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 | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 76 | 144 | 326 | 171 | 311 | 324 | 215 |
N.S. |
1 | 1.00 | 0.84 | 1.58 | 3.58 | 1.88 | 3.42 | 3.56 | 2.36 |
time (sec) |
N/A | 0.100 | 0.187 | 5.561 | 0.196 | 0.256 | 0.356 | 0.259 | 0.224 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 61 | 111 | 222 | 111 | 202 | 204 | 143 |
N.S. |
1 | 1.00 | 0.87 | 1.59 | 3.17 | 1.59 | 2.89 | 2.91 | 2.04 |
time (sec) |
N/A | 0.062 | 0.117 | 0.205 | 0.190 | 0.248 | 0.286 | 0.261 | 1.779 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 44 | 77 | 135 | 64 | 112 | 112 | 82 |
N.S. |
1 | 1.00 | 0.90 | 1.57 | 2.76 | 1.31 | 2.29 | 2.29 | 1.67 |
time (sec) |
N/A | 0.038 | 0.099 | 0.181 | 0.187 | 0.248 | 0.214 | 0.254 | 1.767 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 27 | 37 | 68 | 30 | 46 | 46 | 35 |
N.S. |
1 | 1.00 | 0.96 | 1.32 | 2.43 | 1.07 | 1.64 | 1.64 | 1.25 |
time (sec) |
N/A | 0.014 | 0.074 | 0.060 | 0.190 | 0.256 | 0.161 | 0.259 | 0.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 49 | 82 | 57 | 94 | 0 | 56 | 0 |
N.S. |
1 | 1.00 | 0.96 | 1.61 | 1.12 | 1.84 | 0.00 | 1.10 | 0.00 |
time (sec) |
N/A | 0.079 | 0.057 | 0.273 | 0.223 | 0.239 | 0.000 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 65 | 133 | 81 | 150 | 0 | 615 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.87 | 1.14 | 2.11 | 0.00 | 8.66 | 0.00 |
time (sec) |
N/A | 0.105 | 0.164 | 0.222 | 0.228 | 0.246 | 0.000 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 104 | 88 | 277 | 95 | 254 | 0 | 298 | 0 |
N.S. |
1 | 1.00 | 0.85 | 2.66 | 0.91 | 2.44 | 0.00 | 2.87 | 0.00 |
time (sec) |
N/A | 0.139 | 0.343 | 0.267 | 0.221 | 0.247 | 0.000 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 162 | 162 | 132 | 145 | 382 | 312 | 660 | 372 | 332 |
N.S. |
1 | 1.00 | 0.81 | 0.90 | 2.36 | 1.93 | 4.07 | 2.30 | 2.05 |
time (sec) |
N/A | 0.080 | 0.367 | 0.345 | 0.206 | 0.259 | 0.527 | 0.262 | 2.396 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 134 | 134 | 104 | 121 | 263 | 209 | 456 | 243 | 229 |
N.S. |
1 | 1.00 | 0.78 | 0.90 | 1.96 | 1.56 | 3.40 | 1.81 | 1.71 |
time (sec) |
N/A | 0.060 | 0.271 | 0.281 | 0.195 | 0.259 | 0.391 | 0.273 | 0.440 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 95 | 95 | 75 | 79 | 165 | 123 | 264 | 136 | 127 |
N.S. |
1 | 1.00 | 0.79 | 0.83 | 1.74 | 1.29 | 2.78 | 1.43 | 1.34 |
time (sec) |
N/A | 0.046 | 0.184 | 0.223 | 0.197 | 0.246 | 0.302 | 0.264 | 1.788 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 51 | 52 | 88 | 66 | 126 | 63 | 58 |
N.S. |
1 | 1.00 | 0.93 | 0.95 | 1.60 | 1.20 | 2.29 | 1.15 | 1.05 |
time (sec) |
N/A | 0.022 | 0.167 | 0.094 | 0.191 | 0.255 | 0.208 | 0.264 | 0.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 64 | 97 | 72 | 104 | 0 | 68 | 0 |
N.S. |
1 | 1.00 | 0.82 | 1.24 | 0.92 | 1.33 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.123 | 0.159 | 0.436 | 0.247 | 0.262 | 0.000 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 75 | 152 | 88 | 164 | 0 | 574 | 0 |
N.S. |
1 | 1.00 | 0.93 | 1.88 | 1.09 | 2.02 | 0.00 | 7.09 | 0.00 |
time (sec) |
N/A | 0.109 | 0.286 | 0.360 | 0.228 | 0.261 | 0.000 | 0.297 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 112 | 102 | 299 | 99 | 278 | 0 | 330 | 0 |
N.S. |
1 | 1.00 | 0.91 | 2.67 | 0.88 | 2.48 | 0.00 | 2.95 | 0.00 |
time (sec) |
N/A | 0.138 | 0.615 | 0.458 | 0.223 | 0.256 | 0.000 | 0.280 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 162 | 162 | 121 | 555 | 110 | 409 | 0 | 537 | 0 |
N.S. |
1 | 1.00 | 0.75 | 3.43 | 0.68 | 2.52 | 0.00 | 3.31 | 0.00 |
time (sec) |
N/A | 0.148 | 0.568 | 0.559 | 0.226 | 0.255 | 0.000 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 225 | 225 | 158 | 173 | 644 | 528 | 772 | 654 | 532 |
N.S. |
1 | 1.00 | 0.70 | 0.77 | 2.86 | 2.35 | 3.43 | 2.91 | 2.36 |
time (sec) |
N/A | 0.220 | 0.762 | 0.510 | 0.208 | 0.254 | 0.671 | 0.279 | 2.305 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 175 | 175 | 122 | 284 | 439 | 343 | 495 | 414 | 364 |
N.S. |
1 | 1.00 | 0.70 | 1.62 | 2.51 | 1.96 | 2.83 | 2.37 | 2.08 |
time (sec) |
N/A | 0.160 | 0.655 | 0.316 | 0.201 | 0.251 | 0.497 | 0.276 | 2.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 123 | 123 | 93 | 191 | 272 | 199 | 284 | 230 | 183 |
N.S. |
1 | 1.00 | 0.76 | 1.55 | 2.21 | 1.62 | 2.31 | 1.87 | 1.49 |
time (sec) |
N/A | 0.089 | 0.372 | 0.244 | 0.196 | 0.249 | 0.378 | 0.265 | 2.147 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 52 | 62 | 143 | 95 | 126 | 98 | 77 |
N.S. |
1 | 1.00 | 0.69 | 0.83 | 1.91 | 1.27 | 1.68 | 1.31 | 1.03 |
time (sec) |
N/A | 0.035 | 0.189 | 0.113 | 0.182 | 0.247 | 0.246 | 0.269 | 0.257 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 102 | 166 | 117 | 186 | 0 | 112 | 0 |
N.S. |
1 | 1.00 | 0.84 | 1.37 | 0.97 | 1.54 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.196 | 0.279 | 0.365 | 0.244 | 0.256 | 0.000 | 0.273 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 145 | 145 | 196 | 271 | 145 | 305 | 0 | 1075 | 0 |
N.S. |
1 | 1.00 | 1.35 | 1.87 | 1.00 | 2.10 | 0.00 | 7.41 | 0.00 |
time (sec) |
N/A | 0.205 | 0.468 | 0.421 | 0.244 | 0.248 | 0.000 | 0.316 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 184 | 184 | 218 | 562 | 145 | 527 | 0 | 602 | 0 |
N.S. |
1 | 1.00 | 1.18 | 3.05 | 0.79 | 2.86 | 0.00 | 3.27 | 0.00 |
time (sec) |
N/A | 0.285 | 0.612 | 0.513 | 0.247 | 0.259 | 0.000 | 0.282 | 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 | 172 | 172 | 100 | 102 | 176 | 195 | 253 | 150 | 129 |
N.S. |
1 | 1.00 | 0.58 | 0.59 | 1.02 | 1.13 | 1.47 | 0.87 | 0.75 |
time (sec) |
N/A | 0.110 | 0.279 | 0.366 | 0.194 | 0.255 | 0.559 | 0.272 | 0.428 |
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 | 134 | 134 | 90 | 81 | 132 | 147 | 209 | 118 | 94 |
N.S. |
1 | 1.00 | 0.67 | 0.60 | 0.99 | 1.10 | 1.56 | 0.88 | 0.70 |
time (sec) |
N/A | 0.092 | 0.113 | 0.161 | 0.197 | 0.260 | 0.407 | 0.261 | 0.275 |
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 | 80 | 80 | 53 | 64 | 96 | 114 | 138 | 86 | 68 |
N.S. |
1 | 1.00 | 0.66 | 0.80 | 1.20 | 1.42 | 1.72 | 1.08 | 0.85 |
time (sec) |
N/A | 0.037 | 0.124 | 0.131 | 0.184 | 0.273 | 0.317 | 0.287 | 0.160 |
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 | 179 | 179 | 343 | 0 | 0 | 497 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.92 | 0.00 | 0.00 | 2.78 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.114 | 0.360 | 0.000 | 0.000 | 0.267 | 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 | 119 | 119 | 199 | 0 | 0 | 305 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.67 | 0.00 | 0.00 | 2.56 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.075 | 0.207 | 0.000 | 0.000 | 0.270 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 84 | 101 | 0 | 157 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.38 | 1.66 | 0.00 | 2.57 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.036 | 0.059 | 0.103 | 0.000 | 0.268 | 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 | 14 | 14 | 16 | 14 | 16 | 16 | 12 | 16 | 18 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 1.14 | 0.86 | 1.14 | 1.29 |
time (sec) |
N/A | 0.022 | 2.819 | 0.032 | 0.434 | 0.244 | 0.458 | 0.361 | 1.728 |
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 | 27 | 14 | 16 | 18 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 1.93 | 1.00 | 1.14 | 1.29 |
time (sec) |
N/A | 0.019 | 5.736 | 0.037 | 0.404 | 0.252 | 0.662 | 1.911 | 1.799 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 145 | 298 | 238 | 1332 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.41 | 2.89 | 2.31 | 12.93 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.159 | 0.617 | 0.313 | 0.305 | 0.277 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 91 | 159 | 0 | 715 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.25 | 2.18 | 0.00 | 9.79 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.103 | 0.498 | 0.244 | 0.000 | 0.258 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 51 | 57 | 72 | 161 | 0 | 78 | 50 |
N.S. |
1 | 1.00 | 1.76 | 1.97 | 2.48 | 5.55 | 0.00 | 2.69 | 1.72 |
time (sec) |
N/A | 0.028 | 0.088 | 0.123 | 0.179 | 0.253 | 0.000 | 0.261 | 0.096 |
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 | 102 | 18 | 14 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 6.38 | 1.12 | 0.88 | 1.12 | 1.12 |
time (sec) |
N/A | 0.032 | 25.540 | 0.027 | 0.269 | 0.254 | 0.491 | 0.270 | 1.756 |
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 | 156 | 29 | 15 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 9.75 | 1.81 | 0.94 | 1.12 | 1.12 |
time (sec) |
N/A | 0.030 | 25.787 | 0.028 | 0.307 | 0.253 | 0.668 | 0.325 | 1.803 |
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 | 296 | 296 | 455 | 0 | 0 | 4785 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.54 | 0.00 | 0.00 | 16.17 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.184 | 4.662 | 0.000 | 0.000 | 0.353 | 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 | 175 | 175 | 270 | 0 | 0 | 2651 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.54 | 0.00 | 0.00 | 15.15 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.118 | 1.740 | 0.000 | 0.000 | 0.319 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 156 | 216 | 0 | 1267 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.53 | 2.12 | 0.00 | 12.42 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.050 | 0.477 | 0.153 | 0.000 | 0.288 | 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 | 16 | 16 | 18 | 16 | 321 | 18 | 14 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 20.06 | 1.12 | 0.88 | 1.12 | 1.12 |
time (sec) |
N/A | 0.031 | 124.558 | 0.033 | 0.443 | 0.263 | 0.523 | 2.517 | 1.738 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | F(-1) | 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 | 0 | 16 | 405 | 29 | 15 | 18 | 18 |
N.S. |
1 | 1.00 | 0.00 | 1.00 | 25.31 | 1.81 | 0.94 | 1.12 | 1.12 |
time (sec) |
N/A | 0.030 | 0.000 | 0.034 | 0.516 | 0.267 | 0.748 | 27.399 | 1.823 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | B | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 171 | 171 | 107 | 0 | 308 | 523 | 0 | 232 | 0 |
N.S. |
1 | 1.00 | 0.63 | 0.00 | 1.80 | 3.06 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.272 | 0.043 | 0.000 | 0.190 | 0.268 | 0.000 | 0.312 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | B | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 146 | 146 | 107 | 0 | 268 | 387 | 0 | 202 | 0 |
N.S. |
1 | 1.00 | 0.73 | 0.00 | 1.84 | 2.65 | 0.00 | 1.38 | 0.00 |
time (sec) |
N/A | 0.187 | 0.072 | 0.000 | 0.189 | 0.273 | 0.000 | 0.297 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | B | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 123 | 123 | 105 | 0 | 230 | 302 | 0 | 169 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.00 | 1.87 | 2.46 | 0.00 | 1.37 | 0.00 |
time (sec) |
N/A | 0.145 | 0.054 | 0.000 | 0.188 | 0.274 | 0.000 | 0.279 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | B | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 104 | 104 | 105 | 0 | 180 | 123 | 0 | 89 | 0 |
N.S. |
1 | 1.00 | 1.01 | 0.00 | 1.73 | 1.18 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.090 | 0.027 | 0.000 | 0.197 | 0.266 | 0.000 | 0.266 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 119 | 119 | 118 | 0 | 104 | 338 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.87 | 2.84 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.137 | 0.247 | 0.000 | 0.185 | 0.270 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 149 | 149 | 150 | 0 | 115 | 534 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.01 | 0.00 | 0.77 | 3.58 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.180 | 0.454 | 0.000 | 0.272 | 0.277 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 174 | 174 | 191 | 0 | 115 | 853 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.10 | 0.00 | 0.66 | 4.90 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.216 | 0.289 | 0.000 | 0.263 | 0.280 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 239 | 239 | 137 | 0 | 281 | 1001 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.57 | 0.00 | 1.18 | 4.19 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.306 | 0.333 | 0.000 | 0.276 | 0.287 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 211 | 211 | 137 | 0 | 239 | 755 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.65 | 0.00 | 1.13 | 3.58 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.240 | 0.168 | 0.000 | 0.276 | 0.276 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 166 | 166 | 129 | 0 | 189 | 590 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.78 | 0.00 | 1.14 | 3.55 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.213 | 0.304 | 0.000 | 0.267 | 0.259 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 138 | 138 | 141 | 0 | 107 | 155 | 0 | 115 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.78 | 1.12 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.162 | 0.099 | 0.000 | 0.266 | 0.255 | 0.000 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 142 | 142 | 152 | 0 | 116 | 569 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.07 | 0.00 | 0.82 | 4.01 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.169 | 0.265 | 0.000 | 0.255 | 0.276 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 174 | 174 | 156 | 0 | 118 | 861 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.90 | 0.00 | 0.68 | 4.95 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.236 | 0.924 | 0.000 | 0.255 | 0.282 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 220 | 220 | 204 | 0 | 116 | 1350 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.53 | 6.14 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.226 | 0.299 | 0.000 | 0.258 | 0.307 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 251 | 251 | 222 | 0 | 116 | 1825 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.46 | 7.27 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.298 | 0.535 | 0.000 | 0.259 | 0.306 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 381 | 381 | 195 | 0 | 513 | 2092 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.51 | 0.00 | 1.35 | 5.49 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.688 | 0.370 | 0.000 | 0.288 | 0.287 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 326 | 326 | 209 | 0 | 429 | 1545 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.64 | 0.00 | 1.32 | 4.74 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.493 | 0.334 | 0.000 | 0.285 | 0.286 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 275 | 275 | 210 | 0 | 334 | 1217 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.76 | 0.00 | 1.21 | 4.43 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.341 | 0.214 | 0.000 | 0.283 | 0.283 | 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 | 228 | 228 | 192 | 0 | 177 | 253 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.78 | 1.11 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.254 | 0.152 | 0.000 | 0.273 | 0.265 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 246 | 246 | 246 | 0 | 196 | 1344 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.80 | 5.46 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.298 | 0.585 | 0.000 | 0.296 | 0.266 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 277 | 277 | 253 | 0 | 194 | 2058 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.00 | 0.70 | 7.43 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.409 | 1.886 | 0.000 | 0.303 | 0.285 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 331 | 331 | 376 | 0 | 196 | 3280 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.14 | 0.00 | 0.59 | 9.91 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.460 | 0.665 | 0.000 | 0.315 | 0.319 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | B | C | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 51 | 133 | 174 | 191 | 131 | 145 | 0 |
N.S. |
1 | 1.00 | 0.46 | 1.20 | 1.57 | 1.72 | 1.18 | 1.31 | 0.00 |
time (sec) |
N/A | 0.125 | 0.011 | 0.059 | 0.194 | 0.270 | 11.163 | 0.274 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | B | C | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 48 | 121 | 148 | 138 | 100 | 108 | 0 |
N.S. |
1 | 1.00 | 0.52 | 1.32 | 1.61 | 1.50 | 1.09 | 1.17 | 0.00 |
time (sec) |
N/A | 0.089 | 0.011 | 0.038 | 0.186 | 0.279 | 0.828 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | A | C | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 48 | 72 | 117 | 59 | 66 | 60 | 0 |
N.S. |
1 | 1.00 | 0.62 | 0.94 | 1.52 | 0.77 | 0.86 | 0.78 | 0.00 |
time (sec) |
N/A | 0.059 | 0.009 | 0.029 | 0.192 | 0.259 | 0.543 | 0.255 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 67 | 115 | 76 | 136 | 99 | 0 | 0 |
N.S. |
1 | 1.00 | 0.76 | 1.31 | 0.86 | 1.55 | 1.12 | 0.00 | 0.00 |
time (sec) |
N/A | 0.083 | 0.030 | 0.034 | 0.181 | 0.266 | 1.425 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 114 | 114 | 78 | 126 | 58 | 179 | 124 | 0 | 0 |
N.S. |
1 | 1.00 | 0.68 | 1.11 | 0.51 | 1.57 | 1.09 | 0.00 | 0.00 |
time (sec) |
N/A | 0.110 | 0.067 | 0.034 | 0.230 | 0.266 | 11.478 | 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 | 16 | 16 | 18 | 14 | 16 | 16 | 15 | 16 | 18 |
N.S. |
1 | 1.00 | 1.12 | 0.88 | 1.00 | 1.00 | 0.94 | 1.00 | 1.12 |
time (sec) |
N/A | 0.021 | 3.426 | 0.045 | 0.784 | 0.266 | 1.275 | 0.300 | 1.745 |
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 | 14 | 16 | 16 | 15 | 16 | 18 |
N.S. |
1 | 1.00 | 1.12 | 0.88 | 1.00 | 1.00 | 0.94 | 1.00 | 1.12 |
time (sec) |
N/A | 0.026 | 5.275 | 0.043 | 0.940 | 0.252 | 0.928 | 0.276 | 1.759 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 8 | 10 | 0 | 10 | 10 | 10 |
N.S. |
1 | 1.00 | 1.20 | 0.80 | 1.00 | 0.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.061 | 2.618 | 0.019 | 0.326 | 0.000 | 101.615 | 0.272 | 1.716 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F(-2) | F | F | B |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 46 | 0 | 0 | 0 | 0 | 0 | 39 |
N.S. |
1 | 1.00 | 2.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.95 |
time (sec) |
N/A | 0.041 | 0.311 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.791 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 16 | 0 | 0 | 109 | 0 | 0 | 42 |
N.S. |
1 | 1.00 | 0.67 | 0.00 | 0.00 | 4.54 | 0.00 | 0.00 | 1.75 |
time (sec) |
N/A | 0.047 | 0.076 | 0.000 | 0.000 | 0.245 | 0.000 | 0.000 | 1.802 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F(-1) | F | B |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 64 | 0 | 0 | 0 | 0 | 0 | 110 |
N.S. |
1 | 1.00 | 1.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.34 |
time (sec) |
N/A | 0.054 | 0.489 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.963 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 76 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.072 | 0.776 | 0.000 | 0.000 | 0.000 | 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 | 18 | 18 | 20 | 18 | 20 | 20 | 17 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.11 | 0.94 | 1.11 | 1.11 |
time (sec) |
N/A | 0.031 | 2.379 | 0.045 | 0.337 | 0.269 | 8.059 | 0.328 | 1.819 |
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 | 205 | 0 | 161 | 340 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.68 | 1.43 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.212 | 0.133 | 0.000 | 0.092 | 0.091 | 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 | 144 | 144 | 132 | 0 | 102 | 241 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.71 | 1.67 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.135 | 0.167 | 0.000 | 0.070 | 0.086 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 102 | 0 | 79 | 168 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.72 | 1.53 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.067 | 0.046 | 0.000 | 0.069 | 0.087 | 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 | 14 | 14 | 16 | 14 | 16 | 16 | 14 | 16 | 18 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 1.14 | 1.00 | 1.14 | 1.29 |
time (sec) |
N/A | 0.015 | 4.789 | 0.021 | 0.290 | 0.249 | 1.935 | 0.268 | 1.719 |
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 | 15 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.12 | 0.94 | 1.12 | 1.12 |
time (sec) |
N/A | 0.025 | 3.007 | 0.024 | 0.286 | 0.251 | 4.181 | 0.275 | 1.798 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 54 | 73 | 55 | 86 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.24 | 0.93 | 1.46 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.054 | 0.031 | 0.087 | 0.083 | 0.076 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 54 | 73 | 55 | 86 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.24 | 0.93 | 1.46 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.055 | 0.016 | 0.092 | 0.081 | 0.080 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 54 | 73 | 55 | 86 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.24 | 0.93 | 1.46 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.052 | 0.025 | 0.078 | 0.082 | 0.075 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 54 | 73 | 55 | 78 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.24 | 0.93 | 1.32 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.047 | 0.015 | 0.077 | 0.081 | 0.081 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 49 | 67 | 43 | 78 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.37 | 0.88 | 1.59 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.048 | 0.016 | 0.076 | 0.093 | 0.079 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 52 | 67 | 55 | 86 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.95 | 1.22 | 1.00 | 1.56 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.053 | 0.017 | 0.084 | 0.096 | 0.078 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 55 | 71 | 55 | 86 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.93 | 1.20 | 0.93 | 1.46 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.051 | 0.018 | 0.073 | 0.096 | 0.077 | 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 | 86 | 86 | 79 | 0 | 71 | 136 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.83 | 1.58 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.111 | 0.078 | 0.000 | 0.083 | 0.080 | 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 | 85 | 85 | 78 | 0 | 71 | 136 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.84 | 1.60 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.108 | 0.075 | 0.000 | 0.082 | 0.082 | 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 | 86 | 86 | 79 | 0 | 71 | 136 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.83 | 1.58 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.097 | 0.075 | 0.000 | 0.085 | 0.079 | 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 | 85 | 85 | 76 | 0 | 71 | 122 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.84 | 1.44 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.092 | 0.060 | 0.000 | 0.086 | 0.079 | 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 | 72 | 72 | 64 | 0 | 55 | 117 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.76 | 1.62 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.094 | 0.045 | 0.000 | 0.098 | 0.084 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 73 | 0 | 0 | 136 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.00 | 1.64 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.100 | 0.073 | 0.000 | 0.000 | 0.083 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 84 | 0 | 0 | 136 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 1.62 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.106 | 0.079 | 0.000 | 0.000 | 0.079 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 17 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.065 | 0.058 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 17 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.070 | 0.199 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 45 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.078 | 0.093 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 49 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.125 | 0.097 | 0.000 | 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 | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 122 | 104 | 237 | 168 | 264 | 258 | 187 |
N.S. |
1 | 1.00 | 1.37 | 1.17 | 2.66 | 1.89 | 2.97 | 2.90 | 2.10 |
time (sec) |
N/A | 0.111 | 0.342 | 0.230 | 0.196 | 0.249 | 0.302 | 0.275 | 1.844 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 80 | 77 | 141 | 102 | 151 | 146 | 112 |
N.S. |
1 | 1.00 | 1.19 | 1.15 | 2.10 | 1.52 | 2.25 | 2.18 | 1.67 |
time (sec) |
N/A | 0.071 | 0.232 | 0.202 | 0.189 | 0.254 | 0.217 | 0.274 | 0.145 |