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 | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 51 | 47 | 47 | 51 | 65 | 128 | 53 |
N.S. |
1 | 1.00 | 0.89 | 0.82 | 0.82 | 0.89 | 1.14 | 2.25 | 0.93 |
time (sec) |
N/A | 0.226 | 0.102 | 0.182 | 0.247 | 0.293 | 0.404 | 0.289 | 0.204 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 44 | 39 | 37 | 40 | 49 | 75 | 38 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.84 | 0.91 | 1.11 | 1.70 | 0.86 |
time (sec) |
N/A | 0.197 | 0.005 | 0.135 | 0.236 | 0.267 | 0.231 | 0.286 | 0.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 41 | 22 | 21 | 23 | 31 | 26 | 21 |
N.S. |
1 | 1.00 | 1.64 | 0.88 | 0.84 | 0.92 | 1.24 | 1.04 | 0.84 |
time (sec) |
N/A | 0.173 | 0.037 | 0.134 | 0.238 | 0.262 | 0.085 | 0.282 | 5.598 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 29 | 29 | 50 | 27 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.94 | 1.61 | 0.87 | 0.00 | 1.03 | 0.00 |
time (sec) |
N/A | 0.186 | 0.068 | 0.145 | 0.299 | 0.273 | 0.000 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 48 | 47 | 57 | 49 | 0 | 99 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.89 | 1.08 | 0.92 | 0.00 | 1.87 | 0.00 |
time (sec) |
N/A | 0.246 | 0.094 | 0.164 | 0.328 | 0.266 | 0.000 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 86 | 65 | 58 | 63 | 0 | 204 | 0 |
N.S. |
1 | 1.00 | 1.16 | 0.88 | 0.78 | 0.85 | 0.00 | 2.76 | 0.00 |
time (sec) |
N/A | 0.273 | 0.114 | 0.191 | 0.330 | 0.289 | 0.000 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | B | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 125 | 89 | 92 | 103 | 488 | 165 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.74 | 0.76 | 0.85 | 4.03 | 1.36 | 0.00 |
time (sec) |
N/A | 0.294 | 0.195 | 0.177 | 0.255 | 0.260 | 2.374 | 0.310 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | B | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 104 | 68 | 75 | 86 | 223 | 145 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.67 | 0.74 | 0.84 | 2.19 | 1.42 | 0.00 |
time (sec) |
N/A | 0.232 | 0.154 | 0.140 | 0.257 | 0.290 | 1.868 | 0.294 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 61 | 48 | 53 | 67 | 66 | 100 | 56 |
N.S. |
1 | 1.00 | 0.82 | 0.65 | 0.72 | 0.91 | 0.89 | 1.35 | 0.76 |
time (sec) |
N/A | 0.186 | 0.115 | 0.103 | 0.247 | 0.307 | 0.201 | 0.291 | 6.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 91 | 66 | 81 | 78 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.75 | 0.92 | 0.89 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.234 | 0.146 | 0.155 | 0.401 | 0.276 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 114 | 114 | 119 | 83 | 82 | 98 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.04 | 0.73 | 0.72 | 0.86 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.256 | 0.171 | 0.169 | 0.393 | 0.290 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 163 | 167 | 122 | 111 | 106 | 121 | 209 | 284 | 149 |
N.S. |
1 | 1.02 | 0.75 | 0.68 | 0.65 | 0.74 | 1.28 | 1.74 | 0.91 |
time (sec) |
N/A | 0.437 | 0.248 | 0.254 | 0.264 | 0.290 | 0.547 | 0.283 | 0.478 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 107 | 92 | 89 | 87 | 84 | 136 | 165 | 95 |
N.S. |
1 | 1.05 | 0.90 | 0.87 | 0.85 | 0.82 | 1.33 | 1.62 | 0.93 |
time (sec) |
N/A | 0.333 | 0.149 | 0.217 | 0.241 | 0.301 | 0.316 | 0.283 | 6.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 58 | 62 | 52 | 52 | 52 | 53 | 95 | 57 | 51 |
N.S. |
1 | 1.07 | 0.90 | 0.90 | 0.90 | 0.91 | 1.64 | 0.98 | 0.88 |
time (sec) |
N/A | 0.247 | 0.176 | 0.216 | 0.238 | 0.270 | 0.128 | 0.277 | 5.861 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | C | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 71 | 157 | 108 | 68 | 0 | 77 | 0 |
N.S. |
1 | 1.00 | 0.96 | 2.12 | 1.46 | 0.92 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.284 | 0.123 | 0.577 | 0.362 | 0.262 | 0.000 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | C | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 115 | 115 | 116 | 219 | 124 | 112 | 0 | 226 | 0 |
N.S. |
1 | 1.00 | 1.01 | 1.90 | 1.08 | 0.97 | 0.00 | 1.97 | 0.00 |
time (sec) |
N/A | 0.418 | 0.190 | 0.573 | 0.368 | 0.274 | 0.000 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | C | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 169 | 169 | 158 | 271 | 128 | 156 | 0 | 448 | 0 |
N.S. |
1 | 1.00 | 0.93 | 1.60 | 0.76 | 0.92 | 0.00 | 2.65 | 0.00 |
time (sec) |
N/A | 0.497 | 0.312 | 0.675 | 0.364 | 0.276 | 0.000 | 0.299 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 247 | 247 | 234 | 185 | 207 | 216 | 0 | 329 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.75 | 0.84 | 0.87 | 0.00 | 1.33 | 0.00 |
time (sec) |
N/A | 0.460 | 0.377 | 0.279 | 0.349 | 0.308 | 0.000 | 0.302 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 198 | 198 | 191 | 138 | 171 | 176 | 0 | 283 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.70 | 0.86 | 0.89 | 0.00 | 1.43 | 0.00 |
time (sec) |
N/A | 0.372 | 0.343 | 0.242 | 0.331 | 0.326 | 0.000 | 0.292 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 153 | 153 | 147 | 98 | 129 | 134 | 0 | 195 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.64 | 0.84 | 0.88 | 0.00 | 1.27 | 0.00 |
time (sec) |
N/A | 0.302 | 0.217 | 0.181 | 0.336 | 0.282 | 0.000 | 0.294 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 187 | 187 | 184 | 134 | 170 | 159 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.72 | 0.91 | 0.85 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.356 | 0.341 | 0.223 | 0.458 | 0.298 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 239 | 239 | 226 | 173 | 176 | 206 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.72 | 0.74 | 0.86 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.405 | 0.455 | 0.254 | 0.455 | 0.278 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 117 | 130 | 75 | 85 | 79 | 79 | 143 | 138 | 94 |
N.S. |
1 | 1.11 | 0.64 | 0.73 | 0.68 | 0.68 | 1.22 | 1.18 | 0.80 |
time (sec) |
N/A | 0.641 | 0.201 | 0.200 | 0.252 | 0.280 | 0.771 | 0.283 | 6.402 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 83 | 58 | 66 | 60 | 58 | 92 | 94 | 66 |
N.S. |
1 | 1.05 | 0.73 | 0.84 | 0.76 | 0.73 | 1.16 | 1.19 | 0.84 |
time (sec) |
N/A | 0.402 | 0.115 | 0.312 | 0.250 | 0.305 | 0.396 | 0.276 | 0.234 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 23 | 33 | 26 | 27 | 26 | 46 | 26 | 28 |
N.S. |
1 | 0.70 | 1.00 | 0.79 | 0.82 | 0.79 | 1.39 | 0.79 | 0.85 |
time (sec) |
N/A | 0.241 | 0.021 | 0.321 | 0.232 | 0.278 | 0.156 | 0.294 | 5.980 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | C | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 51 | 125 | 89 | 47 | 0 | 47 | 0 |
N.S. |
1 | 1.00 | 0.93 | 2.27 | 1.62 | 0.85 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.269 | 0.054 | 0.618 | 0.376 | 0.311 | 0.000 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | C | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 90 | 185 | 97 | 90 | 0 | 186 | 0 |
N.S. |
1 | 1.00 | 0.99 | 2.03 | 1.07 | 0.99 | 0.00 | 2.04 | 0.00 |
time (sec) |
N/A | 0.394 | 0.100 | 0.701 | 0.370 | 0.292 | 0.000 | 0.308 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | B | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 188 | 188 | 159 | 132 | 143 | 147 | 439 | 259 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.70 | 0.76 | 0.78 | 2.34 | 1.38 | 0.00 |
time (sec) |
N/A | 0.398 | 0.303 | 0.182 | 0.338 | 0.313 | 1.888 | 0.295 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 153 | 153 | 117 | 99 | 112 | 120 | 129 | 185 | 0 |
N.S. |
1 | 1.00 | 0.76 | 0.65 | 0.73 | 0.78 | 0.84 | 1.21 | 0.00 |
time (sec) |
N/A | 0.266 | 0.157 | 0.158 | 0.345 | 0.310 | 0.510 | 0.312 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 168 | 172 | 167 | 130 | 152 | 147 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.99 | 0.77 | 0.90 | 0.88 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.345 | 0.300 | 0.253 | 0.463 | 0.320 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 63 | 58 | 97 | 51 | 116 | 97 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.82 | 1.37 | 0.72 | 1.63 | 1.37 | 0.00 |
time (sec) |
N/A | 0.234 | 0.050 | 0.250 | 0.338 | 0.310 | 2.161 | 0.298 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | B | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 84 | 89 | 75 | 78 | 117 | 73 | 291 | 125 | 0 |
N.S. |
1 | 1.06 | 0.89 | 0.93 | 1.39 | 0.87 | 3.46 | 1.49 | 0.00 |
time (sec) |
N/A | 0.288 | 0.112 | 0.367 | 0.334 | 0.323 | 2.106 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 35 | 67 | 50 | 55 | 52 | 95 | 52 | 55 |
N.S. |
1 | 0.52 | 1.00 | 0.75 | 0.82 | 0.78 | 1.42 | 0.78 | 0.82 |
time (sec) |
N/A | 0.242 | 0.030 | 0.407 | 0.252 | 0.298 | 0.668 | 0.280 | 6.544 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 41 | 39 | 54 | 38 | 51 | 39 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.89 | 1.23 | 0.86 | 1.16 | 0.89 | 0.00 |
time (sec) |
N/A | 0.262 | 0.079 | 0.322 | 0.294 | 0.321 | 2.184 | 0.281 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 362 | 341 | 289 | 0 | 0 | 1435 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 0.80 | 0.00 | 0.00 | 3.96 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.398 | 0.157 | 0.000 | 0.000 | 0.455 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 245 | 237 | 188 | 0 | 0 | 1041 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.77 | 0.00 | 0.00 | 4.25 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.874 | 0.053 | 0.000 | 0.000 | 0.419 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 54 | 48 | 48 | 8078 | 208 | 165 | 63 | 128 |
N.S. |
1 | 1.12 | 1.00 | 1.00 | 168.29 | 4.33 | 3.44 | 1.31 | 2.67 |
time (sec) |
N/A | 0.272 | 0.063 | 0.161 | 24.834 | 0.324 | 3.557 | 0.293 | 8.488 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 20 | 19 | 15 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.06 | 0.83 | 1.11 | 1.11 |
time (sec) |
N/A | 0.186 | 1.089 | 0.044 | 0.441 | 0.347 | 2.380 | 0.305 | 6.103 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 20 | 23 | 17 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.28 | 0.94 | 1.11 | 1.11 |
time (sec) |
N/A | 0.189 | 0.985 | 0.049 | 0.447 | 0.274 | 3.219 | 0.324 | 6.112 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 20 | 20 | 15 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.11 | 0.83 | 1.11 | 1.11 |
time (sec) |
N/A | 0.185 | 0.555 | 0.045 | 0.470 | 0.287 | 1.856 | 0.301 | 5.963 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 14 | 16 | 16 | 14 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 1.14 | 1.00 | 1.14 | 1.14 |
time (sec) |
N/A | 0.164 | 0.022 | 0.042 | 0.417 | 0.322 | 0.799 | 0.296 | 5.963 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 20 | 23 | 17 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.28 | 0.94 | 1.11 | 1.11 |
time (sec) |
N/A | 0.183 | 0.433 | 0.047 | 0.454 | 0.278 | 3.015 | 0.305 | 6.433 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 663 | 625 | 513 | 0 | 0 | 2469 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 0.77 | 0.00 | 0.00 | 3.72 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.799 | 1.743 | 0.000 | 0.000 | 0.528 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 324 | 326 | 302 | 0 | 0 | 1509 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.93 | 0.00 | 0.00 | 4.66 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.160 | 0.817 | 0.000 | 0.000 | 0.465 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 99 | 91 | 131 | 0 | 366 | 2116 | 144 | 178 |
N.S. |
1 | 1.09 | 1.00 | 1.44 | 0.00 | 4.02 | 23.25 | 1.58 | 1.96 |
time (sec) |
N/A | 0.376 | 0.201 | 0.239 | 0.000 | 0.343 | 54.296 | 0.284 | 6.552 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 3466 | 45 | 17 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 192.56 | 2.50 | 0.94 | 1.11 | 1.11 |
time (sec) |
N/A | 0.182 | 4.684 | 0.298 | 4.106 | 0.308 | 26.566 | 0.444 | 6.275 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 3475 | 51 | 19 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 193.06 | 2.83 | 1.06 | 1.11 | 1.11 |
time (sec) |
N/A | 0.183 | 6.935 | 0.228 | 4.117 | 0.337 | 39.901 | 0.553 | 6.377 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 922 | 46 | 17 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 51.22 | 2.56 | 0.94 | 1.11 | 1.11 |
time (sec) |
N/A | 0.183 | 3.026 | 0.208 | 0.600 | 0.296 | 40.495 | 0.363 | 6.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 14 | 3381 | 43 | 15 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 241.50 | 3.07 | 1.07 | 1.14 | 1.14 |
time (sec) |
N/A | 0.160 | 3.122 | 0.223 | 4.013 | 0.296 | 18.265 | 0.344 | 5.979 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 3486 | 51 | 19 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 193.67 | 2.83 | 1.06 | 1.11 | 1.11 |
time (sec) |
N/A | 0.183 | 5.365 | 0.288 | 4.145 | 0.327 | 44.262 | 0.372 | 6.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 22 | 22 | 19 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 0.95 | 1.10 | 1.10 |
time (sec) |
N/A | 0.186 | 0.796 | 0.059 | 0.723 | 0.359 | 16.095 | 0.558 | 6.386 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 444 | 444 | 373 | 0 | 0 | 323 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.73 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.663 | 1.397 | 0.000 | 0.000 | 0.113 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 279 | 279 | 551 | 0 | 0 | 198 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.97 | 0.00 | 0.00 | 0.71 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.458 | 1.900 | 0.000 | 0.000 | 0.110 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 134 | 134 | 149 | 0 | 0 | 98 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.11 | 0.00 | 0.00 | 0.73 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.287 | 0.345 | 0.000 | 0.000 | 0.106 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 22 | 22 | 17 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 0.85 | 1.10 | 1.10 |
time (sec) |
N/A | 0.183 | 0.687 | 0.062 | 0.521 | 0.285 | 0.434 | 0.302 | 6.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 3886 | 48 | 19 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 194.30 | 2.40 | 0.95 | 1.10 | 1.10 |
time (sec) |
N/A | 0.182 | 1.192 | 0.233 | 8.109 | 0.290 | 1.445 | 0.342 | 6.202 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 44 | 39 | 37 | 40 | 49 | 75 | 38 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.84 | 0.91 | 1.11 | 1.70 | 0.86 |
time (sec) |
N/A | 0.206 | 0.009 | 0.191 | 0.198 | 0.291 | 0.400 | 0.274 | 0.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 41 | 22 | 21 | 23 | 31 | 26 | 21 |
N.S. |
1 | 1.00 | 1.64 | 0.88 | 0.84 | 0.92 | 1.24 | 1.04 | 0.84 |
time (sec) |
N/A | 0.180 | 0.038 | 0.137 | 0.289 | 0.288 | 0.113 | 0.270 | 5.909 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 29 | 0 | 50 | 27 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.00 | 1.61 | 0.87 | 0.00 | 1.03 | 0.00 |
time (sec) |
N/A | 0.193 | 0.077 | 0.000 | 0.386 | 0.309 | 0.000 | 0.279 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 48 | 0 | 57 | 49 | 0 | 99 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.00 | 1.08 | 0.92 | 0.00 | 1.87 | 0.00 |
time (sec) |
N/A | 0.255 | 0.094 | 0.000 | 0.391 | 0.316 | 0.000 | 0.287 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 112 | 112 | 124 | 0 | 109 | 82 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.11 | 0.00 | 0.97 | 0.73 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.268 | 0.176 | 0.000 | 0.207 | 0.112 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 108 | 0 | 93 | 63 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.19 | 0.00 | 1.02 | 0.69 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.229 | 0.113 | 0.000 | 0.198 | 0.109 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 120 | 0 | 89 | 72 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.19 | 0.00 | 0.88 | 0.71 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.255 | 0.170 | 0.000 | 0.186 | 0.118 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 130 | 130 | 143 | 0 | 91 | 101 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.10 | 0.00 | 0.70 | 0.78 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.282 | 0.291 | 0.000 | 0.185 | 0.127 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 106 | 106 | 124 | 0 | 110 | 80 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.17 | 0.00 | 1.04 | 0.75 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.228 | 0.146 | 0.000 | 0.181 | 0.111 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 138 | 0 | 85 | 61 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.68 | 0.00 | 1.04 | 0.74 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.177 | 0.084 | 0.000 | 0.175 | 0.116 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 120 | 0 | 90 | 80 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.19 | 0.00 | 0.89 | 0.79 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.218 | 0.160 | 0.000 | 0.191 | 0.110 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 126 | 126 | 146 | 0 | 91 | 101 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.16 | 0.00 | 0.72 | 0.80 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.243 | 0.290 | 0.000 | 0.181 | 0.101 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 92 | 92 | 87 | 84 | 143 | 165 | 95 |
N.S. |
1 | 1.00 | 0.86 | 0.86 | 0.81 | 0.79 | 1.34 | 1.54 | 0.89 |
time (sec) |
N/A | 0.337 | 0.178 | 0.525 | 0.206 | 0.305 | 0.538 | 0.283 | 5.864 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 60 | 62 | 52 | 52 | 52 | 53 | 99 | 57 | 51 |
N.S. |
1 | 1.03 | 0.87 | 0.87 | 0.87 | 0.88 | 1.65 | 0.95 | 0.85 |
time (sec) |
N/A | 0.258 | 0.100 | 0.225 | 0.204 | 0.304 | 0.179 | 0.290 | 5.928 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 71 | 0 | 108 | 70 | 0 | 79 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 1.35 | 0.88 | 0.00 | 0.99 | 0.00 |
time (sec) |
N/A | 0.279 | 0.131 | 0.000 | 0.323 | 0.286 | 0.000 | 0.292 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 122 | 122 | 116 | 0 | 124 | 112 | 0 | 226 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 1.02 | 0.92 | 0.00 | 1.85 | 0.00 |
time (sec) |
N/A | 0.405 | 0.192 | 0.000 | 0.326 | 0.287 | 0.000 | 0.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 249 | 249 | 339 | 0 | 234 | 186 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.36 | 0.00 | 0.94 | 0.75 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.417 | 0.610 | 0.000 | 0.232 | 0.108 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 193 | 193 | 251 | 0 | 199 | 141 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.30 | 0.00 | 1.03 | 0.73 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.339 | 1.352 | 0.000 | 0.220 | 0.104 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 231 | 229 | 332 | 0 | 187 | 173 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 1.44 | 0.00 | 0.81 | 0.75 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.398 | 0.695 | 0.000 | 0.226 | 0.128 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 285 | 283 | 292 | 0 | 194 | 232 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 1.02 | 0.00 | 0.68 | 0.81 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.463 | 1.843 | 0.000 | 0.234 | 0.119 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 237 | 237 | 339 | 0 | 240 | 182 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.43 | 0.00 | 1.01 | 0.77 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.371 | 0.598 | 0.000 | 0.218 | 0.114 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 183 | 183 | 228 | 0 | 192 | 139 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.25 | 0.00 | 1.05 | 0.76 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.275 | 0.614 | 0.000 | 0.212 | 0.111 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 227 | 225 | 334 | 0 | 188 | 189 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 1.47 | 0.00 | 0.83 | 0.83 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.342 | 0.535 | 0.000 | 0.225 | 0.116 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 277 | 275 | 294 | 0 | 193 | 233 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 1.06 | 0.00 | 0.70 | 0.84 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.393 | 1.957 | 0.000 | 0.231 | 0.119 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 245 | 241 | 188 | 0 | 0 | 1041 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.77 | 0.00 | 0.00 | 4.25 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.856 | 0.117 | 0.000 | 0.000 | 0.419 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 57 | 51 | 49 | 8078 | 208 | 172 | 64 | 136 |
N.S. |
1 | 1.12 | 1.00 | 0.96 | 158.39 | 4.08 | 3.37 | 1.25 | 2.67 |
time (sec) |
N/A | 0.274 | 0.068 | 0.178 | 23.030 | 0.335 | 6.161 | 0.295 | 8.567 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 20 | 19 | 15 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.06 | 0.83 | 1.11 | 1.11 |
time (sec) |
N/A | 0.178 | 1.033 | 0.046 | 0.465 | 0.291 | 2.487 | 0.320 | 6.627 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 20 | 23 | 17 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.28 | 0.94 | 1.11 | 1.11 |
time (sec) |
N/A | 0.184 | 0.924 | 0.063 | 0.467 | 0.299 | 4.425 | 0.338 | 6.285 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 16 | 18 | 18 | 14 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.12 | 0.88 | 1.12 | 1.12 |
time (sec) |
N/A | 0.182 | 0.438 | 0.044 | 0.452 | 0.285 | 2.156 | 0.324 | 5.932 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 20 | 23 | 17 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.28 | 0.94 | 1.11 | 1.11 |
time (sec) |
N/A | 0.183 | 0.440 | 0.047 | 0.500 | 0.308 | 2.712 | 0.336 | 6.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 14 | 16 | 16 | 14 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 1.14 | 1.00 | 1.14 | 1.14 |
time (sec) |
N/A | 0.160 | 0.015 | 0.045 | 0.457 | 0.311 | 0.742 | 0.302 | 5.898 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 20 | 23 | 17 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.28 | 0.94 | 1.11 | 1.11 |
time (sec) |
N/A | 0.182 | 0.465 | 0.049 | 0.491 | 0.344 | 3.987 | 0.307 | 6.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 324 | 326 | 302 | 0 | 0 | 1509 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.93 | 0.00 | 0.00 | 4.66 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.167 | 0.846 | 0.000 | 0.000 | 0.468 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 94 | 99 | 91 | 131 | 0 | 366 | 2116 | 146 | 186 |
N.S. |
1 | 1.05 | 0.97 | 1.39 | 0.00 | 3.89 | 22.51 | 1.55 | 1.98 |
time (sec) |
N/A | 0.389 | 0.144 | 0.240 | 0.000 | 0.326 | 73.187 | 0.294 | 6.595 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 2696 | 45 | 17 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 149.78 | 2.50 | 0.94 | 1.11 | 1.11 |
time (sec) |
N/A | 0.184 | 6.888 | 0.289 | 4.214 | 0.309 | 25.038 | 0.442 | 6.334 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 2705 | 51 | 19 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 150.28 | 2.83 | 1.06 | 1.11 | 1.11 |
time (sec) |
N/A | 0.183 | 10.075 | 0.289 | 4.242 | 0.316 | 50.273 | 0.598 | 6.527 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 16 | 0 | 44 | 15 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 0.00 | 2.75 | 0.94 | 1.12 | 1.12 |
time (sec) |
N/A | 0.173 | 4.337 | 0.217 | 0.000 | 0.324 | 24.651 | 0.367 | 6.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 0 | 51 | 19 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 0.00 | 2.83 | 1.06 | 1.11 | 1.11 |
time (sec) |
N/A | 0.181 | 7.519 | 0.327 | 0.000 | 0.309 | 35.661 | 0.371 | 6.203 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 14 | 2171 | 43 | 15 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 155.07 | 3.07 | 1.07 | 1.14 | 1.14 |
time (sec) |
N/A | 0.160 | 5.192 | 0.235 | 1.840 | 0.323 | 16.636 | 0.315 | 5.957 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 2171 | 51 | 19 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 120.61 | 2.83 | 1.06 | 1.11 | 1.11 |
time (sec) |
N/A | 0.183 | 8.380 | 0.297 | 1.958 | 0.324 | 49.111 | 0.358 | 6.369 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 22 | 22 | 19 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 0.95 | 1.10 | 1.10 |
time (sec) |
N/A | 0.183 | 0.770 | 0.053 | 0.727 | 0.331 | 17.069 | 0.539 | 6.377 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 442 | 442 | 373 | 0 | 0 | 347 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.79 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.652 | 1.524 | 0.000 | 0.000 | 0.142 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 285 | 285 | 556 | 0 | 0 | 214 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.95 | 0.00 | 0.00 | 0.75 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.453 | 1.810 | 0.000 | 0.000 | 0.133 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 134 | 134 | 149 | 0 | 0 | 106 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.11 | 0.00 | 0.00 | 0.79 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.281 | 0.319 | 0.000 | 0.000 | 0.143 | 0.000 | 0.000 | 0.000 |