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 | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 122 | 87 | 120 | 184 | 113 | 151 | 0 | 0 |
N.S. |
1 | 0.98 | 0.70 | 0.97 | 1.48 | 0.91 | 1.22 | 0.00 | 0.00 |
time (sec) |
N/A | 0.309 | 0.073 | 0.064 | 0.197 | 0.286 | 0.691 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 120 | 132 | 88 | 109 | 166 | 109 | 138 | 0 | 0 |
N.S. |
1 | 1.10 | 0.73 | 0.91 | 1.38 | 0.91 | 1.15 | 0.00 | 0.00 |
time (sec) |
N/A | 0.307 | 0.041 | 0.033 | 0.198 | 0.281 | 0.599 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 78 | 101 | 145 | 103 | 126 | 0 | 0 |
N.S. |
1 | 1.00 | 0.76 | 0.99 | 1.42 | 1.01 | 1.24 | 0.00 | 0.00 |
time (sec) |
N/A | 0.304 | 0.063 | 0.045 | 0.200 | 0.286 | 0.369 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 90 | 77 | 85 | 127 | 98 | 117 | 0 | 0 |
N.S. |
1 | 1.03 | 0.89 | 0.98 | 1.46 | 1.13 | 1.34 | 0.00 | 0.00 |
time (sec) |
N/A | 0.244 | 0.040 | 0.077 | 0.205 | 0.268 | 0.297 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 77 | 86 | 73 | 97 | 83 | 90 | 0 | 0 |
N.S. |
1 | 1.03 | 1.15 | 0.97 | 1.29 | 1.11 | 1.20 | 0.00 | 0.00 |
time (sec) |
N/A | 0.260 | 0.032 | 0.015 | 0.187 | 0.274 | 0.166 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 153 | 113 | 159 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.38 | 1.02 | 1.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.664 | 0.041 | 0.154 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 66 | 68 | 74 | 67 | 64 | 156 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 1.12 | 1.02 | 0.97 | 2.36 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.292 | 0.023 | 0.018 | 0.199 | 0.292 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 128 | 154 | 111 | 151 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.20 | 0.87 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.686 | 0.038 | 0.119 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 79 | 93 | 83 | 91 | 169 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 1.16 | 1.04 | 1.14 | 2.11 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.285 | 0.026 | 0.023 | 0.198 | 0.285 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 181 | 169 | 119 | 163 | 319 | 165 | 230 | 0 | 0 |
N.S. |
1 | 0.93 | 0.66 | 0.90 | 1.76 | 0.91 | 1.27 | 0.00 | 0.00 |
time (sec) |
N/A | 0.434 | 0.074 | 0.234 | 0.195 | 0.262 | 1.151 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 180 | 187 | 115 | 152 | 292 | 161 | 218 | 0 | 0 |
N.S. |
1 | 1.04 | 0.64 | 0.84 | 1.62 | 0.89 | 1.21 | 0.00 | 0.00 |
time (sec) |
N/A | 0.414 | 0.063 | 0.236 | 0.200 | 0.266 | 0.996 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 157 | 149 | 111 | 144 | 261 | 153 | 202 | 0 | 0 |
N.S. |
1 | 0.95 | 0.71 | 0.92 | 1.66 | 0.97 | 1.29 | 0.00 | 0.00 |
time (sec) |
N/A | 0.414 | 0.062 | 0.184 | 0.200 | 0.263 | 0.649 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 120 | 117 | 104 | 116 | 234 | 149 | 190 | 0 | 0 |
N.S. |
1 | 0.98 | 0.87 | 0.97 | 1.95 | 1.24 | 1.58 | 0.00 | 0.00 |
time (sec) |
N/A | 0.280 | 0.094 | 0.217 | 0.187 | 0.276 | 0.530 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 128 | 124 | 95 | 116 | 194 | 133 | 165 | 0 | 0 |
N.S. |
1 | 0.97 | 0.74 | 0.91 | 1.52 | 1.04 | 1.29 | 0.00 | 0.00 |
time (sec) |
N/A | 0.357 | 0.069 | 0.214 | 0.193 | 0.261 | 0.321 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 172 | 243 | 173 | 222 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.41 | 1.01 | 1.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.000 | 0.132 | 0.216 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F(-2) | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 120 | 114 | 124 | 112 | 143 | 228 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 1.03 | 0.93 | 1.19 | 1.90 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.424 | 0.087 | 0.197 | 0.187 | 0.287 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 187 | 251 | 151 | 240 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.34 | 0.81 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.033 | 0.164 | 0.242 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F(-2) | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 126 | 134 | 133 | 112 | 137 | 243 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 1.06 | 0.89 | 1.09 | 1.93 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.418 | 0.086 | 0.228 | 0.187 | 0.278 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 226 | 210 | 143 | 202 | 465 | 201 | 289 | 0 | 0 |
N.S. |
1 | 0.93 | 0.63 | 0.89 | 2.06 | 0.89 | 1.28 | 0.00 | 0.00 |
time (sec) |
N/A | 0.612 | 0.099 | 0.207 | 0.201 | 0.287 | 2.235 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 199 | 192 | 139 | 191 | 429 | 197 | 280 | 0 | 0 |
N.S. |
1 | 0.96 | 0.70 | 0.96 | 2.16 | 0.99 | 1.41 | 0.00 | 0.00 |
time (sec) |
N/A | 0.395 | 0.086 | 0.219 | 0.200 | 0.279 | 1.657 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 202 | 190 | 135 | 183 | 388 | 189 | 265 | 0 | 0 |
N.S. |
1 | 0.94 | 0.67 | 0.91 | 1.92 | 0.94 | 1.31 | 0.00 | 0.00 |
time (sec) |
N/A | 0.576 | 0.098 | 0.228 | 0.211 | 0.295 | 1.234 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 145 | 140 | 128 | 143 | 352 | 185 | 253 | 0 | 0 |
N.S. |
1 | 0.97 | 0.88 | 0.99 | 2.43 | 1.28 | 1.74 | 0.00 | 0.00 |
time (sec) |
N/A | 0.302 | 0.118 | 0.168 | 0.194 | 0.277 | 0.877 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 170 | 162 | 119 | 153 | 301 | 169 | 221 | 0 | 0 |
N.S. |
1 | 0.95 | 0.70 | 0.90 | 1.77 | 0.99 | 1.30 | 0.00 | 0.00 |
time (sec) |
N/A | 0.486 | 0.082 | 0.209 | 0.199 | 0.280 | 0.580 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 221 | 348 | 216 | 271 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.57 | 0.98 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.384 | 0.166 | 0.283 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 160 | 146 | 163 | 149 | 231 | 276 | 0 | 0 | 0 |
N.S. |
1 | 0.91 | 1.02 | 0.93 | 1.44 | 1.72 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.551 | 0.112 | 0.162 | 0.196 | 0.330 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 249 | 356 | 244 | 289 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.43 | 0.98 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.461 | 0.154 | 0.293 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 174 | 156 | 171 | 153 | 208 | 289 | 0 | 0 | 0 |
N.S. |
1 | 0.90 | 0.98 | 0.88 | 1.20 | 1.66 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.630 | 0.106 | 0.159 | 0.188 | 0.291 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 156 | 170 | 170 | 208 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 1.09 | 1.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.856 | 0.175 | 0.351 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 135 | 141 | 181 | 146 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.34 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.659 | 0.155 | 0.280 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 99 | 121 | 170 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.92 | 1.12 | 1.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.534 | 0.168 | 0.168 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | B | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 75 | 167 | 84 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 2.29 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.419 | 0.051 | 0.230 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 59 | 135 | 143 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.84 | 1.93 | 2.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.346 | 0.073 | 0.219 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | B | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 65 | 207 | 161 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 3.39 | 2.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.437 | 0.068 | 0.212 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 96 | 182 | 176 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 1.80 | 1.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.565 | 0.113 | 0.195 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | B | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 112 | 240 | 217 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 2.12 | 1.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.655 | 0.182 | 0.241 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 156 | 160 | 247 | 215 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 1.58 | 1.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.856 | 0.143 | 0.171 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 181 | 268 | 224 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 1.57 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.870 | 0.220 | 0.205 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | C | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 145 | 147 | 241 | 140 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.66 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.692 | 0.158 | 0.261 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 117 | 221 | 195 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.92 | 1.74 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.557 | 0.170 | 0.161 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 74 | 61 | 0 | 65 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.35 | 1.11 | 0.00 | 1.18 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.246 | 0.099 | 0.213 | 0.000 | 0.280 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 114 | 216 | 195 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.92 | 1.74 | 1.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.529 | 0.114 | 0.219 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | B | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 115 | 234 | 217 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 2.13 | 1.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.654 | 0.309 | 0.210 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 168 | 182 | 253 | 227 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 1.51 | 1.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.874 | 0.383 | 0.230 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | B | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 146 | 191 | 326 | 242 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.31 | 2.23 | 1.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.968 | 0.315 | 0.229 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 239 | 280 | 311 | 268 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.17 | 1.30 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.228 | 0.425 | 0.234 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 186 | 201 | 341 | 247 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 1.83 | 1.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.893 | 0.489 | 0.168 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 95 | 79 | 108 | 0 | 99 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.81 | 1.11 | 0.00 | 1.02 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.289 | 0.139 | 0.229 | 0.000 | 0.283 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 184 | 170 | 340 | 247 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.92 | 1.85 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.749 | 0.193 | 0.176 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 78 | 56 | 76 | 0 | 98 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.70 | 0.95 | 0.00 | 1.22 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.247 | 0.116 | 0.237 | 0.000 | 0.274 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 178 | 164 | 341 | 248 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.92 | 1.92 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.699 | 0.149 | 0.168 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 159 | 183 | 289 | 280 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.15 | 1.82 | 1.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.915 | 0.448 | 0.257 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 222 | 249 | 298 | 291 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.12 | 1.34 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.100 | 0.775 | 0.168 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 232 | 280 | 353 | 344 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.21 | 1.52 | 1.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.309 | 0.605 | 0.312 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 295 | 364 | 374 | 333 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.23 | 1.27 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.595 | 1.056 | 0.237 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 109 | 102 | 106 | 164 | 134 | 158 | 221 | 0 | 0 |
N.S. |
1 | 0.94 | 0.97 | 1.50 | 1.23 | 1.45 | 2.03 | 0.00 | 0.00 |
time (sec) |
N/A | 0.373 | 0.189 | 0.224 | 0.204 | 0.286 | 0.900 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 114 | 79 | 156 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.66 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.513 | 0.189 | 0.211 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | B | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 58 | 63 | 108 | 73 | 127 | 141 | 0 | 0 |
N.S. |
1 | 0.95 | 1.03 | 1.77 | 1.20 | 2.08 | 2.31 | 0.00 | 0.00 |
time (sec) |
N/A | 0.269 | 0.125 | 0.214 | 0.206 | 0.260 | 0.344 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 69 | 100 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.03 | 1.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.310 | 0.157 | 0.158 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 91 | 131 | 171 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.47 | 1.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.567 | 0.192 | 0.227 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | B | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 75 | 155 | 0 | 0 | 110 | 0 | 0 |
N.S. |
1 | 1.00 | 1.23 | 2.54 | 0.00 | 0.00 | 1.80 | 0.00 | 0.00 |
time (sec) |
N/A | 0.362 | 0.217 | 0.169 | 0.000 | 0.000 | 1.610 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 106 | 185 | 231 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 1.64 | 2.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.593 | 2.484 | 0.184 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 58 | 96 | 501 | 133 | 217 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 1.55 | 8.08 | 2.15 | 3.50 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.299 | 0.168 | 0.164 | 0.217 | 0.300 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 125 | 112 | 100 | 195 | 145 | 199 | 301 | 0 | 0 |
N.S. |
1 | 0.90 | 0.80 | 1.56 | 1.16 | 1.59 | 2.41 | 0.00 | 0.00 |
time (sec) |
N/A | 0.407 | 0.198 | 0.277 | 0.216 | 0.263 | 9.329 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 165 | 178 | 154 | 214 | 0 | 0 | 262 | 0 | 0 |
N.S. |
1 | 1.08 | 0.93 | 1.30 | 0.00 | 0.00 | 1.59 | 0.00 | 0.00 |
time (sec) |
N/A | 0.832 | 0.378 | 0.211 | 0.000 | 0.000 | 5.488 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | B | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 68 | 72 | 139 | 85 | 167 | 221 | 0 | 0 |
N.S. |
1 | 0.88 | 0.94 | 1.81 | 1.10 | 2.17 | 2.87 | 0.00 | 0.00 |
time (sec) |
N/A | 0.286 | 0.146 | 0.171 | 0.213 | 0.273 | 2.929 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 129 | 111 | 152 | 0 | 0 | 185 | 0 | 0 |
N.S. |
1 | 1.16 | 1.00 | 1.37 | 0.00 | 0.00 | 1.67 | 0.00 | 0.00 |
time (sec) |
N/A | 0.498 | 0.246 | 0.194 | 0.000 | 0.000 | 1.578 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 134 | 143 | 180 | 228 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 1.34 | 1.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.871 | 0.366 | 0.222 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 122 | 122 | 208 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 1.13 | 1.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.542 | 0.370 | 0.168 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 155 | 151 | 292 | 291 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 1.88 | 1.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.861 | 1.275 | 0.221 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 121 | 125 | 622 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 1.09 | 5.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.603 | 0.300 | 0.164 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 141 | 120 | 108 | 226 | 156 | 263 | 379 | 0 | 0 |
N.S. |
1 | 0.85 | 0.77 | 1.60 | 1.11 | 1.87 | 2.69 | 0.00 | 0.00 |
time (sec) |
N/A | 0.407 | 0.260 | 0.249 | 0.202 | 0.301 | 90.306 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 213 | 252 | 196 | 267 | 0 | 0 | 350 | 0 | 0 |
N.S. |
1 | 1.18 | 0.92 | 1.25 | 0.00 | 0.00 | 1.64 | 0.00 | 0.00 |
time (sec) |
N/A | 1.165 | 0.648 | 0.234 | 0.000 | 0.000 | 49.520 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | B | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 93 | 75 | 80 | 170 | 96 | 225 | 299 | 0 | 0 |
N.S. |
1 | 0.81 | 0.86 | 1.83 | 1.03 | 2.42 | 3.22 | 0.00 | 0.00 |
time (sec) |
N/A | 0.291 | 0.154 | 0.195 | 0.210 | 0.265 | 28.365 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 165 | 186 | 153 | 202 | 0 | 0 | 265 | 0 | 0 |
N.S. |
1 | 1.13 | 0.93 | 1.22 | 0.00 | 0.00 | 1.61 | 0.00 | 0.00 |
time (sec) |
N/A | 0.668 | 0.408 | 0.216 | 0.000 | 0.000 | 16.114 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 179 | 205 | 257 | 284 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.15 | 1.44 | 1.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.150 | 0.447 | 0.154 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 157 | 197 | 168 | 261 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.25 | 1.07 | 1.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.794 | 0.515 | 0.201 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 205 | 214 | 349 | 348 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.70 | 1.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.204 | 1.489 | 0.167 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 166 | 193 | 179 | 692 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.16 | 1.08 | 4.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.857 | 0.480 | 0.218 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 28 | 26 | 28 | 40 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.81 | 0.88 | 1.25 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.249 | 0.011 | 0.181 | 0.275 | 0.262 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 149 | 160 | 108 | 193 | 174 | 161 | 184 | 0 | 0 |
N.S. |
1 | 1.07 | 0.72 | 1.30 | 1.17 | 1.08 | 1.23 | 0.00 | 0.00 |
time (sec) |
N/A | 0.649 | 0.241 | 0.204 | 0.203 | 0.285 | 3.148 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 126 | 134 | 111 | 165 | 0 | 0 | 185 | 0 | 0 |
N.S. |
1 | 1.06 | 0.88 | 1.31 | 0.00 | 0.00 | 1.47 | 0.00 | 0.00 |
time (sec) |
N/A | 0.584 | 0.337 | 0.161 | 0.000 | 0.000 | 2.078 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 101 | 82 | 133 | 117 | 132 | 124 | 0 | 0 |
N.S. |
1 | 1.03 | 0.84 | 1.36 | 1.19 | 1.35 | 1.27 | 0.00 | 0.00 |
time (sec) |
N/A | 0.438 | 0.196 | 0.205 | 0.199 | 0.299 | 1.323 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 69 | 107 | 0 | 0 | 122 | 0 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.43 | 0.00 | 0.00 | 1.63 | 0.00 | 0.00 |
time (sec) |
N/A | 0.376 | 0.244 | 0.165 | 0.000 | 0.000 | 1.027 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 49 | 72 | 55 | 96 | 60 | 0 | 0 |
N.S. |
1 | 1.00 | 1.17 | 1.71 | 1.31 | 2.29 | 1.43 | 0.00 | 0.00 |
time (sec) |
N/A | 0.244 | 0.149 | 0.201 | 0.197 | 0.284 | 0.797 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 53 | 28 | 0 | 87 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.12 | 1.12 | 0.00 | 3.48 | 0.00 | 0.00 |
time (sec) |
N/A | 0.204 | 0.014 | 0.209 | 0.191 | 0.000 | 0.617 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 57 | 96 | 118 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.71 | 2.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.415 | 0.201 | 0.214 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 52 | 84 | 101 | 132 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.27 | 2.05 | 2.46 | 3.22 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.267 | 0.139 | 0.158 | 0.203 | 0.290 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 109 | 185 | 216 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 1.61 | 1.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.618 | 1.949 | 0.196 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 95 | 106 | 373 | 121 | 222 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 1.09 | 3.85 | 1.25 | 2.29 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.432 | 0.175 | 0.194 | 0.202 | 0.304 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 129 | 131 | 279 | 0 | 196 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 0.96 | 2.04 | 0.00 | 1.43 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.463 | 0.287 | 0.196 | 0.000 | 0.309 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 131 | 153 | 147 | 261 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.17 | 1.12 | 1.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.697 | 0.453 | 0.293 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 80 | 87 | 163 | 119 | 165 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 1.01 | 1.90 | 1.38 | 1.92 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.361 | 0.242 | 0.171 | 0.285 | 0.292 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 78 | 168 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.98 | 2.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.405 | 0.390 | 0.210 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 52 | 103 | 0 | 127 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.16 | 2.29 | 0.00 | 2.82 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.257 | 0.181 | 0.157 | 0.000 | 0.292 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 66 | 110 | 58 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.29 | 2.16 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.229 | 0.120 | 0.234 | 0.205 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 94 | 96 | 143 | 155 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.52 | 1.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.620 | 0.393 | 0.184 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 93 | 88 | 102 | 244 | 119 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 1.10 | 2.62 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.370 | 0.250 | 0.226 | 0.215 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 162 | 160 | 269 | 224 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 1.66 | 1.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.912 | 2.927 | 0.170 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 153 | 142 | 168 | 604 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 1.10 | 3.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.475 | 0.307 | 0.171 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 192 | 251 | 202 | 970 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.31 | 1.05 | 5.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.109 | 0.596 | 0.331 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |