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 | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 146 | 131 | 110 | 155 | 98 | 660 | 326 | 133 | 0 |
N.S. |
1 | 1.06 | 0.95 | 0.80 | 1.12 | 0.71 | 4.78 | 2.36 | 0.96 | 0.00 |
time (sec) |
N/A | 0.458 | 0.232 | 0.263 | 0.109 | 0.091 | 3.330 | 0.146 | 0.186 | 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 | 169 | 181 | 123 | 121 | 180 | 109 | 808 | 463 | 157 | 0 |
N.S. |
1 | 1.07 | 0.73 | 0.72 | 1.07 | 0.64 | 4.78 | 2.74 | 0.93 | 0.00 |
time (sec) |
N/A | 0.527 | 0.403 | 0.253 | 0.112 | 0.101 | 7.723 | 0.147 | 0.187 | 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 | 196 | 213 | 145 | 132 | 205 | 120 | 835 | 518 | 181 | 0 |
N.S. |
1 | 1.09 | 0.74 | 0.67 | 1.05 | 0.61 | 4.26 | 2.64 | 0.92 | 0.00 |
time (sec) |
N/A | 0.615 | 0.340 | 0.271 | 0.113 | 0.123 | 6.825 | 0.147 | 0.188 | 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 | 214 | 252 | 136 | 130 | 174 | 128 | 219 | 118 | 200 | 0 |
N.S. |
1 | 1.18 | 0.64 | 0.61 | 0.81 | 0.60 | 1.02 | 0.55 | 0.93 | 0.00 |
time (sec) |
N/A | 0.831 | 0.455 | 0.237 | 0.107 | 0.130 | 0.473 | 0.136 | 0.202 | 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 | 178 | 212 | 125 | 119 | 149 | 117 | 204 | 106 | 176 | 0 |
N.S. |
1 | 1.19 | 0.70 | 0.67 | 0.84 | 0.66 | 1.15 | 0.60 | 0.99 | 0.00 |
time (sec) |
N/A | 0.751 | 0.408 | 0.241 | 0.110 | 0.101 | 0.460 | 0.146 | 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 | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 182 | 114 | 108 | 124 | 106 | 189 | 94 | 152 | 0 |
N.S. |
1 | 1.19 | 0.75 | 0.71 | 0.81 | 0.69 | 1.24 | 0.61 | 0.99 | 0.00 |
time (sec) |
N/A | 0.653 | 0.374 | 0.210 | 0.108 | 0.112 | 0.467 | 0.138 | 0.197 | 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 | 117 | 148 | 111 | 94 | 96 | 95 | 150 | 81 | 128 | 0 |
N.S. |
1 | 1.26 | 0.95 | 0.80 | 0.82 | 0.81 | 1.28 | 0.69 | 1.09 | 0.00 |
time (sec) |
N/A | 0.406 | 0.289 | 0.223 | 0.108 | 0.120 | 0.524 | 0.151 | 0.184 | 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 | 140 | 142 | 133 | 219 | 124 | 102 | 403 | 105 | 90 | 0 |
N.S. |
1 | 1.01 | 0.95 | 1.56 | 0.89 | 0.73 | 2.88 | 0.75 | 0.64 | 0.00 |
time (sec) |
N/A | 0.667 | 0.401 | 0.201 | 0.110 | 0.109 | 3.205 | 0.140 | 0.185 | 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 | 146 | 136 | 141 | 165 | 132 | 124 | 393 | 177 | 126 | 0 |
N.S. |
1 | 0.93 | 0.97 | 1.13 | 0.90 | 0.85 | 2.69 | 1.21 | 0.86 | 0.00 |
time (sec) |
N/A | 0.636 | 0.354 | 0.220 | 0.109 | 0.094 | 2.464 | 0.141 | 0.184 | 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 | 156 | 140 | 149 | 150 | 139 | 134 | 447 | 244 | 138 | 0 |
N.S. |
1 | 0.90 | 0.96 | 0.96 | 0.89 | 0.86 | 2.87 | 1.56 | 0.88 | 0.00 |
time (sec) |
N/A | 0.695 | 0.410 | 0.208 | 0.110 | 0.125 | 3.202 | 0.139 | 0.195 | 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 | 152 | 144 | 139 | 137 | 134 | 129 | 461 | 284 | 163 | 0 |
N.S. |
1 | 0.95 | 0.91 | 0.90 | 0.88 | 0.85 | 3.03 | 1.87 | 1.07 | 0.00 |
time (sec) |
N/A | 0.680 | 0.480 | 0.250 | 0.110 | 0.090 | 3.485 | 0.135 | 0.197 | 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 | 153 | 150 | 127 | 116 | 159 | 111 | 544 | 325 | 100 | 0 |
N.S. |
1 | 0.98 | 0.83 | 0.76 | 1.04 | 0.73 | 3.56 | 2.12 | 0.65 | 0.00 |
time (sec) |
N/A | 0.704 | 0.569 | 0.231 | 0.111 | 0.108 | 4.567 | 0.139 | 0.196 | 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 | 138 | 152 | 125 | 107 | 153 | 98 | 777 | 388 | 133 | 0 |
N.S. |
1 | 1.10 | 0.91 | 0.78 | 1.11 | 0.71 | 5.63 | 2.81 | 0.96 | 0.00 |
time (sec) |
N/A | 0.607 | 0.389 | 0.265 | 0.114 | 0.128 | 4.264 | 0.130 | 0.187 | 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 | 167 | 187 | 142 | 121 | 178 | 109 | 921 | 463 | 157 | 0 |
N.S. |
1 | 1.12 | 0.85 | 0.72 | 1.07 | 0.65 | 5.51 | 2.77 | 0.94 | 0.00 |
time (sec) |
N/A | 0.685 | 0.412 | 0.273 | 0.105 | 0.125 | 8.124 | 0.138 | 0.204 | 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 | 196 | 217 | 153 | 132 | 203 | 120 | 1040 | 518 | 181 | 0 |
N.S. |
1 | 1.11 | 0.78 | 0.67 | 1.04 | 0.61 | 5.31 | 2.64 | 0.92 | 0.00 |
time (sec) |
N/A | 0.756 | 0.435 | 0.307 | 0.109 | 0.126 | 8.994 | 0.139 | 0.185 | 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 | 225 | 257 | 164 | 143 | 228 | 131 | 1163 | 597 | 205 | 0 |
N.S. |
1 | 1.14 | 0.73 | 0.64 | 1.01 | 0.58 | 5.17 | 2.65 | 0.91 | 0.00 |
time (sec) |
N/A | 0.862 | 0.441 | 0.329 | 0.114 | 0.111 | 26.030 | 0.139 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 186 | 103 | 97 | 125 | 95 | 0 | 88 | 128 | 0 |
N.S. |
1 | 1.14 | 0.63 | 0.60 | 0.77 | 0.58 | 0.00 | 0.54 | 0.79 | 0.00 |
time (sec) |
N/A | 0.591 | 0.301 | 0.224 | 0.115 | 0.085 | 0.000 | 0.136 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 151 | 92 | 86 | 101 | 83 | 0 | 76 | 104 | 0 |
N.S. |
1 | 1.14 | 0.70 | 0.65 | 0.77 | 0.63 | 0.00 | 0.58 | 0.79 | 0.00 |
time (sec) |
N/A | 0.534 | 0.249 | 0.203 | 0.108 | 0.114 | 0.000 | 0.135 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 116 | 83 | 75 | 77 | 73 | 0 | 64 | 80 | 0 |
N.S. |
1 | 1.07 | 0.77 | 0.69 | 0.71 | 0.68 | 0.00 | 0.59 | 0.74 | 0.00 |
time (sec) |
N/A | 0.420 | 0.192 | 0.228 | 0.115 | 0.111 | 0.000 | 0.141 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 81 | 70 | 64 | 56 | 60 | 0 | 52 | 55 | 0 |
N.S. |
1 | 1.05 | 0.91 | 0.83 | 0.73 | 0.78 | 0.00 | 0.68 | 0.71 | 0.00 |
time (sec) |
N/A | 0.347 | 0.186 | 0.204 | 0.116 | 0.100 | 0.000 | 0.135 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 63 | 49 | 31 | 52 | 0 | 36 | 30 | 0 |
N.S. |
1 | 1.00 | 1.37 | 1.07 | 0.67 | 1.13 | 0.00 | 0.78 | 0.65 | 0.00 |
time (sec) |
N/A | 0.277 | 0.138 | 0.217 | 0.105 | 0.107 | 0.000 | 0.133 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 78 | 141 | 56 | 54 | 0 | 60 | 21 | 0 |
N.S. |
1 | 1.00 | 1.70 | 3.07 | 1.22 | 1.17 | 0.00 | 1.30 | 0.46 | 0.00 |
time (sec) |
N/A | 0.372 | 0.148 | 0.206 | 0.112 | 0.083 | 0.000 | 0.137 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 73 | 63 | 0 | 50 | 0 | 115 | 38 | 0 |
N.S. |
1 | 1.00 | 1.43 | 1.24 | 0.00 | 0.98 | 0.00 | 2.25 | 0.75 | 0.00 |
time (sec) |
N/A | 0.333 | 0.142 | 0.208 | 0.000 | 0.089 | 0.000 | 0.144 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 86 | 93 | 75 | 0 | 63 | 0 | 193 | 60 | 0 |
N.S. |
1 | 1.05 | 1.13 | 0.91 | 0.00 | 0.77 | 0.00 | 2.35 | 0.73 | 0.00 |
time (sec) |
N/A | 0.392 | 0.161 | 0.218 | 0.000 | 0.081 | 0.000 | 0.135 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 122 | 109 | 88 | 0 | 75 | 0 | 255 | 85 | 0 |
N.S. |
1 | 1.07 | 0.96 | 0.77 | 0.00 | 0.66 | 0.00 | 2.24 | 0.75 | 0.00 |
time (sec) |
N/A | 0.451 | 0.173 | 0.227 | 0.000 | 0.107 | 0.000 | 0.130 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 157 | 120 | 99 | 0 | 86 | 0 | 329 | 109 | 0 |
N.S. |
1 | 1.10 | 0.84 | 0.69 | 0.00 | 0.60 | 0.00 | 2.30 | 0.76 | 0.00 |
time (sec) |
N/A | 0.532 | 0.185 | 0.226 | 0.000 | 0.114 | 0.000 | 0.134 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 192 | 110 | 131 | 133 | 124 | 0 | 217 | 236 | 0 |
N.S. |
1 | 1.18 | 0.67 | 0.80 | 0.82 | 0.76 | 0.00 | 1.33 | 1.45 | 0.00 |
time (sec) |
N/A | 0.892 | 0.343 | 0.237 | 0.116 | 0.124 | 0.000 | 0.155 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 152 | 107 | 119 | 110 | 111 | 0 | 185 | 201 | 0 |
N.S. |
1 | 1.17 | 0.82 | 0.92 | 0.85 | 0.85 | 0.00 | 1.42 | 1.55 | 0.00 |
time (sec) |
N/A | 0.666 | 0.237 | 0.234 | 0.120 | 0.100 | 0.000 | 0.146 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 112 | 89 | 109 | 88 | 101 | 0 | 153 | 166 | 0 |
N.S. |
1 | 1.04 | 0.82 | 1.01 | 0.81 | 0.94 | 0.00 | 1.42 | 1.54 | 0.00 |
time (sec) |
N/A | 0.494 | 0.276 | 0.214 | 0.113 | 0.095 | 0.000 | 0.147 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 81 | 80 | 96 | 62 | 84 | 0 | 111 | 126 | 0 |
N.S. |
1 | 1.07 | 1.05 | 1.26 | 0.82 | 1.11 | 0.00 | 1.46 | 1.66 | 0.00 |
time (sec) |
N/A | 0.345 | 0.194 | 0.220 | 0.116 | 0.121 | 0.000 | 0.140 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 63 | 130 | 40 | 66 | 0 | 0 | 59 | 0 |
N.S. |
1 | 1.00 | 1.17 | 2.41 | 0.74 | 1.22 | 0.00 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.277 | 0.273 | 0.194 | 0.108 | 0.101 | 0.000 | 0.000 | 0.325 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 75 | 274 | 0 | 65 | 0 | 134 | 106 | 0 |
N.S. |
1 | 1.00 | 1.36 | 4.98 | 0.00 | 1.18 | 0.00 | 2.44 | 1.93 | 0.00 |
time (sec) |
N/A | 0.312 | 0.262 | 0.210 | 0.000 | 0.101 | 0.000 | 0.142 | 0.287 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 86 | 89 | 109 | 0 | 91 | 0 | 161 | 108 | 0 |
N.S. |
1 | 1.06 | 1.10 | 1.35 | 0.00 | 1.12 | 0.00 | 1.99 | 1.33 | 0.00 |
time (sec) |
N/A | 0.394 | 0.298 | 0.227 | 0.000 | 0.114 | 0.000 | 0.149 | 0.310 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 118 | 94 | 118 | 0 | 114 | 0 | 202 | 138 | 0 |
N.S. |
1 | 1.04 | 0.82 | 1.04 | 0.00 | 1.00 | 0.00 | 1.77 | 1.21 | 0.00 |
time (sec) |
N/A | 0.583 | 0.342 | 0.241 | 0.000 | 0.090 | 0.000 | 0.142 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 155 | 117 | 131 | 0 | 123 | 0 | 247 | 166 | 0 |
N.S. |
1 | 1.11 | 0.84 | 0.94 | 0.00 | 0.88 | 0.00 | 1.76 | 1.19 | 0.00 |
time (sec) |
N/A | 0.820 | 0.375 | 0.250 | 0.000 | 0.109 | 0.000 | 0.155 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 186 | 116 | 144 | 0 | 136 | 0 | 277 | 196 | 0 |
N.S. |
1 | 1.07 | 0.67 | 0.83 | 0.00 | 0.78 | 0.00 | 1.59 | 1.13 | 0.00 |
time (sec) |
N/A | 1.089 | 0.443 | 0.273 | 0.000 | 0.106 | 0.000 | 0.160 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 197 | 112 | 165 | 0 | 156 | 0 | 177 | 310 | 0 |
N.S. |
1 | 1.16 | 0.66 | 0.97 | 0.00 | 0.92 | 0.00 | 1.04 | 1.82 | 0.00 |
time (sec) |
N/A | 1.012 | 0.383 | 0.289 | 0.000 | 0.124 | 0.000 | 0.141 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 152 | 101 | 154 | 0 | 146 | 0 | 165 | 275 | 0 |
N.S. |
1 | 1.06 | 0.70 | 1.07 | 0.00 | 1.01 | 0.00 | 1.15 | 1.91 | 0.00 |
time (sec) |
N/A | 0.701 | 0.342 | 0.236 | 0.000 | 0.092 | 0.000 | 0.132 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 122 | 88 | 141 | 0 | 130 | 0 | 147 | 236 | 0 |
N.S. |
1 | 1.09 | 0.79 | 1.26 | 0.00 | 1.16 | 0.00 | 1.31 | 2.11 | 0.00 |
time (sec) |
N/A | 0.433 | 0.290 | 0.238 | 0.000 | 0.112 | 0.000 | 0.140 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 89 | 76 | 173 | 0 | 113 | 0 | 124 | 145 | 0 |
N.S. |
1 | 1.06 | 0.90 | 2.06 | 0.00 | 1.35 | 0.00 | 1.48 | 1.73 | 0.00 |
time (sec) |
N/A | 0.344 | 0.275 | 0.206 | 0.000 | 0.112 | 0.000 | 0.141 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 40 | 36 | 69 | 66 | 0 | 74 | 111 | 35 |
N.S. |
1 | 1.00 | 1.21 | 1.09 | 2.09 | 2.00 | 0.00 | 2.24 | 3.36 | 1.06 |
time (sec) |
N/A | 0.243 | 0.298 | 0.238 | 0.029 | 0.104 | 0.000 | 0.139 | 0.190 | 6.877 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 86 | 88 | 319 | 0 | 109 | 0 | 150 | 195 | 0 |
N.S. |
1 | 1.01 | 1.04 | 3.75 | 0.00 | 1.28 | 0.00 | 1.76 | 2.29 | 0.00 |
time (sec) |
N/A | 0.447 | 0.322 | 0.252 | 0.000 | 0.108 | 0.000 | 0.135 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 123 | 104 | 154 | 0 | 137 | 0 | 242 | 214 | 0 |
N.S. |
1 | 1.03 | 0.87 | 1.29 | 0.00 | 1.15 | 0.00 | 2.03 | 1.80 | 0.00 |
time (sec) |
N/A | 0.646 | 0.412 | 0.287 | 0.000 | 0.105 | 0.000 | 0.139 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 160 | 119 | 160 | 0 | 158 | 0 | 320 | 266 | 0 |
N.S. |
1 | 1.07 | 0.79 | 1.07 | 0.00 | 1.05 | 0.00 | 2.13 | 1.77 | 0.00 |
time (sec) |
N/A | 0.868 | 0.395 | 0.293 | 0.000 | 0.095 | 0.000 | 0.136 | 0.248 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 197 | 112 | 199 | 0 | 190 | 0 | 233 | 410 | 0 |
N.S. |
1 | 1.11 | 0.63 | 1.12 | 0.00 | 1.07 | 0.00 | 1.31 | 2.30 | 0.00 |
time (sec) |
N/A | 1.078 | 0.462 | 0.250 | 0.000 | 0.138 | 0.000 | 0.137 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 154 | 106 | 186 | 0 | 174 | 0 | 211 | 384 | 0 |
N.S. |
1 | 1.05 | 0.73 | 1.27 | 0.00 | 1.19 | 0.00 | 1.45 | 2.63 | 0.00 |
time (sec) |
N/A | 0.716 | 0.408 | 0.292 | 0.000 | 0.114 | 0.000 | 0.137 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 115 | 87 | 268 | 0 | 157 | 0 | 186 | 357 | 0 |
N.S. |
1 | 0.93 | 0.70 | 2.16 | 0.00 | 1.27 | 0.00 | 1.50 | 2.88 | 0.00 |
time (sec) |
N/A | 0.470 | 0.390 | 0.237 | 0.000 | 0.121 | 0.000 | 0.147 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 52 | 42 | 125 | 102 | 0 | 137 | 69 | 46 |
N.S. |
1 | 1.00 | 0.81 | 0.66 | 1.95 | 1.59 | 0.00 | 2.14 | 1.08 | 0.72 |
time (sec) |
N/A | 0.300 | 0.276 | 0.233 | 0.034 | 0.101 | 0.000 | 0.133 | 0.218 | 6.441 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 51 | 43 | 123 | 104 | 0 | 165 | 68 | 47 |
N.S. |
1 | 1.00 | 0.76 | 0.64 | 1.84 | 1.55 | 0.00 | 2.46 | 1.01 | 0.70 |
time (sec) |
N/A | 0.291 | 0.360 | 0.221 | 0.034 | 0.105 | 0.000 | 0.131 | 0.216 | 7.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 114 | 88 | 415 | 0 | 153 | 0 | 212 | 27 | 0 |
N.S. |
1 | 1.03 | 0.79 | 3.74 | 0.00 | 1.38 | 0.00 | 1.91 | 0.24 | 0.00 |
time (sec) |
N/A | 0.655 | 0.549 | 0.243 | 0.000 | 0.109 | 0.000 | 0.139 | 200.034 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 155 | 115 | 199 | 0 | 181 | 0 | 304 | 325 | 0 |
N.S. |
1 | 1.05 | 0.78 | 1.34 | 0.00 | 1.22 | 0.00 | 2.05 | 2.20 | 0.00 |
time (sec) |
N/A | 0.869 | 0.554 | 0.312 | 0.000 | 0.133 | 0.000 | 0.142 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 206 | 116 | 205 | 0 | 202 | 0 | 382 | 27 | 0 |
N.S. |
1 | 1.12 | 0.63 | 1.11 | 0.00 | 1.10 | 0.00 | 2.08 | 0.15 | 0.00 |
time (sec) |
N/A | 1.165 | 0.564 | 0.303 | 0.000 | 0.114 | 0.000 | 0.140 | 200.025 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 146 | 86 | 186 | 0 | 141 | 0 | 0 | 336 | 256 |
N.S. |
1 | 1.07 | 0.63 | 1.37 | 0.00 | 1.04 | 0.00 | 0.00 | 2.47 | 1.88 |
time (sec) |
N/A | 0.843 | 0.311 | 0.253 | 0.000 | 0.103 | 0.000 | 0.000 | 0.190 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 127 | 78 | 181 | 0 | 133 | 0 | 0 | 317 | 201 |
N.S. |
1 | 1.14 | 0.70 | 1.63 | 0.00 | 1.20 | 0.00 | 0.00 | 2.86 | 1.81 |
time (sec) |
N/A | 0.600 | 0.302 | 0.239 | 0.000 | 0.112 | 0.000 | 0.000 | 0.212 | 7.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 95 | 70 | 245 | 0 | 126 | 0 | 0 | 298 | 220 |
N.S. |
1 | 1.02 | 0.75 | 2.63 | 0.00 | 1.35 | 0.00 | 0.00 | 3.20 | 2.37 |
time (sec) |
N/A | 0.429 | 0.268 | 0.214 | 0.000 | 0.095 | 0.000 | 0.000 | 0.216 | 0.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 42 | 36 | 104 | 79 | 0 | 118 | 53 | 105 |
N.S. |
1 | 1.00 | 0.71 | 0.61 | 1.76 | 1.34 | 0.00 | 2.00 | 0.90 | 1.78 |
time (sec) |
N/A | 0.300 | 0.204 | 0.217 | 0.032 | 0.121 | 0.000 | 0.141 | 0.178 | 6.833 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 41 | 35 | 98 | 77 | 0 | 142 | 52 | 38 |
N.S. |
1 | 1.00 | 0.69 | 0.59 | 1.66 | 1.31 | 0.00 | 2.41 | 0.88 | 0.64 |
time (sec) |
N/A | 0.289 | 0.222 | 0.214 | 0.027 | 0.104 | 0.000 | 0.137 | 0.182 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 85 | 61 | 343 | 0 | 117 | 0 | 183 | 26 | 179 |
N.S. |
1 | 0.97 | 0.69 | 3.90 | 0.00 | 1.33 | 0.00 | 2.08 | 0.30 | 2.03 |
time (sec) |
N/A | 0.562 | 0.255 | 0.256 | 0.000 | 0.123 | 0.000 | 0.130 | 200.030 | 6.976 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 122 | 76 | 302 | 0 | 143 | 0 | 260 | 263 | 201 |
N.S. |
1 | 1.03 | 0.64 | 2.54 | 0.00 | 1.20 | 0.00 | 2.18 | 2.21 | 1.69 |
time (sec) |
N/A | 0.752 | 0.306 | 0.266 | 0.000 | 0.114 | 0.000 | 0.134 | 0.205 | 7.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 155 | 89 | 317 | 0 | 161 | 0 | 0 | 26 | 221 |
N.S. |
1 | 1.05 | 0.61 | 2.16 | 0.00 | 1.10 | 0.00 | 0.00 | 0.18 | 1.50 |
time (sec) |
N/A | 0.991 | 0.310 | 0.258 | 0.000 | 0.096 | 0.000 | 0.000 | 200.029 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 156 | 86 | 221 | 0 | 163 | 0 | 0 | 26 | 293 |
N.S. |
1 | 1.12 | 0.62 | 1.59 | 0.00 | 1.17 | 0.00 | 0.00 | 0.19 | 2.11 |
time (sec) |
N/A | 0.715 | 0.410 | 0.237 | 0.000 | 0.097 | 0.000 | 0.000 | 200.035 | 6.951 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 123 | 78 | 377 | 0 | 156 | 0 | 0 | 26 | 236 |
N.S. |
1 | 1.03 | 0.66 | 3.17 | 0.00 | 1.31 | 0.00 | 0.00 | 0.22 | 1.98 |
time (sec) |
N/A | 0.488 | 0.348 | 0.210 | 0.000 | 0.116 | 0.000 | 0.000 | 200.033 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 125 | 50 | 44 | 153 | 102 | 0 | 0 | 26 | 287 |
N.S. |
1 | 1.42 | 0.57 | 0.50 | 1.74 | 1.16 | 0.00 | 0.00 | 0.30 | 3.26 |
time (sec) |
N/A | 0.416 | 0.302 | 0.216 | 0.037 | 0.090 | 0.000 | 0.000 | 200.036 | 7.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | C | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 96 | 50 | 43 | 153 | 100 | 0 | 248 | 24 | 242 |
N.S. |
1 | 1.09 | 0.57 | 0.49 | 1.74 | 1.14 | 0.00 | 2.82 | 0.27 | 2.75 |
time (sec) |
N/A | 0.348 | 0.290 | 0.220 | 0.039 | 0.091 | 0.000 | 0.141 | 200.036 | 6.781 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | C | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 93 | 50 | 44 | 145 | 100 | 0 | 196 | 23 | 277 |
N.S. |
1 | 1.06 | 0.57 | 0.50 | 1.65 | 1.14 | 0.00 | 2.23 | 0.26 | 3.15 |
time (sec) |
N/A | 0.329 | 0.292 | 0.223 | 0.035 | 0.110 | 0.000 | 0.127 | 200.039 | 0.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 125 | 69 | 473 | 0 | 149 | 0 | 237 | 363 | 273 |
N.S. |
1 | 1.08 | 0.59 | 4.08 | 0.00 | 1.28 | 0.00 | 2.04 | 3.13 | 2.35 |
time (sec) |
N/A | 0.665 | 0.325 | 0.218 | 0.000 | 0.081 | 0.000 | 0.144 | 0.207 | 6.435 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 152 | 84 | 469 | 0 | 172 | 0 | 0 | 26 | 295 |
N.S. |
1 | 1.06 | 0.58 | 3.26 | 0.00 | 1.19 | 0.00 | 0.00 | 0.18 | 2.05 |
time (sec) |
N/A | 0.957 | 0.418 | 0.266 | 0.000 | 0.099 | 0.000 | 0.000 | 200.029 | 6.840 |
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 | 36 | 36 | 37 | 25 | 28 | 31 | 29 | 19 | 27 | 20 |
N.S. |
1 | 1.00 | 1.03 | 0.69 | 0.78 | 0.86 | 0.81 | 0.53 | 0.75 | 0.56 |
time (sec) |
N/A | 0.258 | 0.083 | 0.188 | 0.107 | 0.119 | 1.114 | 0.125 | 0.183 | 0.044 |
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 | 188 | 211 | 136 | 130 | 152 | 127 | 189 | 118 | 200 | 0 |
N.S. |
1 | 1.12 | 0.72 | 0.69 | 0.81 | 0.68 | 1.01 | 0.63 | 1.06 | 0.00 |
time (sec) |
N/A | 0.535 | 0.462 | 0.187 | 0.111 | 0.082 | 0.527 | 0.147 | 0.192 | 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 | 157 | 176 | 125 | 119 | 127 | 116 | 173 | 107 | 176 | 0 |
N.S. |
1 | 1.12 | 0.80 | 0.76 | 0.81 | 0.74 | 1.10 | 0.68 | 1.12 | 0.00 |
time (sec) |
N/A | 0.475 | 0.384 | 0.191 | 0.107 | 0.120 | 0.512 | 0.145 | 0.183 | 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 | 133 | 140 | 114 | 108 | 102 | 105 | 158 | 94 | 152 | 0 |
N.S. |
1 | 1.05 | 0.86 | 0.81 | 0.77 | 0.79 | 1.19 | 0.71 | 1.14 | 0.00 |
time (sec) |
N/A | 0.383 | 0.363 | 0.188 | 0.106 | 0.094 | 0.542 | 0.138 | 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 | 100 | 107 | 111 | 94 | 73 | 94 | 143 | 81 | 128 | 67 |
N.S. |
1 | 1.07 | 1.11 | 0.94 | 0.73 | 0.94 | 1.43 | 0.81 | 1.28 | 0.67 |
time (sec) |
N/A | 0.329 | 0.255 | 0.168 | 0.106 | 0.078 | 0.470 | 0.138 | 0.188 | 7.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 118 | 142 | 157 | 124 | 107 | 400 | 113 | 114 | 107 |
N.S. |
1 | 1.04 | 1.26 | 1.39 | 1.10 | 0.95 | 3.54 | 1.00 | 1.01 | 0.95 |
time (sec) |
N/A | 0.456 | 0.394 | 0.201 | 0.109 | 0.091 | 5.958 | 0.138 | 0.190 | 7.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 116 | 143 | 165 | 129 | 124 | 389 | 178 | 126 | 114 |
N.S. |
1 | 0.99 | 1.22 | 1.41 | 1.10 | 1.06 | 3.32 | 1.52 | 1.08 | 0.97 |
time (sec) |
N/A | 0.468 | 0.314 | 0.229 | 0.120 | 0.124 | 2.556 | 0.140 | 0.185 | 7.765 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 108 | 148 | 150 | 160 | 133 | 444 | 244 | 138 | 120 |
N.S. |
1 | 0.91 | 1.24 | 1.26 | 1.34 | 1.12 | 3.73 | 2.05 | 1.16 | 1.01 |
time (sec) |
N/A | 0.468 | 0.356 | 0.228 | 0.117 | 0.108 | 3.536 | 0.146 | 0.184 | 7.426 |
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 | 120 | 118 | 149 | 137 | 184 | 129 | 457 | 285 | 163 | 0 |
N.S. |
1 | 0.98 | 1.24 | 1.14 | 1.53 | 1.08 | 3.81 | 2.38 | 1.36 | 0.00 |
time (sec) |
N/A | 0.478 | 0.332 | 0.230 | 0.125 | 0.143 | 3.458 | 0.145 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 124 | 151 | 125 | 210 | 119 | 541 | 327 | 121 | 0 |
N.S. |
1 | 1.05 | 1.28 | 1.06 | 1.78 | 1.01 | 4.58 | 2.77 | 1.03 | 0.00 |
time (sec) |
N/A | 0.482 | 0.292 | 0.247 | 0.116 | 0.126 | 4.531 | 0.138 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 113 | 122 | 107 | 155 | 98 | 774 | 388 | 133 | 93 |
N.S. |
1 | 1.02 | 1.10 | 0.96 | 1.40 | 0.88 | 6.97 | 3.50 | 1.20 | 0.84 |
time (sec) |
N/A | 0.356 | 0.331 | 0.253 | 0.113 | 0.093 | 4.209 | 0.143 | 0.215 | 8.566 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 148 | 142 | 121 | 180 | 109 | 918 | 463 | 157 | 118 |
N.S. |
1 | 1.05 | 1.01 | 0.86 | 1.28 | 0.77 | 6.51 | 3.28 | 1.11 | 0.84 |
time (sec) |
N/A | 0.402 | 0.314 | 0.276 | 0.110 | 0.166 | 8.019 | 0.145 | 0.195 | 8.717 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 183 | 153 | 132 | 205 | 120 | 1037 | 518 | 181 | 192 |
N.S. |
1 | 1.08 | 0.91 | 0.78 | 1.21 | 0.71 | 6.14 | 3.07 | 1.07 | 1.14 |
time (sec) |
N/A | 0.480 | 0.399 | 0.237 | 0.112 | 0.112 | 8.792 | 0.148 | 0.204 | 9.314 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 218 | 164 | 143 | 230 | 131 | 1159 | 463 | 205 | 212 |
N.S. |
1 | 1.10 | 0.82 | 0.72 | 1.16 | 0.66 | 5.82 | 2.33 | 1.03 | 1.07 |
time (sec) |
N/A | 0.564 | 0.356 | 0.302 | 0.110 | 0.119 | 25.824 | 0.150 | 0.191 | 10.175 |
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 | 238 | 275 | 158 | 152 | 199 | 149 | 231 | 142 | 248 | 0 |
N.S. |
1 | 1.16 | 0.66 | 0.64 | 0.84 | 0.63 | 0.97 | 0.60 | 1.04 | 0.00 |
time (sec) |
N/A | 0.688 | 0.603 | 0.219 | 0.113 | 0.115 | 0.541 | 0.141 | 0.183 | 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 | 214 | 240 | 158 | 141 | 174 | 138 | 216 | 130 | 224 | 0 |
N.S. |
1 | 1.12 | 0.74 | 0.66 | 0.81 | 0.64 | 1.01 | 0.61 | 1.05 | 0.00 |
time (sec) |
N/A | 0.636 | 0.281 | 0.225 | 0.116 | 0.100 | 0.538 | 0.145 | 0.185 | 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 | 195 | 205 | 136 | 130 | 149 | 127 | 204 | 119 | 200 | 0 |
N.S. |
1 | 1.05 | 0.70 | 0.67 | 0.76 | 0.65 | 1.05 | 0.61 | 1.03 | 0.00 |
time (sec) |
N/A | 0.542 | 0.535 | 0.228 | 0.133 | 0.092 | 0.513 | 0.138 | 0.173 | 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 | 147 | 170 | 133 | 119 | 124 | 116 | 185 | 106 | 176 | 0 |
N.S. |
1 | 1.16 | 0.90 | 0.81 | 0.84 | 0.79 | 1.26 | 0.72 | 1.20 | 0.00 |
time (sec) |
N/A | 0.465 | 0.287 | 0.194 | 0.113 | 0.095 | 0.522 | 0.143 | 0.183 | 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 | 110 | 141 | 114 | 105 | 93 | 105 | 163 | 92 | 152 | 0 |
N.S. |
1 | 1.28 | 1.04 | 0.95 | 0.85 | 0.95 | 1.48 | 0.84 | 1.38 | 0.00 |
time (sec) |
N/A | 0.378 | 0.454 | 0.187 | 0.110 | 0.109 | 0.526 | 0.138 | 0.208 | 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 | 165 | 141 | 151 | 177 | 143 | 118 | 430 | 125 | 138 | 0 |
N.S. |
1 | 0.85 | 0.92 | 1.07 | 0.87 | 0.72 | 2.61 | 0.76 | 0.84 | 0.00 |
time (sec) |
N/A | 0.522 | 0.458 | 0.187 | 0.109 | 0.102 | 5.025 | 0.144 | 0.194 | 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 | 172 | 142 | 160 | 190 | 155 | 135 | 425 | 189 | 150 | 0 |
N.S. |
1 | 0.83 | 0.93 | 1.10 | 0.90 | 0.78 | 2.47 | 1.10 | 0.87 | 0.00 |
time (sec) |
N/A | 0.533 | 0.459 | 0.218 | 0.108 | 0.081 | 2.585 | 0.146 | 0.212 | 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 | 183 | 138 | 155 | 175 | 158 | 147 | 388 | 255 | 161 | 0 |
N.S. |
1 | 0.75 | 0.85 | 0.96 | 0.86 | 0.80 | 2.12 | 1.39 | 0.88 | 0.00 |
time (sec) |
N/A | 0.559 | 0.504 | 0.217 | 0.116 | 0.105 | 2.497 | 0.145 | 0.173 | 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 | 183 | 142 | 159 | 161 | 182 | 147 | 439 | 311 | 162 | 0 |
N.S. |
1 | 0.78 | 0.87 | 0.88 | 0.99 | 0.80 | 2.40 | 1.70 | 0.89 | 0.00 |
time (sec) |
N/A | 0.556 | 0.431 | 0.234 | 0.111 | 0.133 | 2.819 | 0.146 | 0.184 | 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 | 186 | 147 | 153 | 149 | 208 | 140 | 549 | 293 | 156 | 0 |
N.S. |
1 | 0.79 | 0.82 | 0.80 | 1.12 | 0.75 | 2.95 | 1.58 | 0.84 | 0.00 |
time (sec) |
N/A | 0.568 | 0.592 | 0.215 | 0.111 | 0.118 | 4.532 | 0.138 | 0.180 | 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 | 185 | 150 | 165 | 136 | 232 | 130 | 785 | 383 | 145 | 0 |
N.S. |
1 | 0.81 | 0.89 | 0.74 | 1.25 | 0.70 | 4.24 | 2.07 | 0.78 | 0.00 |
time (sec) |
N/A | 0.538 | 0.418 | 0.237 | 0.113 | 0.134 | 4.687 | 0.143 | 0.194 | 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 | 140 | 142 | 133 | 118 | 177 | 109 | 833 | 463 | 157 | 0 |
N.S. |
1 | 1.01 | 0.95 | 0.84 | 1.26 | 0.78 | 5.95 | 3.31 | 1.12 | 0.00 |
time (sec) |
N/A | 0.417 | 0.392 | 0.240 | 0.107 | 0.090 | 7.033 | 0.143 | 0.206 | 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 | 167 | 177 | 145 | 132 | 202 | 120 | 799 | 518 | 181 | 0 |
N.S. |
1 | 1.06 | 0.87 | 0.79 | 1.21 | 0.72 | 4.78 | 3.10 | 1.08 | 0.00 |
time (sec) |
N/A | 0.483 | 0.475 | 0.294 | 0.112 | 0.100 | 8.683 | 0.147 | 0.181 | 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 | 198 | 212 | 148 | 143 | 227 | 131 | 1107 | 597 | 205 | 0 |
N.S. |
1 | 1.07 | 0.75 | 0.72 | 1.15 | 0.66 | 5.59 | 3.02 | 1.04 | 0.00 |
time (sec) |
N/A | 0.588 | 0.609 | 0.328 | 0.110 | 0.104 | 22.893 | 0.147 | 0.192 | 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 | 225 | 247 | 175 | 154 | 252 | 142 | 1222 | 518 | 229 | 0 |
N.S. |
1 | 1.10 | 0.78 | 0.68 | 1.12 | 0.63 | 5.43 | 2.30 | 1.02 | 0.00 |
time (sec) |
N/A | 0.648 | 0.480 | 0.343 | 0.114 | 0.178 | 28.234 | 0.145 | 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 | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 264 | 316 | 169 | 163 | 222 | 160 | 260 | 154 | 272 | 0 |
N.S. |
1 | 1.20 | 0.64 | 0.62 | 0.84 | 0.61 | 0.98 | 0.58 | 1.03 | 0.00 |
time (sec) |
N/A | 0.983 | 0.651 | 0.286 | 0.117 | 0.100 | 0.588 | 0.147 | 0.185 | 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 | 238 | 281 | 158 | 152 | 197 | 149 | 240 | 141 | 248 | 0 |
N.S. |
1 | 1.18 | 0.66 | 0.64 | 0.83 | 0.63 | 1.01 | 0.59 | 1.04 | 0.00 |
time (sec) |
N/A | 0.859 | 0.625 | 0.272 | 0.115 | 0.090 | 0.572 | 0.156 | 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 | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 246 | 147 | 141 | 172 | 138 | 235 | 131 | 224 | 0 |
N.S. |
1 | 1.20 | 0.72 | 0.69 | 0.84 | 0.67 | 1.15 | 0.64 | 1.09 | 0.00 |
time (sec) |
N/A | 0.800 | 0.593 | 0.249 | 0.121 | 0.091 | 0.554 | 0.144 | 0.197 | 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 | 180 | 211 | 136 | 130 | 147 | 127 | 216 | 118 | 200 | 0 |
N.S. |
1 | 1.17 | 0.76 | 0.72 | 0.82 | 0.71 | 1.20 | 0.66 | 1.11 | 0.00 |
time (sec) |
N/A | 0.670 | 0.571 | 0.216 | 0.115 | 0.101 | 0.556 | 0.248 | 0.188 | 0.000 |