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 | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 172 | 176 | 175 | 175 | 226 | 216 | 172 | 182 |
N.S. |
1 | 1.00 | 2.23 | 2.29 | 2.27 | 2.27 | 2.94 | 2.81 | 2.23 | 2.36 |
time (sec) |
N/A | 0.310 | 0.038 | 0.149 | 0.042 | 0.081 | 0.031 | 0.120 | 0.155 | 0.058 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 130 | 135 | 134 | 134 | 168 | 163 | 131 | 141 |
N.S. |
1 | 1.00 | 1.69 | 1.75 | 1.74 | 1.74 | 2.18 | 2.12 | 1.70 | 1.83 |
time (sec) |
N/A | 0.295 | 0.028 | 0.144 | 0.040 | 0.091 | 0.026 | 0.120 | 0.156 | 0.893 |
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 | 77 | 77 | 96 | 94 | 93 | 93 | 116 | 113 | 90 | 98 |
N.S. |
1 | 1.00 | 1.25 | 1.22 | 1.21 | 1.21 | 1.51 | 1.47 | 1.17 | 1.27 |
time (sec) |
N/A | 0.268 | 0.020 | 0.141 | 0.036 | 0.068 | 0.022 | 0.115 | 0.155 | 0.871 |
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 | 56 | 56 | 53 | 53 | 52 | 62 | 63 | 62 | 49 | 54 |
N.S. |
1 | 1.00 | 0.95 | 0.95 | 0.93 | 1.11 | 1.12 | 1.11 | 0.88 | 0.96 |
time (sec) |
N/A | 0.228 | 0.013 | 0.045 | 0.038 | 0.035 | 0.017 | 0.126 | 0.154 | 0.027 |
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 | 28 | 28 | 28 | 25 | 24 | 26 | 26 | 26 | 21 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.86 | 0.93 | 0.93 | 0.93 | 0.75 | 0.89 |
time (sec) |
N/A | 0.187 | 0.003 | 0.029 | 0.037 | 0.036 | 0.017 | 0.127 | 0.158 | 0.022 |
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 | 60 | 56 | 66 | 66 | 68 | 53 | 68 | 72 | 68 |
N.S. |
1 | 1.00 | 0.93 | 1.10 | 1.10 | 1.13 | 0.88 | 1.13 | 1.20 | 1.13 |
time (sec) |
N/A | 0.224 | 0.016 | 0.191 | 0.033 | 0.063 | 0.135 | 0.124 | 0.168 | 0.889 |
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 | 63 | 63 | 56 | 70 | 74 | 102 | 71 | 114 | 112 | 75 |
N.S. |
1 | 1.00 | 0.89 | 1.11 | 1.17 | 1.62 | 1.13 | 1.81 | 1.78 | 1.19 |
time (sec) |
N/A | 0.238 | 0.029 | 0.198 | 0.033 | 0.109 | 0.231 | 0.128 | 0.163 | 0.059 |
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 | 70 | 70 | 72 | 72 | 87 | 105 | 94 | 77 | 113 | 82 |
N.S. |
1 | 1.00 | 1.03 | 1.03 | 1.24 | 1.50 | 1.34 | 1.10 | 1.61 | 1.17 |
time (sec) |
N/A | 0.265 | 0.022 | 0.191 | 0.051 | 0.072 | 0.393 | 0.121 | 0.161 | 0.908 |
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 | 75 | 75 | 63 | 70 | 93 | 93 | 107 | 70 | 69 | 91 |
N.S. |
1 | 1.00 | 0.84 | 0.93 | 1.24 | 1.24 | 1.43 | 0.93 | 0.92 | 1.21 |
time (sec) |
N/A | 0.262 | 0.019 | 0.194 | 0.037 | 0.072 | 0.705 | 0.127 | 0.155 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 62 | 68 | 102 | 102 | 117 | 121 | 95 | 101 |
N.S. |
1 | 1.00 | 0.81 | 0.88 | 1.32 | 1.32 | 1.52 | 1.57 | 1.23 | 1.31 |
time (sec) |
N/A | 0.240 | 0.019 | 0.203 | 0.029 | 0.073 | 1.140 | 0.114 | 0.158 | 0.911 |
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 | 77 | 77 | 65 | 73 | 117 | 117 | 134 | 72 | 106 | 118 |
N.S. |
1 | 1.00 | 0.84 | 0.95 | 1.52 | 1.52 | 1.74 | 0.94 | 1.38 | 1.53 |
time (sec) |
N/A | 0.258 | 0.021 | 0.208 | 0.041 | 0.071 | 1.721 | 0.121 | 0.157 | 0.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 120 | 283 | 305 | 304 | 304 | 384 | 374 | 247 | 305 |
N.S. |
1 | 1.00 | 2.36 | 2.54 | 2.53 | 2.53 | 3.20 | 3.12 | 2.06 | 2.54 |
time (sec) |
N/A | 0.438 | 0.059 | 0.180 | 0.032 | 0.062 | 0.036 | 0.120 | 0.157 | 0.949 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 120 | 216 | 237 | 236 | 236 | 296 | 287 | 189 | 231 |
N.S. |
1 | 1.00 | 1.80 | 1.98 | 1.97 | 1.97 | 2.47 | 2.39 | 1.58 | 1.92 |
time (sec) |
N/A | 0.364 | 0.047 | 0.175 | 0.030 | 0.083 | 0.032 | 0.121 | 0.157 | 0.052 |
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 | 118 | 118 | 157 | 169 | 168 | 168 | 202 | 199 | 131 | 157 |
N.S. |
1 | 1.00 | 1.33 | 1.43 | 1.42 | 1.42 | 1.71 | 1.69 | 1.11 | 1.33 |
time (sec) |
N/A | 0.388 | 0.034 | 0.170 | 0.041 | 0.064 | 0.027 | 0.124 | 0.160 | 0.039 |
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 | 75 | 75 | 96 | 99 | 100 | 100 | 116 | 113 | 73 | 98 |
N.S. |
1 | 1.00 | 1.28 | 1.32 | 1.33 | 1.33 | 1.55 | 1.51 | 0.97 | 1.31 |
time (sec) |
N/A | 0.283 | 0.018 | 0.146 | 0.034 | 0.070 | 0.024 | 0.117 | 0.160 | 0.903 |
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 | 38 | 38 | 46 | 48 | 48 | 48 | 49 | 49 | 32 | 47 |
N.S. |
1 | 1.00 | 1.21 | 1.26 | 1.26 | 1.26 | 1.29 | 1.29 | 0.84 | 1.24 |
time (sec) |
N/A | 0.211 | 0.007 | 0.131 | 0.027 | 0.068 | 0.023 | 0.117 | 0.155 | 0.026 |
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 | 92 | 92 | 102 | 148 | 152 | 153 | 117 | 166 | 132 | 159 |
N.S. |
1 | 1.00 | 1.11 | 1.61 | 1.65 | 1.66 | 1.27 | 1.80 | 1.43 | 1.73 |
time (sec) |
N/A | 0.281 | 0.036 | 0.217 | 0.029 | 0.073 | 0.247 | 0.119 | 0.159 | 0.925 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 98 | 151 | 156 | 238 | 151 | 230 | 197 | 165 |
N.S. |
1 | 1.00 | 0.97 | 1.50 | 1.54 | 2.36 | 1.50 | 2.28 | 1.95 | 1.63 |
time (sec) |
N/A | 0.319 | 0.053 | 0.214 | 0.041 | 0.080 | 0.467 | 0.119 | 0.160 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 106 | 143 | 155 | 166 | 247 | 187 | 159 | 209 | 170 |
N.S. |
1 | 1.00 | 1.35 | 1.46 | 1.57 | 2.33 | 1.76 | 1.50 | 1.97 | 1.60 |
time (sec) |
N/A | 0.305 | 0.049 | 0.212 | 0.038 | 0.077 | 1.105 | 0.119 | 0.160 | 0.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 104 | 138 | 157 | 184 | 221 | 211 | 166 | 180 | 178 |
N.S. |
1 | 1.03 | 1.37 | 1.55 | 1.82 | 2.19 | 2.09 | 1.64 | 1.78 | 1.76 |
time (sec) |
N/A | 0.297 | 0.043 | 0.208 | 0.038 | 0.069 | 2.364 | 0.126 | 0.159 | 0.081 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 125 | 152 | 187 | 187 | 223 | 232 | 122 | 184 |
N.S. |
1 | 1.00 | 1.45 | 1.77 | 2.17 | 2.17 | 2.59 | 2.70 | 1.42 | 2.14 |
time (sec) |
N/A | 0.220 | 0.039 | 0.217 | 0.036 | 0.080 | 4.644 | 0.121 | 0.161 | 0.984 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 120 | 129 | 157 | 203 | 203 | 238 | 168 | 159 | 201 |
N.S. |
1 | 1.00 | 1.08 | 1.31 | 1.69 | 1.69 | 1.98 | 1.40 | 1.32 | 1.68 |
time (sec) |
N/A | 0.314 | 0.038 | 0.214 | 0.041 | 0.067 | 8.336 | 0.121 | 0.158 | 0.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 120 | 126 | 151 | 208 | 208 | 246 | 166 | 170 | 206 |
N.S. |
1 | 1.00 | 1.05 | 1.26 | 1.73 | 1.73 | 2.05 | 1.38 | 1.42 | 1.72 |
time (sec) |
N/A | 0.297 | 0.038 | 0.219 | 0.047 | 0.073 | 15.406 | 0.121 | 0.159 | 0.982 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 120 | 129 | 157 | 225 | 225 | 262 | 168 | 181 | 223 |
N.S. |
1 | 1.00 | 1.08 | 1.31 | 1.88 | 1.88 | 2.18 | 1.40 | 1.51 | 1.86 |
time (sec) |
N/A | 0.304 | 0.039 | 0.224 | 0.042 | 0.068 | 27.267 | 0.118 | 0.159 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 163 | 471 | 529 | 518 | 518 | 678 | 658 | 397 | 544 |
N.S. |
1 | 1.00 | 2.89 | 3.25 | 3.18 | 3.18 | 4.16 | 4.04 | 2.44 | 3.34 |
time (sec) |
N/A | 0.627 | 0.103 | 0.182 | 0.040 | 0.065 | 0.071 | 0.123 | 0.156 | 0.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 163 | 397 | 434 | 425 | 425 | 546 | 534 | 322 | 439 |
N.S. |
1 | 1.00 | 2.44 | 2.66 | 2.61 | 2.61 | 3.35 | 3.28 | 1.98 | 2.69 |
time (sec) |
N/A | 0.551 | 0.087 | 0.181 | 0.036 | 0.079 | 0.050 | 0.121 | 0.150 | 0.960 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 297 | 339 | 325 | 325 | 422 | 410 | 247 | 334 |
N.S. |
1 | 1.00 | 1.87 | 2.13 | 2.04 | 2.04 | 2.65 | 2.58 | 1.55 | 2.10 |
time (sec) |
N/A | 0.492 | 0.067 | 0.173 | 0.033 | 0.069 | 0.050 | 0.121 | 0.158 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 224 | 244 | 239 | 239 | 296 | 287 | 172 | 231 |
N.S. |
1 | 1.00 | 1.90 | 2.07 | 2.03 | 2.03 | 2.51 | 2.43 | 1.46 | 1.96 |
time (sec) |
N/A | 0.391 | 0.049 | 0.174 | 0.042 | 0.077 | 0.052 | 0.124 | 0.156 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 130 | 142 | 146 | 146 | 168 | 163 | 97 | 141 |
N.S. |
1 | 1.00 | 1.73 | 1.89 | 1.95 | 1.95 | 2.24 | 2.17 | 1.29 | 1.88 |
time (sec) |
N/A | 0.313 | 0.027 | 0.166 | 0.037 | 0.084 | 0.029 | 0.118 | 0.154 | 0.929 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 67 | 70 | 69 | 69 | 73 | 72 | 43 | 65 |
N.S. |
1 | 1.00 | 1.76 | 1.84 | 1.82 | 1.82 | 1.92 | 1.89 | 1.13 | 1.71 |
time (sec) |
N/A | 0.205 | 0.007 | 0.125 | 0.027 | 0.062 | 0.027 | 0.121 | 0.155 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 124 | 169 | 260 | 258 | 260 | 221 | 297 | 208 | 268 |
N.S. |
1 | 1.00 | 1.36 | 2.10 | 2.08 | 2.10 | 1.78 | 2.40 | 1.68 | 2.16 |
time (sec) |
N/A | 0.340 | 0.056 | 0.217 | 0.032 | 0.098 | 0.493 | 0.123 | 0.157 | 0.953 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 150 | 244 | 276 | 267 | 396 | 257 | 372 | 297 | 293 |
N.S. |
1 | 1.00 | 1.63 | 1.84 | 1.78 | 2.64 | 1.71 | 2.48 | 1.98 | 1.95 |
time (sec) |
N/A | 0.422 | 0.066 | 0.214 | 0.039 | 0.073 | 0.747 | 0.119 | 0.157 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 145 | 238 | 267 | 274 | 420 | 299 | 286 | 330 | 290 |
N.S. |
1 | 1.00 | 1.64 | 1.84 | 1.89 | 2.90 | 2.06 | 1.97 | 2.28 | 2.00 |
time (sec) |
N/A | 0.418 | 0.072 | 0.218 | 0.040 | 0.073 | 2.432 | 0.120 | 0.163 | 0.966 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 149 | 232 | 271 | 284 | 406 | 337 | 279 | 309 | 301 |
N.S. |
1 | 1.00 | 1.56 | 1.82 | 1.91 | 2.72 | 2.26 | 1.87 | 2.07 | 2.02 |
time (sec) |
N/A | 0.398 | 0.070 | 0.223 | 0.045 | 0.084 | 5.580 | 0.117 | 0.173 | 0.968 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 131 | 222 | 267 | 302 | 354 | 359 | 449 | 269 | 303 |
N.S. |
1 | 1.02 | 1.72 | 2.07 | 2.34 | 2.74 | 2.78 | 3.48 | 2.09 | 2.35 |
time (sec) |
N/A | 0.358 | 0.068 | 0.225 | 0.048 | 0.079 | 13.089 | 0.128 | 0.165 | 0.979 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 211 | 264 | 304 | 304 | 372 | 298 | 192 | 307 |
N.S. |
1 | 1.00 | 2.45 | 3.07 | 3.53 | 3.53 | 4.33 | 3.47 | 2.23 | 3.57 |
time (sec) |
N/A | 0.228 | 0.063 | 0.217 | 0.044 | 0.070 | 35.073 | 0.124 | 0.155 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 130 | 211 | 266 | 317 | 317 | 386 | 299 | 240 | 321 |
N.S. |
1 | 0.98 | 1.59 | 2.00 | 2.38 | 2.38 | 2.90 | 2.25 | 1.80 | 2.41 |
time (sec) |
N/A | 0.266 | 0.057 | 0.222 | 0.044 | 0.069 | 100.278 | 0.127 | 0.170 | 0.927 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 163 | 215 | 270 | 332 | 332 | 0 | 300 | 251 | 336 |
N.S. |
1 | 1.00 | 1.32 | 1.66 | 2.04 | 2.04 | 0.00 | 1.84 | 1.54 | 2.06 |
time (sec) |
N/A | 0.459 | 0.060 | 0.222 | 0.056 | 0.070 | 0.000 | 0.122 | 0.167 | 0.904 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 163 | 211 | 262 | 335 | 335 | 0 | 298 | 262 | 339 |
N.S. |
1 | 1.00 | 1.29 | 1.61 | 2.06 | 2.06 | 0.00 | 1.83 | 1.61 | 2.08 |
time (sec) |
N/A | 0.386 | 0.058 | 0.233 | 0.046 | 0.075 | 0.000 | 0.121 | 0.159 | 0.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 163 | 214 | 270 | 354 | 354 | 0 | 300 | 273 | 358 |
N.S. |
1 | 1.00 | 1.31 | 1.66 | 2.17 | 2.17 | 0.00 | 1.84 | 1.67 | 2.20 |
time (sec) |
N/A | 0.382 | 0.062 | 0.231 | 0.054 | 0.086 | 0.000 | 0.116 | 0.155 | 0.951 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 292 | 1385 | 1525 | 1532 | 1532 | 1969 | 1943 | 1051 | 1625 |
N.S. |
1 | 1.00 | 4.74 | 5.22 | 5.25 | 5.25 | 6.74 | 6.65 | 3.60 | 5.57 |
time (sec) |
N/A | 1.713 | 0.327 | 0.234 | 0.052 | 0.078 | 0.119 | 0.128 | 0.154 | 1.197 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 292 | 1224 | 1349 | 1356 | 1356 | 1756 | 1712 | 925 | 1431 |
N.S. |
1 | 1.00 | 4.19 | 4.62 | 4.64 | 4.64 | 6.01 | 5.86 | 3.17 | 4.90 |
time (sec) |
N/A | 1.489 | 0.287 | 0.229 | 0.040 | 0.071 | 0.112 | 0.128 | 0.169 | 0.295 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 290 | 290 | 1069 | 1173 | 1172 | 1172 | 1504 | 1480 | 799 | 1221 |
N.S. |
1 | 1.00 | 3.69 | 4.04 | 4.04 | 4.04 | 5.19 | 5.10 | 2.76 | 4.21 |
time (sec) |
N/A | 1.308 | 0.231 | 0.237 | 0.041 | 0.079 | 0.091 | 0.125 | 0.162 | 1.147 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 240 | 240 | 907 | 997 | 997 | 997 | 1278 | 1246 | 673 | 1039 |
N.S. |
1 | 1.00 | 3.78 | 4.15 | 4.15 | 4.15 | 5.32 | 5.19 | 2.80 | 4.33 |
time (sec) |
N/A | 1.061 | 0.197 | 0.208 | 0.044 | 0.085 | 0.083 | 0.122 | 0.163 | 0.215 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 204 | 762 | 821 | 828 | 828 | 1035 | 1015 | 547 | 845 |
N.S. |
1 | 1.00 | 3.74 | 4.02 | 4.06 | 4.06 | 5.07 | 4.98 | 2.68 | 4.14 |
time (sec) |
N/A | 0.887 | 0.159 | 0.201 | 0.039 | 0.087 | 0.070 | 0.128 | 0.166 | 1.012 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 586 | 645 | 643 | 643 | 802 | 782 | 421 | 649 |
N.S. |
1 | 1.00 | 3.69 | 4.06 | 4.04 | 4.04 | 5.04 | 4.92 | 2.65 | 4.08 |
time (sec) |
N/A | 0.683 | 0.126 | 0.194 | 0.045 | 0.078 | 0.061 | 0.124 | 0.167 | 1.004 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 386 | 469 | 476 | 476 | 568 | 552 | 295 | 457 |
N.S. |
1 | 1.00 | 3.27 | 3.97 | 4.03 | 4.03 | 4.81 | 4.68 | 2.50 | 3.87 |
time (sec) |
N/A | 0.553 | 0.140 | 0.182 | 0.035 | 0.068 | 0.055 | 0.120 | 0.170 | 0.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 231 | 279 | 297 | 297 | 333 | 321 | 169 | 257 |
N.S. |
1 | 1.00 | 3.08 | 3.72 | 3.96 | 3.96 | 4.44 | 4.28 | 2.25 | 3.43 |
time (sec) |
N/A | 0.393 | 0.089 | 0.154 | 0.032 | 0.071 | 0.040 | 0.124 | 0.159 | 0.087 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 122 | 140 | 142 | 142 | 148 | 145 | 76 | 126 |
N.S. |
1 | 1.00 | 3.21 | 3.68 | 3.74 | 3.74 | 3.89 | 3.82 | 2.00 | 3.32 |
time (sec) |
N/A | 0.204 | 0.025 | 0.142 | 0.041 | 0.075 | 0.034 | 0.135 | 0.159 | 0.963 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 220 | 220 | 501 | 776 | 762 | 763 | 736 | 910 | 538 | 769 |
N.S. |
1 | 1.00 | 2.28 | 3.53 | 3.46 | 3.47 | 3.35 | 4.14 | 2.45 | 3.50 |
time (sec) |
N/A | 0.510 | 0.163 | 0.232 | 0.057 | 0.075 | 0.866 | 0.122 | 0.155 | 0.944 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 277 | 277 | 643 | 795 | 771 | 1067 | 782 | 979 | 700 | 1228 |
N.S. |
1 | 1.00 | 2.32 | 2.87 | 2.78 | 3.85 | 2.82 | 3.53 | 2.53 | 4.43 |
time (sec) |
N/A | 0.932 | 0.176 | 0.224 | 0.057 | 0.090 | 1.843 | 0.129 | 0.164 | 0.087 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 276 | 276 | 352 | 789 | 779 | 1177 | 821 | 862 | 799 | 1053 |
N.S. |
1 | 1.00 | 1.28 | 2.86 | 2.82 | 4.26 | 2.97 | 3.12 | 2.89 | 3.82 |
time (sec) |
N/A | 0.825 | 0.111 | 0.234 | 0.051 | 0.085 | 6.152 | 0.122 | 0.165 | 0.973 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 279 | 279 | 297 | 795 | 793 | 1225 | 867 | 848 | 840 | 907 |
N.S. |
1 | 1.00 | 1.06 | 2.85 | 2.84 | 4.39 | 3.11 | 3.04 | 3.01 | 3.25 |
time (sec) |
N/A | 0.815 | 0.111 | 0.240 | 0.067 | 0.097 | 29.906 | 0.125 | 0.164 | 0.970 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 279 | 279 | 263 | 798 | 801 | 1222 | 0 | 1175 | 851 | 863 |
N.S. |
1 | 1.00 | 0.94 | 2.86 | 2.87 | 4.38 | 0.00 | 4.21 | 3.05 | 3.09 |
time (sec) |
N/A | 0.732 | 0.117 | 0.237 | 0.088 | 0.095 | 0.000 | 0.137 | 0.159 | 0.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 272 | 272 | 633 | 800 | 814 | 1157 | 0 | 831 | 816 | 862 |
N.S. |
1 | 1.00 | 2.33 | 2.94 | 2.99 | 4.25 | 0.00 | 3.06 | 3.00 | 3.17 |
time (sec) |
N/A | 0.670 | 0.195 | 0.230 | 0.074 | 0.126 | 0.000 | 0.135 | 0.158 | 0.142 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 278 | 278 | 619 | 805 | 824 | 1063 | 0 | 826 | 735 | 875 |
N.S. |
1 | 1.00 | 2.23 | 2.90 | 2.96 | 3.82 | 0.00 | 2.97 | 2.64 | 3.15 |
time (sec) |
N/A | 0.646 | 0.204 | 0.227 | 0.077 | 0.124 | 0.000 | 0.117 | 0.159 | 1.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 212 | 615 | 791 | 842 | 939 | 0 | 830 | 638 | 1046 |
N.S. |
1 | 1.00 | 2.89 | 3.71 | 3.95 | 4.41 | 0.00 | 3.90 | 3.00 | 4.91 |
time (sec) |
N/A | 0.571 | 0.283 | 0.227 | 0.065 | 0.109 | 0.000 | 0.119 | 0.160 | 1.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 597 | 780 | 823 | 823 | 0 | 910 | 504 | 854 |
N.S. |
1 | 1.00 | 6.94 | 9.07 | 9.57 | 9.57 | 0.00 | 10.58 | 5.86 | 9.93 |
time (sec) |
N/A | 0.255 | 0.164 | 0.240 | 0.077 | 0.089 | 0.000 | 0.127 | 0.158 | 0.143 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 131 | 603 | 789 | 861 | 861 | 0 | 912 | 585 | 877 |
N.S. |
1 | 0.97 | 4.47 | 5.84 | 6.38 | 6.38 | 0.00 | 6.76 | 4.33 | 6.50 |
time (sec) |
N/A | 0.269 | 0.171 | 0.232 | 0.072 | 0.090 | 0.000 | 0.125 | 0.159 | 1.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 175 | 602 | 789 | 872 | 872 | 0 | 912 | 596 | 888 |
N.S. |
1 | 0.95 | 3.25 | 4.26 | 4.71 | 4.71 | 0.00 | 4.93 | 3.22 | 4.80 |
time (sec) |
N/A | 0.290 | 0.165 | 0.242 | 0.079 | 0.114 | 0.000 | 0.135 | 0.162 | 1.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 219 | 605 | 789 | 883 | 883 | 0 | 912 | 607 | 899 |
N.S. |
1 | 0.93 | 2.57 | 3.36 | 3.76 | 3.76 | 0.00 | 3.88 | 2.58 | 3.83 |
time (sec) |
N/A | 0.317 | 0.164 | 0.239 | 0.130 | 0.088 | 0.000 | 0.131 | 0.157 | 0.183 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 292 | 600 | 789 | 894 | 894 | 0 | 912 | 618 | 910 |
N.S. |
1 | 1.00 | 2.05 | 2.70 | 3.06 | 3.06 | 0.00 | 3.12 | 2.12 | 3.12 |
time (sec) |
N/A | 0.702 | 0.165 | 0.246 | 0.076 | 0.099 | 0.000 | 0.124 | 0.158 | 1.211 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 292 | 605 | 789 | 905 | 905 | 0 | 912 | 629 | 921 |
N.S. |
1 | 1.00 | 2.07 | 2.70 | 3.10 | 3.10 | 0.00 | 3.12 | 2.15 | 3.15 |
time (sec) |
N/A | 0.658 | 0.170 | 0.248 | 0.069 | 0.129 | 0.000 | 0.129 | 0.167 | 1.406 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 292 | 602 | 775 | 902 | 902 | 0 | 910 | 640 | 918 |
N.S. |
1 | 1.00 | 2.06 | 2.65 | 3.09 | 3.09 | 0.00 | 3.12 | 2.19 | 3.14 |
time (sec) |
N/A | 0.644 | 0.173 | 0.260 | 0.089 | 0.125 | 0.000 | 0.123 | 0.166 | 1.566 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 464 | 464 | 3532 | 3893 | 3905 | 3905 | 5092 | 5039 | 2593 | 4206 |
N.S. |
1 | 1.00 | 7.61 | 8.39 | 8.42 | 8.42 | 10.97 | 10.86 | 5.59 | 9.06 |
time (sec) |
N/A | 5.233 | 0.962 | 0.327 | 0.071 | 0.128 | 0.362 | 0.132 | 0.168 | 1.007 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 464 | 464 | 3320 | 3609 | 3621 | 3621 | 4655 | 4663 | 2399 | 3891 |
N.S. |
1 | 1.00 | 7.16 | 7.78 | 7.80 | 7.80 | 10.03 | 10.05 | 5.17 | 8.39 |
time (sec) |
N/A | 5.348 | 0.883 | 0.326 | 0.067 | 0.132 | 0.272 | 0.133 | 0.158 | 1.821 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 461 | 461 | 3018 | 3325 | 3334 | 3334 | 4328 | 4288 | 2205 | 3577 |
N.S. |
1 | 1.00 | 6.55 | 7.21 | 7.23 | 7.23 | 9.39 | 9.30 | 4.78 | 7.76 |
time (sec) |
N/A | 4.892 | 0.759 | 0.317 | 0.052 | 0.106 | 0.248 | 0.130 | 0.164 | 1.661 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 460 | 460 | 2815 | 3041 | 3048 | 3048 | 3936 | 3912 | 2011 | 3262 |
N.S. |
1 | 1.00 | 6.12 | 6.61 | 6.63 | 6.63 | 8.56 | 8.50 | 4.37 | 7.09 |
time (sec) |
N/A | 4.132 | 0.711 | 0.287 | 0.056 | 0.132 | 0.252 | 0.134 | 0.166 | 1.638 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 415 | 415 | 2553 | 2757 | 2771 | 2771 | 3541 | 3536 | 1817 | 2947 |
N.S. |
1 | 1.00 | 6.15 | 6.64 | 6.68 | 6.68 | 8.53 | 8.52 | 4.38 | 7.10 |
time (sec) |
N/A | 3.405 | 0.619 | 0.274 | 0.047 | 0.098 | 0.253 | 0.121 | 0.168 | 1.577 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 372 | 372 | 2307 | 2473 | 2487 | 2487 | 3165 | 3159 | 1623 | 2631 |
N.S. |
1 | 1.00 | 6.20 | 6.65 | 6.69 | 6.69 | 8.51 | 8.49 | 4.36 | 7.07 |
time (sec) |
N/A | 2.842 | 0.534 | 0.264 | 0.045 | 0.115 | 0.224 | 0.123 | 0.159 | 1.490 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 329 | 329 | 2034 | 2189 | 2198 | 2198 | 2824 | 2783 | 1429 | 2316 |
N.S. |
1 | 1.00 | 6.18 | 6.65 | 6.68 | 6.68 | 8.58 | 8.46 | 4.34 | 7.04 |
time (sec) |
N/A | 2.093 | 0.472 | 0.250 | 0.046 | 0.087 | 0.248 | 0.131 | 0.160 | 1.419 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 290 | 290 | 1788 | 1905 | 1917 | 1917 | 2424 | 2407 | 1235 | 2001 |
N.S. |
1 | 1.00 | 6.17 | 6.57 | 6.61 | 6.61 | 8.36 | 8.30 | 4.26 | 6.90 |
time (sec) |
N/A | 1.910 | 0.423 | 0.241 | 0.056 | 0.095 | 0.161 | 0.132 | 0.156 | 1.405 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 243 | 243 | 1509 | 1621 | 1625 | 1625 | 2076 | 2032 | 1041 | 1685 |
N.S. |
1 | 1.00 | 6.21 | 6.67 | 6.69 | 6.69 | 8.54 | 8.36 | 4.28 | 6.93 |
time (sec) |
N/A | 1.639 | 0.336 | 0.227 | 0.047 | 0.103 | 0.137 | 0.117 | 0.154 | 0.390 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 204 | 1098 | 1337 | 1352 | 1352 | 1676 | 1656 | 847 | 1386 |
N.S. |
1 | 1.00 | 5.38 | 6.55 | 6.63 | 6.63 | 8.22 | 8.12 | 4.15 | 6.79 |
time (sec) |
N/A | 1.179 | 0.450 | 0.217 | 0.043 | 0.076 | 0.180 | 0.125 | 0.161 | 1.230 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 855 | 1053 | 1068 | 1068 | 1302 | 1279 | 653 | 1070 |
N.S. |
1 | 1.00 | 5.38 | 6.62 | 6.72 | 6.72 | 8.19 | 8.04 | 4.11 | 6.73 |
time (sec) |
N/A | 0.927 | 0.332 | 0.210 | 0.042 | 0.095 | 0.132 | 0.122 | 0.155 | 1.169 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 614 | 769 | 781 | 781 | 921 | 904 | 459 | 757 |
N.S. |
1 | 1.00 | 5.20 | 6.52 | 6.62 | 6.62 | 7.81 | 7.66 | 3.89 | 6.42 |
time (sec) |
N/A | 0.706 | 0.225 | 0.195 | 0.049 | 0.090 | 0.093 | 0.128 | 0.157 | 1.164 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 383 | 459 | 493 | 493 | 549 | 529 | 265 | 409 |
N.S. |
1 | 1.00 | 5.11 | 6.12 | 6.57 | 6.57 | 7.32 | 7.05 | 3.53 | 5.45 |
time (sec) |
N/A | 0.497 | 0.108 | 0.167 | 0.038 | 0.073 | 0.073 | 0.121 | 0.165 | 0.153 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 198 | 232 | 240 | 240 | 248 | 241 | 120 | 208 |
N.S. |
1 | 1.00 | 5.21 | 6.11 | 6.32 | 6.32 | 6.53 | 6.34 | 3.16 | 5.47 |
time (sec) |
N/A | 0.183 | 0.038 | 0.135 | 0.043 | 0.088 | 0.049 | 0.125 | 0.170 | 0.983 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 348 | 348 | 1252 | 1884 | 1804 | 1805 | 1912 | 2230 | 1216 | 1795 |
N.S. |
1 | 1.00 | 3.60 | 5.41 | 5.18 | 5.19 | 5.49 | 6.41 | 3.49 | 5.16 |
time (sec) |
N/A | 0.642 | 0.768 | 0.235 | 0.051 | 0.083 | 2.193 | 0.123 | 0.162 | 1.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 445 | 445 | 1486 | 1907 | 1817 | 2329 | 1974 | 2207 | 1474 | 7792 |
N.S. |
1 | 1.00 | 3.34 | 4.29 | 4.08 | 5.23 | 4.44 | 4.96 | 3.31 | 17.51 |
time (sec) |
N/A | 1.714 | 0.420 | 0.239 | 0.050 | 0.123 | 5.009 | 0.148 | 1.444 | 1.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 445 | 445 | 1480 | 1902 | 1826 | 2547 | 2004 | 2134 | 1661 | 8104 |
N.S. |
1 | 1.00 | 3.33 | 4.27 | 4.10 | 5.72 | 4.50 | 4.80 | 3.73 | 18.21 |
time (sec) |
N/A | 1.614 | 0.417 | 0.239 | 0.082 | 0.151 | 22.447 | 0.140 | 0.838 | 1.208 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 445 | 445 | 814 | 1907 | 1839 | 2702 | 0 | 2096 | 1786 | 5544 |
N.S. |
1 | 1.00 | 1.83 | 4.29 | 4.13 | 6.07 | 0.00 | 4.71 | 4.01 | 12.46 |
time (sec) |
N/A | 1.535 | 0.265 | 0.239 | 0.109 | 0.130 | 0.000 | 0.131 | 0.332 | 1.180 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 444 | 444 | 686 | 1910 | 1846 | 2808 | 0 | 2571 | 1889 | 3655 |
N.S. |
1 | 1.00 | 1.55 | 4.30 | 4.16 | 6.32 | 0.00 | 5.79 | 4.25 | 8.23 |
time (sec) |
N/A | 1.442 | 0.257 | 0.237 | 0.116 | 0.139 | 0.000 | 0.141 | 0.222 | 1.164 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 447 | 447 | 587 | 1916 | 1861 | 2851 | 0 | 2032 | 1946 | 2681 |
N.S. |
1 | 1.00 | 1.31 | 4.29 | 4.16 | 6.38 | 0.00 | 4.55 | 4.35 | 6.00 |
time (sec) |
N/A | 1.405 | 0.264 | 0.237 | 0.138 | 0.155 | 0.000 | 0.135 | 0.174 | 1.209 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 447 | 447 | 505 | 1921 | 1869 | 2850 | 0 | 2009 | 1957 | 2252 |
N.S. |
1 | 1.00 | 1.13 | 4.30 | 4.18 | 6.38 | 0.00 | 4.49 | 4.38 | 5.04 |
time (sec) |
N/A | 1.351 | 0.293 | 0.238 | 0.163 | 0.173 | 0.000 | 0.131 | 0.163 | 1.179 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 444 | 444 | 450 | 1925 | 1883 | 2783 | 0 | 1992 | 1922 | 2092 |
N.S. |
1 | 1.00 | 1.01 | 4.34 | 4.24 | 6.27 | 0.00 | 4.49 | 4.33 | 4.71 |
time (sec) |
N/A | 1.322 | 0.312 | 0.243 | 0.181 | 0.224 | 0.000 | 0.130 | 0.170 | 1.221 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 445 | 445 | 415 | 1929 | 1892 | 2677 | 0 | 1981 | 1841 | 2048 |
N.S. |
1 | 1.00 | 0.93 | 4.33 | 4.25 | 6.02 | 0.00 | 4.45 | 4.14 | 4.60 |
time (sec) |
N/A | 1.246 | 0.327 | 0.243 | 0.194 | 0.251 | 0.000 | 0.130 | 0.165 | 0.307 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 441 | 441 | 1460 | 1928 | 1904 | 2501 | 0 | 1975 | 1714 | 2048 |
N.S. |
1 | 1.00 | 3.31 | 4.37 | 4.32 | 5.67 | 0.00 | 4.48 | 3.89 | 4.64 |
time (sec) |
N/A | 1.207 | 0.556 | 0.243 | 0.169 | 0.230 | 0.000 | 0.125 | 0.166 | 1.249 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 446 | 446 | 1447 | 1922 | 1914 | 2309 | 0 | 1970 | 1541 | 2874 |
N.S. |
1 | 1.00 | 3.24 | 4.31 | 4.29 | 5.18 | 0.00 | 4.42 | 3.46 | 6.44 |
time (sec) |
N/A | 1.207 | 0.540 | 0.257 | 0.132 | 0.241 | 0.000 | 0.130 | 0.167 | 1.363 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 321 | 316 | 1443 | 1903 | 1932 | 2089 | 0 | 1974 | 1368 | 2446 |
N.S. |
1 | 0.98 | 4.50 | 5.93 | 6.02 | 6.51 | 0.00 | 6.15 | 4.26 | 7.62 |
time (sec) |
N/A | 0.695 | 1.223 | 0.259 | 0.116 | 0.174 | 0.000 | 0.130 | 0.169 | 1.295 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 1421 | 1888 | 1875 | 1875 | 0 | 2230 | 1158 | 2008 |
N.S. |
1 | 1.00 | 16.52 | 21.95 | 21.80 | 21.80 | 0.00 | 25.93 | 13.47 | 23.35 |
time (sec) |
N/A | 0.211 | 0.521 | 0.258 | 0.130 | 0.138 | 0.000 | 0.134 | 0.166 | 0.470 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 131 | 1433 | 1901 | 1951 | 1951 | 0 | 2232 | 1283 | 2031 |
N.S. |
1 | 0.97 | 10.61 | 14.08 | 14.45 | 14.45 | 0.00 | 16.53 | 9.50 | 15.04 |
time (sec) |
N/A | 0.222 | 0.482 | 0.266 | 0.131 | 0.134 | 0.000 | 0.129 | 0.168 | 1.540 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 175 | 1430 | 1901 | 1962 | 1962 | 0 | 2232 | 1294 | 2044 |
N.S. |
1 | 0.95 | 7.73 | 10.28 | 10.61 | 10.61 | 0.00 | 12.06 | 6.99 | 11.05 |
time (sec) |
N/A | 0.250 | 0.546 | 0.279 | 0.161 | 0.197 | 0.000 | 0.134 | 0.171 | 1.778 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 219 | 1430 | 1901 | 1973 | 1973 | 0 | 2232 | 1305 | 2055 |
N.S. |
1 | 0.93 | 6.09 | 8.09 | 8.40 | 8.40 | 0.00 | 9.50 | 5.55 | 8.74 |
time (sec) |
N/A | 0.296 | 0.558 | 0.296 | 0.127 | 0.164 | 0.000 | 0.126 | 0.172 | 2.239 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 263 | 1429 | 1901 | 1984 | 1984 | 0 | 2232 | 1316 | 2066 |
N.S. |
1 | 0.92 | 5.01 | 6.67 | 6.96 | 6.96 | 0.00 | 7.83 | 4.62 | 7.25 |
time (sec) |
N/A | 0.301 | 0.462 | 0.313 | 0.141 | 0.177 | 0.000 | 0.129 | 0.169 | 1.318 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 335 | 307 | 1433 | 1901 | 1995 | 1995 | 0 | 2232 | 1327 | 2077 |
N.S. |
1 | 0.92 | 4.28 | 5.67 | 5.96 | 5.96 | 0.00 | 6.66 | 3.96 | 6.20 |
time (sec) |
N/A | 0.333 | 0.524 | 0.324 | 0.157 | 0.175 | 0.000 | 0.131 | 0.167 | 1.400 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 385 | 351 | 1428 | 1901 | 2006 | 2006 | 0 | 2232 | 1338 | 2088 |
N.S. |
1 | 0.91 | 3.71 | 4.94 | 5.21 | 5.21 | 0.00 | 5.80 | 3.48 | 5.42 |
time (sec) |
N/A | 0.368 | 0.480 | 0.340 | 0.133 | 0.204 | 0.000 | 0.129 | 0.166 | 9.644 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 460 | 460 | 1433 | 1901 | 2017 | 2017 | 0 | 2232 | 1349 | 2099 |
N.S. |
1 | 1.00 | 3.12 | 4.13 | 4.38 | 4.38 | 0.00 | 4.85 | 2.93 | 4.56 |
time (sec) |
N/A | 1.274 | 0.501 | 0.354 | 0.146 | 0.220 | 0.000 | 0.133 | 0.165 | 17.868 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 462 | 462 | 1428 | 1901 | 2028 | 2028 | 0 | 2232 | 1360 | 2110 |
N.S. |
1 | 1.00 | 3.09 | 4.11 | 4.39 | 4.39 | 0.00 | 4.83 | 2.94 | 4.57 |
time (sec) |
N/A | 1.212 | 0.525 | 0.372 | 0.151 | 0.247 | 0.000 | 0.135 | 0.166 | 1.457 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 464 | 464 | 1431 | 1901 | 2039 | 2039 | 0 | 2232 | 1371 | 2121 |
N.S. |
1 | 1.00 | 3.08 | 4.10 | 4.39 | 4.39 | 0.00 | 4.81 | 2.95 | 4.57 |
time (sec) |
N/A | 1.207 | 0.540 | 0.379 | 0.157 | 0.256 | 0.000 | 0.132 | 0.170 | 1.628 |