Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 99 | 64 | 63 | 119 | 62 | 0 | 180 | 111 | 62 |
N.S. |
1 | 1.03 | 0.67 | 0.66 | 1.24 | 0.65 | 0.00 | 1.88 | 1.16 | 0.65 |
time (sec) |
N/A | 0.471 | 0.112 | 0.421 | 0.044 | 0.087 | 0.000 | 0.494 | 0.193 | 8.931 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 133 | 89 | 85 | 167 | 86 | 0 | 236 | 152 | 121 |
N.S. |
1 | 1.00 | 0.67 | 0.64 | 1.26 | 0.65 | 0.00 | 1.77 | 1.14 | 0.91 |
time (sec) |
N/A | 0.533 | 0.133 | 0.440 | 0.040 | 0.098 | 0.000 | 0.710 | 0.203 | 9.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 167 | 110 | 104 | 215 | 110 | 0 | 292 | 191 | 156 |
N.S. |
1 | 0.98 | 0.65 | 0.61 | 1.26 | 0.65 | 0.00 | 1.72 | 1.12 | 0.92 |
time (sec) |
N/A | 0.607 | 0.162 | 0.440 | 0.039 | 0.114 | 0.000 | 0.918 | 0.283 | 9.428 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 127 | 85 | 84 | 106 | 83 | 0 | 130 | 74 | 87 |
N.S. |
1 | 0.97 | 0.65 | 0.64 | 0.81 | 0.63 | 0.00 | 0.99 | 0.56 | 0.66 |
time (sec) |
N/A | 0.492 | 0.065 | 0.997 | 0.046 | 0.093 | 0.000 | 0.217 | 0.242 | 9.153 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 93 | 63 | 60 | 83 | 59 | 0 | 98 | 51 | 64 |
N.S. |
1 | 0.99 | 0.67 | 0.64 | 0.88 | 0.63 | 0.00 | 1.04 | 0.54 | 0.68 |
time (sec) |
N/A | 0.410 | 0.061 | 0.855 | 0.052 | 0.092 | 0.000 | 0.198 | 0.308 | 9.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 40 | 37 | 50 | 36 | 0 | 67 | 29 | 41 |
N.S. |
1 | 1.00 | 0.68 | 0.63 | 0.85 | 0.61 | 0.00 | 1.14 | 0.49 | 0.69 |
time (sec) |
N/A | 0.330 | 0.031 | 0.752 | 0.052 | 0.087 | 0.000 | 0.217 | 0.205 | 8.782 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 73 | 72 | 0 | 133 | 0 | 80 | 75 | 0 |
N.S. |
1 | 1.00 | 1.33 | 1.31 | 0.00 | 2.42 | 0.00 | 1.45 | 1.36 | 0.00 |
time (sec) |
N/A | 0.317 | 0.048 | 0.674 | 0.000 | 0.096 | 0.000 | 0.197 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 86 | 90 | 0 | 147 | 0 | 66 | 146 | 0 |
N.S. |
1 | 1.00 | 1.26 | 1.32 | 0.00 | 2.16 | 0.00 | 0.97 | 2.15 | 0.00 |
time (sec) |
N/A | 0.354 | 0.155 | 0.691 | 0.000 | 0.098 | 0.000 | 0.229 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 102 | 104 | 110 | 0 | 194 | 0 | 125 | 187 | 0 |
N.S. |
1 | 0.99 | 1.01 | 1.07 | 0.00 | 1.88 | 0.00 | 1.21 | 1.82 | 0.00 |
time (sec) |
N/A | 0.438 | 0.139 | 0.761 | 0.000 | 0.107 | 0.000 | 0.235 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 188 | 156 | 145 | 237 | 340 | 0 | 183 | 296 | 0 |
N.S. |
1 | 1.09 | 0.91 | 0.84 | 1.38 | 1.98 | 0.00 | 1.06 | 1.72 | 0.00 |
time (sec) |
N/A | 1.009 | 0.526 | 0.489 | 0.045 | 0.112 | 0.000 | 0.199 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 139 | 132 | 140 | 187 | 289 | 0 | 145 | 253 | 0 |
N.S. |
1 | 1.04 | 0.99 | 1.04 | 1.40 | 2.16 | 0.00 | 1.08 | 1.89 | 0.00 |
time (sec) |
N/A | 0.695 | 0.366 | 0.466 | 0.044 | 0.104 | 0.000 | 0.203 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 100 | 108 | 114 | 138 | 230 | 0 | 104 | 210 | 0 |
N.S. |
1 | 1.03 | 1.11 | 1.18 | 1.42 | 2.37 | 0.00 | 1.07 | 2.16 | 0.00 |
time (sec) |
N/A | 0.482 | 0.234 | 0.457 | 0.044 | 0.102 | 0.000 | 0.185 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 72 | 77 | 75 | 79 | 188 | 0 | 70 | 134 | 78 |
N.S. |
1 | 1.07 | 1.15 | 1.12 | 1.18 | 2.81 | 0.00 | 1.04 | 2.00 | 1.16 |
time (sec) |
N/A | 0.394 | 0.092 | 0.440 | 0.043 | 0.096 | 0.000 | 0.207 | 0.196 | 9.722 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 37 | 37 | 65 | 49 | 0 | 65 | 102 | 53 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.76 | 1.32 | 0.00 | 1.76 | 2.76 | 1.43 |
time (sec) |
N/A | 0.316 | 0.080 | 0.440 | 0.043 | 0.084 | 0.000 | 0.242 | 0.208 | 9.307 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 70 | 64 | 59 | 112 | 72 | 0 | 189 | 140 | 70 |
N.S. |
1 | 1.06 | 0.97 | 0.89 | 1.70 | 1.09 | 0.00 | 2.86 | 2.12 | 1.06 |
time (sec) |
N/A | 0.387 | 0.115 | 0.445 | 0.043 | 0.088 | 0.000 | 0.363 | 0.198 | 9.247 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 104 | 85 | 80 | 160 | 98 | 0 | 302 | 184 | 95 |
N.S. |
1 | 1.03 | 0.84 | 0.79 | 1.58 | 0.97 | 0.00 | 2.99 | 1.82 | 0.94 |
time (sec) |
N/A | 0.463 | 0.141 | 0.454 | 0.045 | 0.089 | 0.000 | 0.780 | 0.187 | 9.368 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 138 | 108 | 97 | 208 | 121 | 0 | 415 | 225 | 173 |
N.S. |
1 | 1.00 | 0.78 | 0.70 | 1.51 | 0.88 | 0.00 | 3.01 | 1.63 | 1.25 |
time (sec) |
N/A | 0.535 | 0.163 | 0.449 | 0.044 | 0.101 | 0.000 | 1.393 | 0.224 | 9.327 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 135 | 82 | 91 | 82 | 93 | 0 | 145 | 83 | 92 |
N.S. |
1 | 0.97 | 0.59 | 0.65 | 0.59 | 0.67 | 0.00 | 1.04 | 0.60 | 0.66 |
time (sec) |
N/A | 0.531 | 0.061 | 1.214 | 0.047 | 0.085 | 0.000 | 0.235 | 0.208 | 9.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 101 | 60 | 66 | 59 | 68 | 0 | 107 | 59 | 67 |
N.S. |
1 | 0.97 | 0.58 | 0.63 | 0.57 | 0.65 | 0.00 | 1.03 | 0.57 | 0.64 |
time (sec) |
N/A | 0.436 | 0.045 | 1.017 | 0.047 | 0.086 | 0.000 | 0.224 | 0.180 | 9.276 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 35 | 44 | 39 | 45 | 0 | 63 | 37 | 44 |
N.S. |
1 | 1.00 | 0.51 | 0.64 | 0.57 | 0.65 | 0.00 | 0.91 | 0.54 | 0.64 |
time (sec) |
N/A | 0.368 | 0.042 | 0.876 | 0.048 | 0.095 | 0.000 | 0.254 | 0.182 | 9.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 73 | 79 | 0 | 194 | 0 | 109 | 164 | 0 |
N.S. |
1 | 1.00 | 1.14 | 1.23 | 0.00 | 3.03 | 0.00 | 1.70 | 2.56 | 0.00 |
time (sec) |
N/A | 0.346 | 0.072 | 0.754 | 0.000 | 0.104 | 0.000 | 0.218 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 130 | 96 | 126 | 0 | 255 | 0 | 107 | 324 | 0 |
N.S. |
1 | 0.92 | 0.68 | 0.89 | 0.00 | 1.80 | 0.00 | 0.75 | 2.28 | 0.00 |
time (sec) |
N/A | 0.485 | 0.119 | 0.691 | 0.000 | 0.099 | 0.000 | 0.237 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 130 | 117 | 153 | 0 | 310 | 0 | 149 | 371 | 89 |
N.S. |
1 | 0.95 | 0.85 | 1.12 | 0.00 | 2.26 | 0.00 | 1.09 | 2.71 | 0.65 |
time (sec) |
N/A | 0.512 | 0.165 | 0.701 | 0.000 | 0.104 | 0.000 | 0.229 | 0.205 | 9.791 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 243 | 232 | 136 | 241 | 0 | 123 | 0 | 0 | 196 | 0 |
N.S. |
1 | 0.95 | 0.56 | 0.99 | 0.00 | 0.51 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.712 | 10.135 | 0.939 | 0.000 | 0.100 | 0.000 | 0.000 | 0.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 369 | 353 | 111 | 267 | 0 | 103 | 0 | 0 | 151 | 0 |
N.S. |
1 | 0.96 | 0.30 | 0.72 | 0.00 | 0.28 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.848 | 10.114 | 0.720 | 0.000 | 0.095 | 0.000 | 0.000 | 0.255 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 196 | 111 | 217 | 0 | 98 | 0 | 0 | 153 | 0 |
N.S. |
1 | 0.96 | 0.54 | 1.06 | 0.00 | 0.48 | 0.00 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 0.617 | 10.106 | 0.561 | 0.000 | 0.095 | 0.000 | 0.000 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 326 | 316 | 94 | 243 | 0 | 77 | 0 | 0 | 108 | 0 |
N.S. |
1 | 0.97 | 0.29 | 0.75 | 0.00 | 0.24 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.758 | 10.074 | 0.494 | 0.000 | 0.090 | 0.000 | 0.000 | 0.260 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 162 | 94 | 193 | 0 | 74 | 0 | 0 | 110 | 0 |
N.S. |
1 | 0.98 | 0.57 | 1.17 | 0.00 | 0.45 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.531 | 10.040 | 0.477 | 0.000 | 0.089 | 0.000 | 0.000 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 323 | 311 | 97 | 232 | 0 | 71 | 0 | 0 | 114 | 0 |
N.S. |
1 | 0.96 | 0.30 | 0.72 | 0.00 | 0.22 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.755 | 9.418 | 0.514 | 0.000 | 0.098 | 0.000 | 0.000 | 0.243 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 158 | 97 | 180 | 0 | 61 | 0 | 0 | 120 | 0 |
N.S. |
1 | 0.97 | 0.60 | 1.10 | 0.00 | 0.37 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.530 | 10.033 | 0.595 | 0.000 | 0.098 | 0.000 | 0.000 | 0.273 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 328 | 312 | 96 | 243 | 0 | 76 | 0 | 0 | 125 | 0 |
N.S. |
1 | 0.95 | 0.29 | 0.74 | 0.00 | 0.23 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.749 | 10.032 | 0.719 | 0.000 | 0.113 | 0.000 | 0.000 | 0.303 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 163 | 98 | 194 | 0 | 71 | 0 | 0 | 125 | 0 |
N.S. |
1 | 0.98 | 0.59 | 1.16 | 0.00 | 0.43 | 0.00 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 0.550 | 10.035 | 0.813 | 0.000 | 0.094 | 0.000 | 0.000 | 0.330 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 369 | 349 | 99 | 267 | 0 | 103 | 0 | 0 | 125 | 0 |
N.S. |
1 | 0.95 | 0.27 | 0.72 | 0.00 | 0.28 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.823 | 10.037 | 0.987 | 0.000 | 0.094 | 0.000 | 0.000 | 0.387 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 196 | 98 | 218 | 0 | 96 | 0 | 0 | 125 | 0 |
N.S. |
1 | 0.96 | 0.48 | 1.07 | 0.00 | 0.47 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.612 | 10.052 | 1.126 | 0.000 | 0.097 | 0.000 | 0.000 | 0.452 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 486 | 455 | 160 | 339 | 0 | 175 | 0 | 0 | 280 | 0 |
N.S. |
1 | 0.94 | 0.33 | 0.70 | 0.00 | 0.36 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 1.077 | 10.179 | 2.176 | 0.000 | 0.117 | 0.000 | 0.000 | 0.249 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 321 | 298 | 160 | 289 | 0 | 170 | 0 | 0 | 282 | 0 |
N.S. |
1 | 0.93 | 0.50 | 0.90 | 0.00 | 0.53 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.871 | 10.163 | 1.848 | 0.000 | 0.119 | 0.000 | 0.000 | 0.311 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 447 | 419 | 138 | 315 | 0 | 150 | 0 | 0 | 237 | 0 |
N.S. |
1 | 0.94 | 0.31 | 0.70 | 0.00 | 0.34 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 1.048 | 10.143 | 1.606 | 0.000 | 0.115 | 0.000 | 0.000 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 282 | 262 | 138 | 265 | 0 | 147 | 0 | 0 | 239 | 0 |
N.S. |
1 | 0.93 | 0.49 | 0.94 | 0.00 | 0.52 | 0.00 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.770 | 10.128 | 1.305 | 0.000 | 0.100 | 0.000 | 0.000 | 0.253 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 408 | 383 | 115 | 291 | 0 | 127 | 0 | 0 | 194 | 0 |
N.S. |
1 | 0.94 | 0.28 | 0.71 | 0.00 | 0.31 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.920 | 10.119 | 1.113 | 0.000 | 0.100 | 0.000 | 0.000 | 0.276 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 225 | 115 | 241 | 0 | 121 | 0 | 0 | 196 | 0 |
N.S. |
1 | 0.94 | 0.48 | 1.01 | 0.00 | 0.51 | 0.00 | 0.00 | 0.82 | 0.00 |
time (sec) |
N/A | 0.668 | 10.120 | 0.906 | 0.000 | 0.109 | 0.000 | 0.000 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 369 | 347 | 98 | 267 | 0 | 102 | 0 | 0 | 151 | 0 |
N.S. |
1 | 0.94 | 0.27 | 0.72 | 0.00 | 0.28 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.835 | 10.088 | 0.750 | 0.000 | 0.102 | 0.000 | 0.000 | 0.249 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 192 | 97 | 217 | 0 | 97 | 0 | 0 | 153 | 0 |
N.S. |
1 | 0.96 | 0.48 | 1.08 | 0.00 | 0.48 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.615 | 10.055 | 0.726 | 0.000 | 0.114 | 0.000 | 0.000 | 0.279 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 356 | 341 | 85 | 249 | 0 | 94 | 0 | 0 | 155 | 0 |
N.S. |
1 | 0.96 | 0.24 | 0.70 | 0.00 | 0.26 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.838 | 10.051 | 0.716 | 0.000 | 0.099 | 0.000 | 0.000 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 193 | 101 | 200 | 0 | 86 | 0 | 0 | 160 | 0 |
N.S. |
1 | 0.96 | 0.50 | 1.00 | 0.00 | 0.43 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.606 | 10.046 | 0.701 | 0.000 | 0.103 | 0.000 | 0.000 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 354 | 338 | 99 | 243 | 0 | 81 | 0 | 0 | 163 | 0 |
N.S. |
1 | 0.95 | 0.28 | 0.69 | 0.00 | 0.23 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.794 | 10.039 | 0.787 | 0.000 | 0.103 | 0.000 | 0.000 | 0.351 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 191 | 101 | 196 | 0 | 75 | 0 | 0 | 164 | 0 |
N.S. |
1 | 0.94 | 0.50 | 0.96 | 0.00 | 0.37 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.601 | 10.038 | 0.993 | 0.000 | 0.097 | 0.000 | 0.000 | 0.355 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 364 | 342 | 100 | 267 | 0 | 102 | 0 | 0 | 164 | 0 |
N.S. |
1 | 0.94 | 0.27 | 0.73 | 0.00 | 0.28 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.853 | 10.043 | 1.144 | 0.000 | 0.097 | 0.000 | 0.000 | 0.564 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 243 | 238 | 143 | 239 | 0 | 122 | 0 | 0 | 196 | 0 |
N.S. |
1 | 0.98 | 0.59 | 0.98 | 0.00 | 0.50 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.705 | 10.139 | 1.570 | 0.000 | 0.097 | 0.000 | 0.000 | 0.411 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 369 | 359 | 122 | 265 | 0 | 102 | 0 | 0 | 151 | 0 |
N.S. |
1 | 0.97 | 0.33 | 0.72 | 0.00 | 0.28 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.811 | 10.112 | 1.257 | 0.000 | 0.092 | 0.000 | 0.000 | 0.280 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 202 | 122 | 215 | 0 | 99 | 0 | 0 | 153 | 0 |
N.S. |
1 | 0.99 | 0.60 | 1.05 | 0.00 | 0.49 | 0.00 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 0.643 | 10.119 | 0.962 | 0.000 | 0.097 | 0.000 | 0.000 | 0.296 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 330 | 323 | 97 | 241 | 0 | 79 | 0 | 0 | 108 | 0 |
N.S. |
1 | 0.98 | 0.29 | 0.73 | 0.00 | 0.24 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.764 | 10.103 | 0.889 | 0.000 | 0.095 | 0.000 | 0.000 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 166 | 97 | 191 | 0 | 73 | 0 | 0 | 110 | 0 |
N.S. |
1 | 0.99 | 0.58 | 1.14 | 0.00 | 0.44 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.544 | 10.101 | 0.565 | 0.000 | 0.086 | 0.000 | 0.000 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 293 | 287 | 81 | 225 | 0 | 55 | 0 | 0 | 73 | 0 |
N.S. |
1 | 0.98 | 0.28 | 0.77 | 0.00 | 0.19 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.697 | 10.075 | 0.523 | 0.000 | 0.092 | 0.000 | 0.000 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 130 | 80 | 175 | 0 | 51 | 0 | 0 | 76 | 0 |
N.S. |
1 | 1.00 | 0.62 | 1.35 | 0.00 | 0.39 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.454 | 10.061 | 0.594 | 0.000 | 0.087 | 0.000 | 0.000 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 281 | 281 | 82 | 225 | 0 | 62 | 0 | 0 | 83 | 0 |
N.S. |
1 | 1.00 | 0.29 | 0.80 | 0.00 | 0.22 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.689 | 10.044 | 0.662 | 0.000 | 0.087 | 0.000 | 0.000 | 0.264 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 131 | 82 | 177 | 0 | 57 | 0 | 0 | 89 | 0 |
N.S. |
1 | 1.00 | 0.63 | 1.35 | 0.00 | 0.44 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.454 | 10.035 | 0.815 | 0.000 | 0.086 | 0.000 | 0.000 | 0.279 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 332 | 319 | 83 | 242 | 0 | 76 | 0 | 0 | 95 | 0 |
N.S. |
1 | 0.96 | 0.25 | 0.73 | 0.00 | 0.23 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.768 | 10.036 | 0.991 | 0.000 | 0.083 | 0.000 | 0.000 | 0.299 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 166 | 85 | 193 | 0 | 69 | 0 | 0 | 95 | 0 |
N.S. |
1 | 0.99 | 0.51 | 1.16 | 0.00 | 0.41 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.540 | 10.044 | 1.191 | 0.000 | 0.095 | 0.000 | 0.000 | 0.308 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 369 | 355 | 84 | 266 | 0 | 104 | 0 | 0 | 95 | 0 |
N.S. |
1 | 0.96 | 0.23 | 0.72 | 0.00 | 0.28 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.904 | 10.051 | 1.441 | 0.000 | 0.082 | 0.000 | 0.000 | 0.375 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 202 | 84 | 216 | 0 | 96 | 0 | 0 | 95 | 0 |
N.S. |
1 | 0.99 | 0.41 | 1.06 | 0.00 | 0.47 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.611 | 10.048 | 1.798 | 0.000 | 0.088 | 0.000 | 0.000 | 0.453 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 249 | 134 | 281 | 0 | 156 | 0 | 0 | 318 | 0 |
N.S. |
1 | 0.99 | 0.53 | 1.12 | 0.00 | 0.62 | 0.00 | 0.00 | 1.27 | 0.00 |
time (sec) |
N/A | 0.747 | 10.121 | 1.793 | 0.000 | 0.104 | 0.000 | 0.000 | 0.372 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 377 | 370 | 110 | 420 | 0 | 134 | 0 | 0 | 269 | 0 |
N.S. |
1 | 0.98 | 0.29 | 1.11 | 0.00 | 0.36 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.863 | 10.108 | 1.893 | 0.000 | 0.101 | 0.000 | 0.000 | 0.315 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 213 | 110 | 255 | 0 | 129 | 0 | 0 | 275 | 0 |
N.S. |
1 | 1.00 | 0.51 | 1.19 | 0.00 | 0.60 | 0.00 | 0.00 | 1.29 | 0.00 |
time (sec) |
N/A | 0.651 | 10.097 | 1.332 | 0.000 | 0.101 | 0.000 | 0.000 | 0.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 340 | 334 | 85 | 394 | 0 | 106 | 0 | 0 | 226 | 0 |
N.S. |
1 | 0.98 | 0.25 | 1.16 | 0.00 | 0.31 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.791 | 10.083 | 1.361 | 0.000 | 0.097 | 0.000 | 0.000 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 177 | 86 | 230 | 0 | 102 | 0 | 0 | 232 | 0 |
N.S. |
1 | 0.99 | 0.48 | 1.29 | 0.00 | 0.57 | 0.00 | 0.00 | 1.30 | 0.00 |
time (sec) |
N/A | 0.571 | 10.090 | 1.187 | 0.000 | 0.104 | 0.000 | 0.000 | 0.306 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 295 | 78 | 388 | 0 | 98 | 0 | 0 | 186 | 0 |
N.S. |
1 | 0.99 | 0.26 | 1.30 | 0.00 | 0.33 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.727 | 10.076 | 0.735 | 0.000 | 0.106 | 0.000 | 0.000 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 137 | 76 | 222 | 0 | 90 | 0 | 0 | 191 | 0 |
N.S. |
1 | 1.00 | 0.55 | 1.62 | 0.00 | 0.66 | 0.00 | 0.00 | 1.39 | 0.00 |
time (sec) |
N/A | 0.494 | 10.063 | 0.879 | 0.000 | 0.093 | 0.000 | 0.000 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 318 | 311 | 77 | 392 | 0 | 115 | 0 | 0 | 214 | 0 |
N.S. |
1 | 0.98 | 0.24 | 1.23 | 0.00 | 0.36 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.732 | 10.037 | 1.439 | 0.000 | 0.086 | 0.000 | 0.000 | 0.327 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 163 | 92 | 235 | 0 | 111 | 0 | 0 | 219 | 0 |
N.S. |
1 | 0.98 | 0.55 | 1.41 | 0.00 | 0.66 | 0.00 | 0.00 | 1.31 | 0.00 |
time (sec) |
N/A | 0.535 | 10.053 | 1.529 | 0.000 | 0.091 | 0.000 | 0.000 | 0.384 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 368 | 351 | 79 | 420 | 0 | 134 | 0 | 0 | 223 | 0 |
N.S. |
1 | 0.95 | 0.21 | 1.14 | 0.00 | 0.36 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.843 | 10.041 | 1.917 | 0.000 | 0.089 | 0.000 | 0.000 | 0.455 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 198 | 79 | 254 | 0 | 126 | 0 | 0 | 223 | 0 |
N.S. |
1 | 0.98 | 0.39 | 1.25 | 0.00 | 0.62 | 0.00 | 0.00 | 1.10 | 0.00 |
time (sec) |
N/A | 0.617 | 10.042 | 2.156 | 0.000 | 0.097 | 0.000 | 0.000 | 0.554 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 405 | 387 | 79 | 450 | 0 | 163 | 0 | 0 | 223 | 0 |
N.S. |
1 | 0.96 | 0.20 | 1.11 | 0.00 | 0.40 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.931 | 10.065 | 2.501 | 0.000 | 0.088 | 0.000 | 0.000 | 0.614 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 96 | 89 | 474 | 129 | 381 | 2077 | 603 | 469 | 291 |
N.S. |
1 | 1.00 | 0.93 | 4.94 | 1.34 | 3.97 | 21.64 | 6.28 | 4.89 | 3.03 |
time (sec) |
N/A | 0.432 | 0.136 | 0.517 | 0.034 | 0.088 | 1.228 | 0.762 | 0.195 | 9.621 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 66 | 262 | 91 | 217 | 1051 | 340 | 262 | 179 |
N.S. |
1 | 1.00 | 0.93 | 3.69 | 1.28 | 3.06 | 14.80 | 4.79 | 3.69 | 2.52 |
time (sec) |
N/A | 0.381 | 0.081 | 0.392 | 0.035 | 0.097 | 0.636 | 0.235 | 0.206 | 9.642 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 42 | 55 | 53 | 94 | 415 | 149 | 113 | 97 |
N.S. |
1 | 1.00 | 0.93 | 1.22 | 1.18 | 2.09 | 9.22 | 3.31 | 2.51 | 2.16 |
time (sec) |
N/A | 0.325 | 0.052 | 0.076 | 0.038 | 0.092 | 0.390 | 0.413 | 0.254 | 9.411 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 55 | 0 | 0 | 0 | 0 | 0 | 116 | 0 |
N.S. |
1 | 1.00 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.63 | 0.00 |
time (sec) |
N/A | 0.342 | 0.084 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 80 | 0 | 0 | 0 | 0 | 0 | 822 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 8.39 | 0.00 |
time (sec) |
N/A | 0.375 | 0.113 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 131 | 135 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.508 | 0.108 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 92 | 63 | 0 | 112 | 140 | 0 | 0 | 103 | 0 |
N.S. |
1 | 0.97 | 0.66 | 0.00 | 1.18 | 1.47 | 0.00 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 0.459 | 0.129 | 0.000 | 0.109 | 0.096 | 0.000 | 0.000 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 111 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.561 | 0.381 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.465 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 145 | 210 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.12 | 1.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.646 | 1.228 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 40.329 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 52 | 0 | 0 | 0 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 0.379 | 0.093 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | B | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 116 | 0 | 37 | 43 | 0 | 48 | 23 | 0 |
N.S. |
1 | 1.00 | 6.44 | 0.00 | 2.06 | 2.39 | 0.00 | 2.67 | 1.28 | 0.00 |
time (sec) |
N/A | 0.277 | 0.329 | 0.000 | 0.100 | 0.088 | 0.000 | 0.292 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 214 | 157 | 0 | 0 | 0 | 0 | 0 | 584 | 0 |
N.S. |
1 | 1.10 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.99 | 0.00 |
time (sec) |
N/A | 0.671 | 0.252 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 140 | 119 | 0 | 0 | 0 | 0 | 0 | 265 | 0 |
N.S. |
1 | 1.07 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.02 | 0.00 |
time (sec) |
N/A | 0.465 | 0.225 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.249 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 97 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.384 | 0.152 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 54 | 0 | 0 | 0 | 0 | 0 | 138 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.56 | 0.00 |
time (sec) |
N/A | 0.331 | 0.141 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 77 | 0 | 0 | 0 | 0 | 0 | 277 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.30 | 0.00 |
time (sec) |
N/A | 0.375 | 0.155 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 115 | 112 | 0 | 0 | 0 | 0 | 0 | 532 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 4.63 | 0.00 |
time (sec) |
N/A | 0.508 | 0.209 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 207 | 184 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.703 | 0.289 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 231 | 179 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.14 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.676 | 0.246 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.270 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 174 | 120 | 0 | 0 | 0 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.16 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.510 | 0.206 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 57 | 0 | 0 | 0 | 0 | 0 | 1528 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 27.29 | 0.00 |
time (sec) |
N/A | 0.338 | 0.137 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 88 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.411 | 0.186 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 150 | 125 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.512 | 0.196 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 229 | 182 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.676 | 0.285 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.272 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 0 | 0 | 0 | 0 | 0 | 0 | 1701 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 25.77 | 0.00 |
time (sec) |
N/A | 0.438 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.436 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.400 | 0.000 |