270 | 0.000 | 0.000 | 0.227 | 0.000 | 0.000 | 0.165 | 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 | 245 | 237 | 188 | 0 | 0 | 1041 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.97 | 0.77 | 0.00 | 0.00 | 4.25 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.879 | 0.077 | 0.000 | 0.000 | 0.190 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 54 | 48 | 48 | 8078 | 208 | 165 | 63 | 54 | 128 |
N.S. |
1 | 1.12 | 1.00 | 1.00 | 168.29 | 4.33 | 3.44 | 1.31 | 1.12 | 2.67 |
time (sec) |
N/A | 0.273 | 0.134 | 0.440 | 23.684 | 0.089 | 3.507 | 0.134 | 0.153 | 40.715 |
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 | 19 | 15 | 20 | 38 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.06 | 0.83 | 1.11 | 2.11 | 1.11 |
time (sec) |
N/A | 0.186 | 1.864 | 0.158 | 0.230 | 0.071 | 2.394 | 0.112 | 0.167 | 39.437 |
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 | 23 | 17 | 20 | 48 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.28 | 0.94 | 1.11 | 2.67 | 1.11 |
time (sec) |
N/A | 0.186 | 1.552 | 0.165 | 0.224 | 0.071 | 3.125 | 0.139 | 0.169 | 39.157 |
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 | 15 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.11 | 0.83 | 1.11 | 1.11 | 1.11 |
time (sec) |
N/A | 0.189 | 0.916 | 0.155 | 0.331 | 0.073 | 1.840 | 0.126 | 0.175 | 38.596 |
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 | 14 | 14 | 16 | 14 | 16 | 16 | 14 | 16 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 1.14 | 1.00 | 1.14 | 1.14 | 1.14 |
time (sec) |
N/A | 0.167 | 0.037 | 0.152 | 0.212 | 0.071 | 0.801 | 0.146 | 0.160 | 38.596 |
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 | 23 | 17 | 20 | 45 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.28 | 0.94 | 1.11 | 2.50 | 1.11 |
time (sec) |
N/A | 0.184 | 0.817 | 0.163 | 0.233 | 0.070 | 2.990 | 0.137 | 0.164 | 38.842 |
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 | 663 | 625 | 513 | 0 | 0 | 2469 | 0 | 0 | 38 | 0 |
N.S. |
1 | 0.94 | 0.77 | 0.00 | 0.00 | 3.72 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 2.828 | 2.845 | 0.000 | 0.000 | 0.254 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 324 | 326 | 302 | 0 | 0 | 1509 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.01 | 0.93 | 0.00 | 0.00 | 4.66 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 1.197 | 1.428 | 0.000 | 0.000 | 0.218 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 99 | 91 | 131 | 0 | 366 | 2116 | 144 | 187 | 178 |
N.S. |
1 | 1.09 | 1.00 | 1.44 | 0.00 | 4.02 | 23.25 | 1.58 | 2.05 | 1.96 |
time (sec) |
N/A | 0.385 | 0.238 | 0.524 | 0.000 | 0.117 | 53.750 | 0.114 | 0.176 | 39.163 |
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 | 3466 | 45 | 17 | 20 | 112 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 192.56 | 2.50 | 0.94 | 1.11 | 6.22 | 1.11 |
time (sec) |
N/A | 0.193 | 8.207 | 0.727 | 4.707 | 0.087 | 26.650 | 0.252 | 0.189 | 39.154 |
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 | 3475 | 51 | 19 | 20 | 1331 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 193.06 | 2.83 | 1.06 | 1.11 | 73.94 | 1.11 |
time (sec) |
N/A | 0.191 | 12.636 | 0.731 | 4.573 | 0.085 | 38.698 | 0.393 | 0.261 | 39.322 |
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 | 922 | 46 | 17 | 20 | 38 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 51.22 | 2.56 | 0.94 | 1.11 | 2.11 | 1.11 |
time (sec) |
N/A | 0.188 | 5.064 | 0.743 | 0.492 | 0.082 | 39.002 | 0.190 | 0.162 | 38.565 |
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 | 14 | 14 | 16 | 14 | 3381 | 43 | 15 | 16 | 34 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 241.50 | 3.07 | 1.07 | 1.14 | 2.43 | 1.14 |
time (sec) |
N/A | 0.167 | 5.290 | 0.813 | 4.067 | 0.079 | 17.666 | 0.164 | 0.153 | 38.746 |
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 | 3486 | 51 | 19 | 20 | 128 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 193.67 | 2.83 | 1.06 | 1.11 | 7.11 | 1.11 |
time (sec) |
N/A | 0.189 | 10.115 | 0.728 | 4.993 | 0.080 | 41.768 | 0.208 | 0.168 | 38.687 |
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 | 0.189 | 1.386 | 0.159 | 0.570 | 0.089 | 10.736 | 0.396 | 0.172 | 38.692 |
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 | 444 | 444 | 373 | 0 | 0 | 323 | 0 | 0 | 178 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.73 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.693 | 2.379 | 0.000 | 0.000 | 0.094 | 0.000 | 0.000 | 0.153 | 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 | 279 | 279 | 551 | 0 | 0 | 198 | 0 | 0 | 126 | 0 |
N.S. |
1 | 1.00 | 1.97 | 0.00 | 0.00 | 0.71 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.481 | 3.152 | 0.000 | 0.000 | 0.090 | 0.000 | 0.000 | 0.158 | 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 | 134 | 134 | 149 | 0 | 0 | 98 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.00 | 1.11 | 0.00 | 0.00 | 0.73 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.297 | 0.561 | 0.000 | 0.000 | 0.082 | 0.000 | 0.000 | 0.163 | 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 | 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 | 0.191 | 1.158 | 0.193 | 0.473 | 0.081 | 0.412 | 0.148 | 0.155 | 38.395 |
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 | 3886 | 48 | 19 | 22 | 226 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 194.30 | 2.40 | 0.95 | 1.10 | 11.30 | 1.10 |
time (sec) |
N/A | 0.192 | 1.995 | 0.787 | 9.536 | 0.080 | 1.506 | 0.197 | 0.169 | 38.492 |
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 | 44 | 44 | 44 | 39 | 37 | 40 | 49 | 75 | 40 | 38 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.84 | 0.91 | 1.11 | 1.70 | 0.91 | 0.86 |
time (sec) |
N/A | 0.231 | 0.016 | 0.828 | 0.039 | 0.083 | 0.393 | 0.107 | 0.160 | 0.341 |
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 | 25 | 41 | 22 | 21 | 23 | 31 | 26 | 23 | 21 |
N.S. |
1 | 1.00 | 1.64 | 0.88 | 0.84 | 0.92 | 1.24 | 1.04 | 0.92 | 0.84 |
time (sec) |
N/A | 0.189 | 0.066 | 0.655 | 0.033 | 0.079 | 0.110 | 0.119 | 0.152 | 38.382 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | C | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 29 | 0 | 50 | 27 | 0 | 32 | 21 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.00 | 1.61 | 0.87 | 0.00 | 1.03 | 0.68 | 0.00 |
time (sec) |
N/A | 0.205 | 0.128 | 0.000 | 0.112 | 0.076 | 0.000 | 0.113 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | C | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 48 | 0 | 57 | 49 | 0 | 99 | 29 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.00 | 1.08 | 0.92 | 0.00 | 1.87 | 0.55 | 0.00 |
time (sec) |
N/A | 0.262 | 0.215 | 0.000 | 0.149 | 0.079 | 0.000 | 0.126 | 0.154 | 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 | 112 | 112 | 124 | 0 | 109 | 82 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 1.11 | 0.00 | 0.97 | 0.73 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.268 | 0.293 | 0.000 | 0.185 | 0.084 | 0.000 | 0.000 | 0.150 | 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 | 91 | 91 | 108 | 0 | 93 | 63 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 1.19 | 0.00 | 1.02 | 0.69 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.232 | 0.171 | 0.000 | 0.182 | 0.080 | 0.000 | 0.000 | 0.164 | 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 | 101 | 101 | 120 | 0 | 89 | 72 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.00 | 1.19 | 0.00 | 0.88 | 0.71 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.252 | 0.302 | 0.000 | 0.188 | 0.084 | 0.000 | 0.000 | 0.157 | 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 | 130 | 130 | 143 | 0 | 91 | 101 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 1.10 | 0.00 | 0.70 | 0.78 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.284 | 0.499 | 0.000 | 0.185 | 0.080 | 0.000 | 0.000 | 0.154 | 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 | 106 | 106 | 124 | 0 | 110 | 80 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 1.17 | 0.00 | 1.04 | 0.75 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.235 | 0.243 | 0.000 | 0.179 | 0.082 | 0.000 | 0.000 | 0.171 | 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 | 82 | 82 | 138 | 0 | 85 | 61 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.00 | 1.68 | 0.00 | 1.04 | 0.74 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.190 | 0.190 | 0.000 | 0.181 | 0.077 | 0.000 | 0.000 | 0.151 | 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 | 101 | 101 | 120 | 0 | 90 | 80 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.00 | 1.19 | 0.00 | 0.89 | 0.79 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.225 | 0.258 | 0.000 | 0.189 | 0.084 | 0.000 | 0.000 | 0.152 | 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 | 126 | 126 | 146 | 0 | 91 | 101 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 1.16 | 0.00 | 0.72 | 0.80 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.260 | 0.452 | 0.000 | 0.201 | 0.083 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 92 | 92 | 87 | 84 | 143 | 165 | 68 | 95 |
N.S. |
1 | 1.00 | 0.86 | 0.86 | 0.81 | 0.79 | 1.34 | 1.54 | 0.64 | 0.89 |
time (sec) |
N/A | 0.353 | 0.296 | 2.725 | 0.045 | 0.086 | 0.530 | 0.162 | 0.152 | 39.069 |
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 | 62 | 52 | 52 | 52 | 53 | 99 | 57 | 60 | 51 |
N.S. |
1 | 1.03 | 0.87 | 0.87 | 0.87 | 0.88 | 1.65 | 0.95 | 1.00 | 0.85 |
time (sec) |
N/A | 0.252 | 0.162 | 1.902 | 0.039 | 0.087 | 0.165 | 0.138 | 0.151 | 0.169 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | C | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 71 | 0 | 108 | 70 | 0 | 79 | 45 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 1.35 | 0.88 | 0.00 | 0.99 | 0.56 | 0.00 |
time (sec) |
N/A | 0.291 | 0.216 | 0.000 | 0.163 | 0.095 | 0.000 | 0.129 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | C | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 122 | 116 | 0 | 124 | 112 | 0 | 226 | 883 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 1.02 | 0.92 | 0.00 | 1.85 | 7.24 | 0.00 |
time (sec) |
N/A | 0.424 | 0.301 | 0.000 | 0.148 | 0.085 | 0.000 | 0.144 | 0.173 | 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 | 249 | 249 | 339 | 0 | 234 | 186 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.00 | 1.36 | 0.00 | 0.94 | 0.75 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.433 | 0.987 | 0.000 | 0.222 | 0.105 | 0.000 | 0.000 | 0.161 | 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 | 193 | 193 | 251 | 0 | 199 | 141 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.00 | 1.30 | 0.00 | 1.03 | 0.73 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.354 | 2.214 | 0.000 | 0.224 | 0.091 | 0.000 | 0.000 | 0.177 | 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 | 231 | 229 | 332 | 0 | 187 | 173 | 0 | 0 | 94 | 0 |
N.S. |
1 | 0.99 | 1.44 | 0.00 | 0.81 | 0.75 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.408 | 1.193 | 0.000 | 0.224 | 0.116 | 0.000 | 0.000 | 0.162 | 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 | 285 | 283 | 292 | 0 | 194 | 232 | 0 | 0 | 56 | 0 |
N.S. |
1 | 0.99 | 1.02 | 0.00 | 0.68 | 0.81 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.475 | 3.177 | 0.000 | 0.230 | 0.094 | 0.000 | 0.000 | 0.180 | 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 | 237 | 237 | 339 | 0 | 240 | 182 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.00 | 1.43 | 0.00 | 1.01 | 0.77 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.376 | 1.141 | 0.000 | 0.237 | 0.097 | 0.000 | 0.000 | 0.173 | 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 | 183 | 183 | 228 | 0 | 192 | 139 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 1.25 | 0.00 | 1.05 | 0.76 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.294 | 1.044 | 0.000 | 0.299 | 0.086 | 0.000 | 0.000 | 0.159 | 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 | 227 | 225 | 334 | 0 | 188 | 189 | 0 | 0 | 56 | 0 |
N.S. |
1 | 0.99 | 1.47 | 0.00 | 0.83 | 0.83 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.359 | 0.884 | 0.000 | 0.229 | 0.091 | 0.000 | 0.000 | 0.174 | 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 | 277 | 275 | 294 | 0 | 193 | 233 | 0 | 0 | 56 | 0 |
N.S. |
1 | 0.99 | 1.06 | 0.00 | 0.70 | 0.84 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.429 | 3.363 | 0.000 | 0.243 | 0.092 | 0.000 | 0.000 | 0.164 | 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 | 245 | 241 | 188 | 0 | 0 | 1041 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.98 | 0.77 | 0.00 | 0.00 | 4.25 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.894 | 0.193 | 0.000 | 0.000 | 0.202 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 57 | 51 | 49 | 8078 | 208 | 172 | 64 | 55 | 136 |
N.S. |
1 | 1.12 | 1.00 | 0.96 | 158.39 | 4.08 | 3.37 | 1.25 | 1.08 | 2.67 |
time (sec) |
N/A | 0.270 | 0.113 | 0.459 | 23.610 | 0.093 | 6.440 | 0.115 | 0.164 | 42.347 |
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 | 19 | 15 | 20 | 38 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.06 | 0.83 | 1.11 | 2.11 | 1.11 |
time (sec) |
N/A | 0.181 | 1.845 | 0.171 | 0.315 | 0.075 | 2.581 | 0.117 | 0.158 | 40.482 |
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 | 23 | 17 | 20 | 48 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.28 | 0.94 | 1.11 | 2.67 | 1.11 |
time (sec) |
N/A | 0.185 | 1.563 | 0.160 | 0.316 | 0.076 | 4.470 | 0.135 | 0.158 | 40.858 |
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 | 16 | 16 | 18 | 16 | 18 | 18 | 14 | 18 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.12 | 0.88 | 1.12 | 1.12 | 1.12 |
time (sec) |
N/A | 0.177 | 0.718 | 0.165 | 0.297 | 0.068 | 2.038 | 0.141 | 0.160 | 40.541 |
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 | 23 | 17 | 20 | 45 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.28 | 0.94 | 1.11 | 2.50 | 1.11 |
time (sec) |
N/A | 0.188 | 0.736 | 0.152 | 0.320 | 0.072 | 2.669 | 0.123 | 0.157 | 39.835 |
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 | 14 | 14 | 16 | 14 | 16 | 16 | 14 | 16 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 1.14 | 1.00 | 1.14 | 1.14 | 1.14 |
time (sec) |
N/A | 0.163 | 0.023 | 0.148 | 0.295 | 0.077 | 0.690 | 0.115 | 0.157 | 39.936 |
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 | 23 | 17 | 20 | 48 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.28 | 0.94 | 1.11 | 2.67 | 1.11 |
time (sec) |
N/A | 0.183 | 0.864 | 0.157 | 0.335 | 0.083 | 3.901 | 0.142 | 0.158 | 39.769 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 324 | 326 | 302 | 0 | 0 | 1509 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.01 | 0.93 | 0.00 | 0.00 | 4.66 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 1.160 | 1.414 | 0.000 | 0.000 | 0.220 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 99 | 91 | 131 | 0 | 366 | 2116 | 146 | 187 | 186 |
N.S. |
1 | 1.05 | 0.97 | 1.39 | 0.00 | 3.89 | 22.51 | 1.55 | 1.99 | 1.98 |
time (sec) |
N/A | 0.388 | 0.240 | 0.560 | 0.000 | 0.098 | 68.839 | 0.134 | 0.161 | 41.311 |
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 | 2696 | 45 | 17 | 20 | 112 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 149.78 | 2.50 | 0.94 | 1.11 | 6.22 | 1.11 |
time (sec) |
N/A | 0.193 | 13.683 | 0.743 | 4.450 | 0.080 | 23.650 | 0.276 | 0.166 | 41.136 |
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 | 2705 | 51 | 19 | 20 | 1331 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 150.28 | 2.83 | 1.06 | 1.11 | 73.94 | 1.11 |
time (sec) |
N/A | 0.191 | 20.426 | 0.719 | 4.436 | 0.091 | 46.662 | 0.434 | 0.239 | 41.323 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | 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 | 16 | 16 | 18 | 16 | 0 | 44 | 15 | 18 | 36 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 0.00 | 2.75 | 0.94 | 1.12 | 2.25 | 1.12 |
time (sec) |
N/A | 0.181 | 8.079 | 0.714 | 0.000 | 0.088 | 22.951 | 0.176 | 0.160 | 40.906 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | 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 | 0 | 51 | 19 | 20 | 1445 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 0.00 | 2.83 | 1.06 | 1.11 | 80.28 | 1.11 |
time (sec) |
N/A | 0.186 | 15.433 | 1.047 | 0.000 | 0.085 | 32.873 | 0.179 | 0.175 | 41.151 |
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 | 14 | 14 | 16 | 14 | 2171 | 43 | 15 | 16 | 34 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 155.07 | 3.07 | 1.07 | 1.14 | 2.43 | 1.14 |
time (sec) |
N/A | 0.164 | 10.594 | 0.784 | 1.834 | 0.086 | 15.386 | 0.144 | 0.163 | 41.112 |
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 | 2171 | 51 | 19 | 20 | 133 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 120.61 | 2.83 | 1.06 | 1.11 | 7.39 | 1.11 |
time (sec) |
N/A | 0.185 | 17.470 | 0.730 | 2.176 | 0.080 | 46.068 | 0.210 | 0.170 | 40.306 |
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 | 0.186 | 1.260 | 0.164 | 0.528 | 0.089 | 17.128 | 0.433 | 0.160 | 39.954 |
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 | 442 | 442 | 373 | 0 | 0 | 347 | 0 | 0 | 178 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.79 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.690 | 2.772 | 0.000 | 0.000 | 0.103 | 0.000 | 0.000 | 0.170 | 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 | 285 | 285 | 556 | 0 | 0 | 214 | 0 | 0 | 126 | 0 |
N.S. |
1 | 1.00 | 1.95 | 0.00 | 0.00 | 0.75 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.460 | 3.013 | 0.000 | 0.000 | 0.089 | 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 | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 134 | 149 | 0 | 0 | 106 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.00 | 1.11 | 0.00 | 0.00 | 0.79 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.283 | 0.503 | 0.000 | 0.000 | 0.082 | 0.000 | 0.000 | 0.158 | 0.000 |