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 | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 69 | 68 | 61 | 70 | 92 | 76 | 101 | 105 | 68 |
N.S. |
1 | 0.93 | 0.92 | 0.82 | 0.95 | 1.24 | 1.03 | 1.36 | 1.42 | 0.92 |
time (sec) |
N/A | 0.409 | 0.020 | 0.162 | 0.032 | 0.096 | 0.209 | 0.118 | 0.148 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 98 | 104 | 85 | 98 | 137 | 104 | 140 | 153 | 94 |
N.S. |
1 | 0.90 | 0.95 | 0.78 | 0.90 | 1.26 | 0.95 | 1.28 | 1.40 | 0.86 |
time (sec) |
N/A | 0.442 | 0.030 | 0.171 | 0.030 | 0.070 | 0.344 | 0.133 | 0.151 | 14.384 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 127 | 121 | 109 | 146 | 233 | 158 | 164 | 277 | 142 |
N.S. |
1 | 0.88 | 0.84 | 0.76 | 1.01 | 1.62 | 1.10 | 1.14 | 1.92 | 0.99 |
time (sec) |
N/A | 0.497 | 0.034 | 0.181 | 0.035 | 0.077 | 0.494 | 0.124 | 0.153 | 14.505 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 179 | 191 | 152 | 0 | 176 | 1110 | 506 | 190 | 229 |
N.S. |
1 | 0.73 | 0.78 | 0.62 | 0.00 | 0.72 | 4.51 | 2.06 | 0.77 | 0.93 |
time (sec) |
N/A | 0.663 | 0.160 | 0.554 | 0.000 | 0.106 | 12.704 | 0.142 | 0.148 | 14.711 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 143 | 186 | 144 | 0 | 154 | 695 | 386 | 152 | 183 |
N.S. |
1 | 0.74 | 0.97 | 0.75 | 0.00 | 0.80 | 3.62 | 2.01 | 0.79 | 0.95 |
time (sec) |
N/A | 0.605 | 0.077 | 0.455 | 0.000 | 0.093 | 6.860 | 0.141 | 0.150 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 109 | 128 | 128 | 0 | 132 | 384 | 263 | 134 | 137 |
N.S. |
1 | 0.77 | 0.91 | 0.91 | 0.00 | 0.94 | 2.72 | 1.87 | 0.95 | 0.97 |
time (sec) |
N/A | 0.537 | 0.062 | 0.349 | 0.000 | 0.098 | 4.107 | 0.151 | 0.152 | 14.342 |
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 | 74 | 69 | 57 | 99 | 0 | 86 | 0 | 130 | 58 | 82 |
N.S. |
1 | 0.93 | 0.77 | 1.34 | 0.00 | 1.16 | 0.00 | 1.76 | 0.78 | 1.11 |
time (sec) |
N/A | 0.483 | 0.048 | 0.296 | 0.000 | 0.155 | 0.000 | 0.125 | 0.147 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 97 | 78 | 139 | 0 | 101 | 0 | 0 | 180 | 129 |
N.S. |
1 | 1.03 | 0.83 | 1.48 | 0.00 | 1.07 | 0.00 | 0.00 | 1.91 | 1.37 |
time (sec) |
N/A | 0.442 | 0.035 | 0.332 | 0.000 | 0.109 | 0.000 | 0.000 | 0.149 | 0.036 |
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 | 128 | 127 | 86 | 173 | 0 | 142 | 0 | 181 | 269 | 271 |
N.S. |
1 | 0.99 | 0.67 | 1.35 | 0.00 | 1.11 | 0.00 | 1.41 | 2.10 | 2.12 |
time (sec) |
N/A | 0.707 | 0.044 | 0.388 | 0.000 | 0.088 | 0.000 | 0.130 | 0.154 | 14.393 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 159 | 94 | 250 | 0 | 213 | 0 | 0 | 230 | 436 |
N.S. |
1 | 0.92 | 0.55 | 1.45 | 0.00 | 1.24 | 0.00 | 0.00 | 1.34 | 2.53 |
time (sec) |
N/A | 0.871 | 0.051 | 0.473 | 0.000 | 0.105 | 0.000 | 0.000 | 0.152 | 14.482 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 218 | 198 | 122 | 325 | 0 | 278 | 0 | 0 | 346 | 671 |
N.S. |
1 | 0.91 | 0.56 | 1.49 | 0.00 | 1.28 | 0.00 | 0.00 | 1.59 | 3.08 |
time (sec) |
N/A | 1.038 | 0.077 | 0.622 | 0.000 | 0.119 | 0.000 | 0.000 | 0.154 | 14.696 |
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 | 299 | 97 | 98 | 102 | 0 | 544 | 0 | 110 | 70 | 0 |
N.S. |
1 | 0.32 | 0.33 | 0.34 | 0.00 | 1.82 | 0.00 | 0.37 | 0.23 | 0.00 |
time (sec) |
N/A | 0.476 | 0.044 | 0.190 | 0.000 | 0.109 | 0.000 | 0.119 | 0.150 | 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 | 219 | 75 | 82 | 86 | 0 | 480 | 0 | 84 | 54 | 0 |
N.S. |
1 | 0.34 | 0.37 | 0.39 | 0.00 | 2.19 | 0.00 | 0.38 | 0.25 | 0.00 |
time (sec) |
N/A | 0.475 | 0.037 | 0.185 | 0.000 | 0.102 | 0.000 | 0.139 | 0.147 | 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 | 146 | 60 | 72 | 70 | 0 | 375 | 0 | 49 | 36 | 0 |
N.S. |
1 | 0.41 | 0.49 | 0.48 | 0.00 | 2.57 | 0.00 | 0.34 | 0.25 | 0.00 |
time (sec) |
N/A | 0.443 | 0.027 | 0.184 | 0.000 | 0.124 | 0.000 | 0.131 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 37 | 37 | 40 | 17 | 322 | 0 | 25 | 13 | 0 |
N.S. |
1 | 0.54 | 0.54 | 0.59 | 0.25 | 4.74 | 0.00 | 0.37 | 0.19 | 0.00 |
time (sec) |
N/A | 0.398 | 0.019 | 0.178 | 0.076 | 0.107 | 0.000 | 0.116 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 52 | 48 | 50 | 21 | 366 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.66 | 0.61 | 0.63 | 0.27 | 4.63 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.405 | 0.020 | 0.184 | 0.109 | 0.138 | 0.000 | 0.000 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 81 | 91 | 94 | 0 | 0 | 0 | 0 | 65 | 0 |
N.S. |
1 | 0.46 | 0.52 | 0.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.460 | 0.034 | 0.185 | 0.000 | 0.000 | 0.000 | 0.000 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 267 | 109 | 87 | 176 | 0 | 0 | 0 | 0 | 148 | 0 |
N.S. |
1 | 0.41 | 0.33 | 0.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.506 | 0.105 | 0.198 | 0.000 | 0.000 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 361 | 139 | 147 | 250 | 0 | 0 | 0 | 0 | 235 | 0 |
N.S. |
1 | 0.39 | 0.41 | 0.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.522 | 0.070 | 0.190 | 0.000 | 0.000 | 0.000 | 0.000 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 181 | 150 | 251 | 0 | 425 | 1059 | 561 | 184 | 0 |
N.S. |
1 | 0.95 | 0.79 | 1.31 | 0.00 | 2.23 | 5.54 | 2.94 | 0.96 | 0.00 |
time (sec) |
N/A | 0.470 | 0.136 | 0.313 | 0.000 | 0.112 | 17.758 | 0.295 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 146 | 134 | 235 | 0 | 381 | 500 | 416 | 148 | 0 |
N.S. |
1 | 0.93 | 0.85 | 1.50 | 0.00 | 2.43 | 3.18 | 2.65 | 0.94 | 0.00 |
time (sec) |
N/A | 0.440 | 0.106 | 0.302 | 0.000 | 0.111 | 9.687 | 0.233 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 111 | 115 | 203 | 0 | 303 | 377 | 265 | 100 | 0 |
N.S. |
1 | 0.90 | 0.93 | 1.65 | 0.00 | 2.46 | 3.07 | 2.15 | 0.81 | 0.00 |
time (sec) |
N/A | 0.389 | 0.096 | 0.281 | 0.000 | 0.121 | 6.924 | 0.184 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 71 | 81 | 198 | 0 | 255 | 0 | 0 | 53 | 0 |
N.S. |
1 | 0.81 | 0.92 | 2.25 | 0.00 | 2.90 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.350 | 0.043 | 0.243 | 0.000 | 0.086 | 0.000 | 0.000 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 92 | 69 | 162 | 0 | 216 | 0 | 0 | 85 | 0 |
N.S. |
1 | 1.16 | 0.87 | 2.05 | 0.00 | 2.73 | 0.00 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 0.321 | 0.025 | 0.262 | 0.000 | 0.089 | 0.000 | 0.000 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 125 | 95 | 216 | 0 | 281 | 0 | 0 | 142 | 0 |
N.S. |
1 | 0.95 | 0.72 | 1.64 | 0.00 | 2.13 | 0.00 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 0.452 | 0.052 | 0.217 | 0.000 | 0.114 | 0.000 | 0.000 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 157 | 105 | 300 | 0 | 353 | 0 | 0 | 217 | 0 |
N.S. |
1 | 0.85 | 0.57 | 1.62 | 0.00 | 1.91 | 0.00 | 0.00 | 1.17 | 0.00 |
time (sec) |
N/A | 0.583 | 0.067 | 0.232 | 0.000 | 0.139 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 238 | 189 | 133 | 384 | 0 | 497 | 0 | 0 | 370 | 0 |
N.S. |
1 | 0.79 | 0.56 | 1.61 | 0.00 | 2.09 | 0.00 | 0.00 | 1.55 | 0.00 |
time (sec) |
N/A | 0.738 | 0.084 | 0.240 | 0.000 | 0.176 | 0.000 | 0.000 | 0.186 | 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 | 301 | 99 | 98 | 102 | 0 | 544 | 0 | 111 | 70 | 0 |
N.S. |
1 | 0.33 | 0.33 | 0.34 | 0.00 | 1.81 | 0.00 | 0.37 | 0.23 | 0.00 |
time (sec) |
N/A | 0.480 | 0.041 | 0.207 | 0.000 | 0.144 | 0.000 | 0.140 | 0.143 | 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 | 220 | 76 | 90 | 86 | 0 | 476 | 0 | 85 | 54 | 0 |
N.S. |
1 | 0.35 | 0.41 | 0.39 | 0.00 | 2.16 | 0.00 | 0.39 | 0.25 | 0.00 |
time (sec) |
N/A | 0.482 | 0.034 | 0.202 | 0.000 | 0.106 | 0.000 | 0.131 | 0.146 | 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 | 145 | 59 | 64 | 70 | 0 | 380 | 0 | 50 | 36 | 0 |
N.S. |
1 | 0.41 | 0.44 | 0.48 | 0.00 | 2.62 | 0.00 | 0.34 | 0.25 | 0.00 |
time (sec) |
N/A | 0.461 | 0.029 | 0.201 | 0.000 | 0.145 | 0.000 | 0.117 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | F | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 47 | 47 | 51 | 148 | 0 | 0 | 41 | 22 | 0 |
N.S. |
1 | 0.44 | 0.44 | 0.47 | 1.37 | 0.00 | 0.00 | 0.38 | 0.20 | 0.00 |
time (sec) |
N/A | 0.427 | 0.017 | 0.201 | 0.122 | 0.000 | 0.000 | 0.138 | 0.143 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 64 | 59 | 77 | 0 | 440 | 0 | 0 | 48 | 0 |
N.S. |
1 | 0.52 | 0.48 | 0.63 | 0.00 | 3.58 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.453 | 0.034 | 0.201 | 0.000 | 0.119 | 0.000 | 0.000 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 80 | 87 | 106 | 0 | 477 | 0 | 0 | 76 | 0 |
N.S. |
1 | 0.46 | 0.50 | 0.61 | 0.00 | 2.74 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.472 | 0.035 | 0.203 | 0.000 | 0.123 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 269 | 111 | 113 | 176 | 0 | 0 | 0 | 0 | 148 | 0 |
N.S. |
1 | 0.41 | 0.42 | 0.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.513 | 0.053 | 0.203 | 0.000 | 0.000 | 0.000 | 0.000 | 0.143 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 363 | 141 | 146 | 241 | 0 | 0 | 0 | 0 | 236 | 0 |
N.S. |
1 | 0.39 | 0.40 | 0.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.537 | 0.069 | 0.217 | 0.000 | 0.000 | 0.000 | 0.000 | 0.148 | 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 | 299 | 97 | 98 | 102 | 0 | 544 | 0 | 110 | 70 | 0 |
N.S. |
1 | 0.32 | 0.33 | 0.34 | 0.00 | 1.82 | 0.00 | 0.37 | 0.23 | 0.00 |
time (sec) |
N/A | 0.485 | 0.041 | 0.214 | 0.000 | 0.117 | 0.000 | 0.134 | 0.150 | 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 | 220 | 76 | 82 | 86 | 0 | 480 | 0 | 84 | 54 | 0 |
N.S. |
1 | 0.35 | 0.37 | 0.39 | 0.00 | 2.18 | 0.00 | 0.38 | 0.25 | 0.00 |
time (sec) |
N/A | 0.477 | 0.034 | 0.210 | 0.000 | 0.120 | 0.000 | 0.116 | 0.148 | 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 | 144 | 58 | 72 | 70 | 0 | 379 | 0 | 50 | 36 | 0 |
N.S. |
1 | 0.40 | 0.50 | 0.49 | 0.00 | 2.63 | 0.00 | 0.35 | 0.25 | 0.00 |
time (sec) |
N/A | 0.438 | 0.026 | 0.207 | 0.000 | 0.108 | 0.000 | 0.139 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 38 | 38 | 41 | 0 | 323 | 0 | 27 | 15 | 0 |
N.S. |
1 | 0.55 | 0.55 | 0.59 | 0.00 | 4.68 | 0.00 | 0.39 | 0.22 | 0.00 |
time (sec) |
N/A | 0.408 | 0.019 | 0.210 | 0.000 | 0.115 | 0.000 | 0.127 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 50 | 50 | 51 | 21 | 367 | 0 | 0 | 21 | 0 |
N.S. |
1 | 0.65 | 0.65 | 0.66 | 0.27 | 4.77 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.400 | 0.020 | 0.210 | 0.063 | 0.127 | 0.000 | 0.000 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 81 | 91 | 95 | 0 | 0 | 0 | 0 | 67 | 0 |
N.S. |
1 | 0.46 | 0.52 | 0.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.465 | 0.032 | 0.207 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 265 | 107 | 88 | 176 | 0 | 0 | 0 | 0 | 147 | 0 |
N.S. |
1 | 0.40 | 0.33 | 0.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.521 | 0.098 | 0.214 | 0.000 | 0.000 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 361 | 139 | 145 | 250 | 0 | 0 | 0 | 0 | 234 | 0 |
N.S. |
1 | 0.39 | 0.40 | 0.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.556 | 0.066 | 0.218 | 0.000 | 0.000 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 181 | 150 | 251 | 0 | 425 | 1059 | 561 | 184 | 0 |
N.S. |
1 | 0.95 | 0.79 | 1.31 | 0.00 | 2.23 | 5.54 | 2.94 | 0.96 | 0.00 |
time (sec) |
N/A | 0.496 | 0.164 | 0.292 | 0.000 | 0.133 | 15.772 | 0.288 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 146 | 134 | 235 | 0 | 381 | 500 | 416 | 148 | 0 |
N.S. |
1 | 0.93 | 0.85 | 1.50 | 0.00 | 2.43 | 3.18 | 2.65 | 0.94 | 0.00 |
time (sec) |
N/A | 0.460 | 0.105 | 0.296 | 0.000 | 0.142 | 8.066 | 0.219 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 109 | 115 | 203 | 0 | 304 | 376 | 265 | 100 | 0 |
N.S. |
1 | 0.90 | 0.95 | 1.68 | 0.00 | 2.51 | 3.11 | 2.19 | 0.83 | 0.00 |
time (sec) |
N/A | 0.397 | 0.083 | 0.243 | 0.000 | 0.114 | 5.146 | 0.175 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 71 | 80 | 195 | 0 | 255 | 0 | 0 | 53 | 0 |
N.S. |
1 | 0.81 | 0.91 | 2.22 | 0.00 | 2.90 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.369 | 0.050 | 0.216 | 0.000 | 0.106 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 92 | 69 | 156 | 0 | 214 | 0 | 0 | 85 | 0 |
N.S. |
1 | 1.14 | 0.85 | 1.93 | 0.00 | 2.64 | 0.00 | 0.00 | 1.05 | 0.00 |
time (sec) |
N/A | 0.324 | 0.025 | 0.227 | 0.000 | 0.102 | 0.000 | 0.000 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 126 | 95 | 204 | 0 | 280 | 0 | 0 | 142 | 0 |
N.S. |
1 | 0.94 | 0.71 | 1.52 | 0.00 | 2.09 | 0.00 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 0.479 | 0.060 | 0.200 | 0.000 | 0.091 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 158 | 105 | 288 | 0 | 352 | 0 | 0 | 217 | 0 |
N.S. |
1 | 0.84 | 0.56 | 1.54 | 0.00 | 1.88 | 0.00 | 0.00 | 1.16 | 0.00 |
time (sec) |
N/A | 0.594 | 0.069 | 0.204 | 0.000 | 0.110 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 240 | 190 | 131 | 372 | 0 | 496 | 0 | 0 | 370 | 0 |
N.S. |
1 | 0.79 | 0.55 | 1.55 | 0.00 | 2.07 | 0.00 | 0.00 | 1.54 | 0.00 |
time (sec) |
N/A | 0.781 | 0.083 | 0.214 | 0.000 | 0.140 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 301 | 99 | 98 | 102 | 0 | 546 | 0 | 111 | 70 | 0 |
N.S. |
1 | 0.33 | 0.33 | 0.34 | 0.00 | 1.81 | 0.00 | 0.37 | 0.23 | 0.00 |
time (sec) |
N/A | 0.497 | 0.038 | 0.221 | 0.000 | 0.119 | 0.000 | 0.133 | 0.147 | 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 | 218 | 74 | 92 | 86 | 0 | 482 | 0 | 84 | 54 | 0 |
N.S. |
1 | 0.34 | 0.42 | 0.39 | 0.00 | 2.21 | 0.00 | 0.39 | 0.25 | 0.00 |
time (sec) |
N/A | 0.479 | 0.035 | 0.221 | 0.000 | 0.129 | 0.000 | 0.125 | 0.153 | 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 | 146 | 60 | 64 | 70 | 0 | 378 | 0 | 51 | 36 | 0 |
N.S. |
1 | 0.41 | 0.44 | 0.48 | 0.00 | 2.59 | 0.00 | 0.35 | 0.25 | 0.00 |
time (sec) |
N/A | 0.446 | 0.031 | 0.220 | 0.000 | 0.120 | 0.000 | 0.130 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 45 | 45 | 52 | 0 | 0 | 0 | 39 | 24 | 0 |
N.S. |
1 | 0.42 | 0.42 | 0.49 | 0.00 | 0.00 | 0.00 | 0.37 | 0.23 | 0.00 |
time (sec) |
N/A | 0.420 | 0.016 | 0.233 | 0.000 | 0.000 | 0.000 | 0.243 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 63 | 58 | 78 | 53 | 439 | 0 | 0 | 47 | 0 |
N.S. |
1 | 0.52 | 0.48 | 0.64 | 0.43 | 3.60 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.433 | 0.033 | 0.225 | 0.057 | 0.106 | 0.000 | 0.000 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 76 | 86 | 106 | 0 | 477 | 0 | 0 | 76 | 0 |
N.S. |
1 | 0.45 | 0.51 | 0.62 | 0.00 | 2.81 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.475 | 0.046 | 0.210 | 0.000 | 0.125 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 267 | 109 | 110 | 176 | 0 | 0 | 0 | 0 | 148 | 0 |
N.S. |
1 | 0.41 | 0.41 | 0.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.514 | 0.065 | 0.211 | 0.000 | 0.000 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 359 | 137 | 146 | 241 | 0 | 0 | 0 | 0 | 236 | 0 |
N.S. |
1 | 0.38 | 0.41 | 0.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.573 | 0.072 | 0.220 | 0.000 | 0.000 | 0.000 | 0.000 | 0.152 | 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 | 41 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.404 | 0.016 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.148 | 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 | 53 | 53 | 53 | 0 | 0 | 0 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.409 | 0.007 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 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 | 331 | 330 | 229 | 0 | 0 | 0 | 0 | 0 | 367 | 0 |
N.S. |
1 | 1.00 | 0.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.11 | 0.00 |
time (sec) |
N/A | 1.061 | 0.184 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 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 | 137 | 225 | 126 | 0 | 0 | 0 | 0 | 0 | 62 | 0 |
N.S. |
1 | 1.64 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.533 | 0.256 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 1 | 82 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 0.01 | 0.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.393 | 0.030 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 373 | 370 | 178 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 0.99 | 0.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.744 | 0.098 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 430 | 317 | 190 | 0 | 0 | 0 | 0 | 0 | 62 | 0 |
N.S. |
1 | 0.74 | 0.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.944 | 2.138 | 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(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 272 | 226 | 208 | 0 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 0.83 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.631 | 0.173 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.170 | 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 | 182 | 154 | 130 | 0 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 0.85 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.535 | 0.109 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 322 | 212 | 186 | 0 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 0.66 | 0.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.617 | 0.256 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1027 | 650 | 227 | 0 | 0 | 0 | 0 | 0 | 73 | 0 |
N.S. |
1 | 0.63 | 0.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 1.108 | 0.724 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.193 | 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 | 72 | 72 | 0 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.404 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 230 | 217 | 0 | 0 | 0 | 0 | 0 | 726 | 0 |
N.S. |
1 | 1.25 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.95 | 0.00 |
time (sec) |
N/A | 0.702 | 0.157 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 151 | 142 | 0 | 0 | 0 | 700 | 0 | 85 | 0 |
N.S. |
1 | 1.34 | 1.26 | 0.00 | 0.00 | 0.00 | 6.19 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 0.365 | 0.085 | 0.000 | 0.000 | 0.000 | 9.221 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 151 | 142 | 0 | 0 | 0 | 699 | 0 | 79 | 0 |
N.S. |
1 | 1.35 | 1.27 | 0.00 | 0.00 | 0.00 | 6.24 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.395 | 0.079 | 0.000 | 0.000 | 0.000 | 10.919 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 230 | 215 | 0 | 0 | 0 | 0 | 0 | 729 | 0 |
N.S. |
1 | 1.25 | 1.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.96 | 0.00 |
time (sec) |
N/A | 0.763 | 0.164 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 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 | 217 | 202 | 175 | 0 | 0 | 0 | 0 | 0 | 194 | 0 |
N.S. |
1 | 0.93 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.716 | 0.139 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 126 | 112 | 0 | 0 | 0 | 178 | 0 | 86 | 0 |
N.S. |
1 | 0.92 | 0.82 | 0.00 | 0.00 | 0.00 | 1.30 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.429 | 0.034 | 0.000 | 0.000 | 0.000 | 17.176 | 0.000 | 0.152 | 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 | 137 | 126 | 112 | 0 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 0.92 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.444 | 0.021 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.154 | 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 | 216 | 201 | 173 | 0 | 0 | 0 | 0 | 0 | 127 | 0 |
N.S. |
1 | 0.93 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.690 | 0.122 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 51 | 51 | 46 | 30 | 78 | 0 | 0 | 25 | 45 |
N.S. |
1 | 0.64 | 0.64 | 0.58 | 0.38 | 0.98 | 0.00 | 0.00 | 0.31 | 0.56 |
time (sec) |
N/A | 0.488 | 0.029 | 0.181 | 0.088 | 0.102 | 0.000 | 0.000 | 0.142 | 14.189 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 47 | 42 | 37 | 20 | 58 | 0 | 28 | 17 | 38 |
N.S. |
1 | 0.64 | 0.57 | 0.50 | 0.27 | 0.78 | 0.00 | 0.38 | 0.23 | 0.51 |
time (sec) |
N/A | 0.465 | 0.014 | 0.181 | 0.079 | 0.100 | 0.000 | 0.133 | 0.147 | 14.058 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 41 | 36 | 18 | 57 | 0 | 25 | 14 | 36 |
N.S. |
1 | 1.00 | 0.93 | 0.82 | 0.41 | 1.30 | 0.00 | 0.57 | 0.32 | 0.82 |
time (sec) |
N/A | 0.400 | 0.021 | 0.178 | 0.080 | 0.085 | 0.000 | 0.132 | 0.149 | 14.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 37 | 37 | 40 | 17 | 322 | 0 | 25 | 13 | 0 |
N.S. |
1 | 0.54 | 0.54 | 0.59 | 0.25 | 4.74 | 0.00 | 0.37 | 0.19 | 0.00 |
time (sec) |
N/A | 0.394 | 0.015 | 0.167 | 0.079 | 0.115 | 0.000 | 0.127 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 41 | 37 | 40 | 19 | 296 | 0 | 26 | 17 | 0 |
N.S. |
1 | 0.62 | 0.56 | 0.61 | 0.29 | 4.48 | 0.00 | 0.39 | 0.26 | 0.00 |
time (sec) |
N/A | 0.480 | 0.015 | 0.180 | 0.087 | 0.114 | 0.000 | 0.134 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 42 | 37 | 20 | 63 | 0 | 24 | 17 | 35 |
N.S. |
1 | 1.00 | 0.98 | 0.86 | 0.47 | 1.47 | 0.00 | 0.56 | 0.40 | 0.81 |
time (sec) |
N/A | 0.464 | 0.012 | 0.181 | 0.083 | 0.081 | 0.000 | 0.138 | 0.154 | 14.042 |
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 | 155 | 175 | 101 | 142 | 0 | 238 | 0 | 139 | 105 | 0 |
N.S. |
1 | 1.13 | 0.65 | 0.92 | 0.00 | 1.54 | 0.00 | 0.90 | 0.68 | 0.00 |
time (sec) |
N/A | 0.508 | 0.071 | 0.262 | 0.000 | 0.127 | 0.000 | 0.167 | 0.150 | 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 | 130 | 148 | 93 | 134 | 0 | 222 | 0 | 128 | 87 | 0 |
N.S. |
1 | 1.14 | 0.72 | 1.03 | 0.00 | 1.71 | 0.00 | 0.98 | 0.67 | 0.00 |
time (sec) |
N/A | 0.476 | 0.055 | 0.247 | 0.000 | 0.134 | 0.000 | 0.159 | 0.146 | 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 | 101 | 111 | 84 | 125 | 0 | 204 | 0 | 116 | 69 | 0 |
N.S. |
1 | 1.10 | 0.83 | 1.24 | 0.00 | 2.02 | 0.00 | 1.15 | 0.68 | 0.00 |
time (sec) |
N/A | 0.435 | 0.042 | 0.245 | 0.000 | 0.110 | 0.000 | 0.154 | 0.150 | 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 | 78 | 90 | 77 | 114 | 0 | 188 | 0 | 106 | 51 | 0 |
N.S. |
1 | 1.15 | 0.99 | 1.46 | 0.00 | 2.41 | 0.00 | 1.36 | 0.65 | 0.00 |
time (sec) |
N/A | 0.351 | 0.055 | 0.240 | 0.000 | 0.103 | 0.000 | 0.127 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 71 | 81 | 198 | 0 | 255 | 0 | 0 | 53 | 0 |
N.S. |
1 | 0.81 | 0.92 | 2.25 | 0.00 | 2.90 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.347 | 0.044 | 0.234 | 0.000 | 0.109 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 75 | 85 | 148 | 0 | 241 | 0 | 128 | 64 | 0 |
N.S. |
1 | 0.91 | 1.04 | 1.80 | 0.00 | 2.94 | 0.00 | 1.56 | 0.78 | 0.00 |
time (sec) |
N/A | 0.428 | 0.041 | 0.245 | 0.000 | 0.114 | 0.000 | 0.166 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 96 | 79 | 142 | 0 | 162 | 0 | 195 | 60 | 0 |
N.S. |
1 | 1.22 | 1.00 | 1.80 | 0.00 | 2.05 | 0.00 | 2.47 | 0.76 | 0.00 |
time (sec) |
N/A | 0.418 | 0.049 | 0.247 | 0.000 | 0.108 | 0.000 | 0.170 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 118 | 71 | 150 | 0 | 186 | 0 | 231 | 86 | 0 |
N.S. |
1 | 1.15 | 0.69 | 1.46 | 0.00 | 1.81 | 0.00 | 2.24 | 0.83 | 0.00 |
time (sec) |
N/A | 0.462 | 0.069 | 0.250 | 0.000 | 0.112 | 0.000 | 0.175 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 150 | 95 | 159 | 0 | 202 | 0 | 316 | 152 | 0 |
N.S. |
1 | 1.13 | 0.71 | 1.20 | 0.00 | 1.52 | 0.00 | 2.38 | 1.14 | 0.00 |
time (sec) |
N/A | 0.504 | 0.064 | 0.251 | 0.000 | 0.098 | 0.000 | 0.172 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 172 | 103 | 167 | 0 | 218 | 0 | 362 | 122 | 0 |
N.S. |
1 | 1.09 | 0.65 | 1.06 | 0.00 | 1.38 | 0.00 | 2.29 | 0.77 | 0.00 |
time (sec) |
N/A | 0.532 | 0.069 | 0.250 | 0.000 | 0.091 | 0.000 | 0.318 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 71 | 71 | 74 | 196 | 419 | 0 | 66 | 45 | 0 |
N.S. |
1 | 0.38 | 0.38 | 0.39 | 1.04 | 2.23 | 0.00 | 0.35 | 0.24 | 0.00 |
time (sec) |
N/A | 0.513 | 0.029 | 0.203 | 0.123 | 0.118 | 0.000 | 0.124 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 65 | 65 | 67 | 172 | 405 | 0 | 57 | 37 | 0 |
N.S. |
1 | 0.42 | 0.42 | 0.44 | 1.12 | 2.65 | 0.00 | 0.37 | 0.24 | 0.00 |
time (sec) |
N/A | 0.501 | 0.024 | 0.198 | 0.123 | 0.108 | 0.000 | 0.147 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 55 | 55 | 58 | 149 | 387 | 0 | 46 | 29 | 0 |
N.S. |
1 | 0.48 | 0.48 | 0.51 | 1.31 | 3.39 | 0.00 | 0.40 | 0.25 | 0.00 |
time (sec) |
N/A | 0.412 | 0.021 | 0.203 | 0.120 | 0.121 | 0.000 | 0.129 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | F | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 47 | 47 | 51 | 148 | 0 | 0 | 41 | 22 | 0 |
N.S. |
1 | 0.44 | 0.44 | 0.47 | 1.37 | 0.00 | 0.00 | 0.38 | 0.20 | 0.00 |
time (sec) |
N/A | 0.410 | 0.017 | 0.198 | 0.124 | 0.000 | 0.000 | 0.115 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | F | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 52 | 49 | 52 | 144 | 0 | 0 | 39 | 28 | 0 |
N.S. |
1 | 0.49 | 0.46 | 0.49 | 1.35 | 0.00 | 0.00 | 0.36 | 0.26 | 0.00 |
time (sec) |
N/A | 0.508 | 0.017 | 0.204 | 0.124 | 0.000 | 0.000 | 0.139 | 0.151 | 0.000 |