Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 71 | 71 | 61 | 70 | 93 | 75 | 95 | 68 |
N.S. |
1 | 0.93 | 0.93 | 0.80 | 0.92 | 1.22 | 0.99 | 1.25 | 0.89 |
time (sec) |
N/A | 0.387 | 0.062 | 0.098 | 0.181 | 0.245 | 0.218 | 0.266 | 3.570 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 140 | 128 | 438 | 153 | 0 | 177 | 0 | 265 | 161 |
N.S. |
1 | 0.91 | 3.13 | 1.09 | 0.00 | 1.26 | 0.00 | 1.89 | 1.15 |
time (sec) |
N/A | 0.731 | 0.492 | 0.276 | 0.000 | 0.267 | 0.000 | 0.305 | 0.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 92 | 321 | 134 | 0 | 149 | 0 | 197 | 138 |
N.S. |
1 | 0.83 | 2.89 | 1.21 | 0.00 | 1.34 | 0.00 | 1.77 | 1.24 |
time (sec) |
N/A | 0.582 | 0.330 | 0.237 | 0.000 | 0.264 | 0.000 | 0.286 | 3.461 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 66 | 156 | 498 | 0 | 97 | 0 | 104 | 102 |
N.S. |
1 | 0.86 | 2.03 | 6.47 | 0.00 | 1.26 | 0.00 | 1.35 | 1.32 |
time (sec) |
N/A | 0.455 | 0.143 | 0.175 | 0.000 | 0.277 | 0.000 | 0.293 | 3.441 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 64 | 67 | 102 | 0 | 67 | 0 | 73 | 90 |
N.S. |
1 | 0.98 | 1.03 | 1.57 | 0.00 | 1.03 | 0.00 | 1.12 | 1.38 |
time (sec) |
N/A | 0.345 | 0.023 | 0.145 | 0.000 | 0.266 | 0.000 | 0.294 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 65 | 38 | 102 | 0 | 71 | 0 | 73 | 89 |
N.S. |
1 | 1.03 | 0.60 | 1.62 | 0.00 | 1.13 | 0.00 | 1.16 | 1.41 |
time (sec) |
N/A | 0.366 | 0.067 | 0.169 | 0.000 | 0.261 | 0.000 | 0.272 | 0.059 |
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 | 45 | 49 | 30 | 29 | 45 | 53 | 68 | 38 | 116 |
N.S. |
1 | 1.09 | 0.67 | 0.64 | 1.00 | 1.18 | 1.51 | 0.84 | 2.58 |
time (sec) |
N/A | 0.366 | 0.045 | 0.123 | 0.211 | 0.271 | 18.883 | 0.266 | 3.392 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 96 | 106 | 78 | 186 | 0 | 142 | 0 | 0 | 188 |
N.S. |
1 | 1.10 | 0.81 | 1.94 | 0.00 | 1.48 | 0.00 | 0.00 | 1.96 |
time (sec) |
N/A | 0.416 | 0.101 | 0.221 | 0.000 | 0.264 | 0.000 | 0.000 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 125 | 132 | 76 | 227 | 0 | 151 | 0 | 0 | 275 |
N.S. |
1 | 1.06 | 0.61 | 1.82 | 0.00 | 1.21 | 0.00 | 0.00 | 2.20 |
time (sec) |
N/A | 0.621 | 0.119 | 0.234 | 0.000 | 0.255 | 0.000 | 0.000 | 3.506 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 225 | 169 | 101 | 172 | 0 | 386 | 0 | 0 | 0 |
N.S. |
1 | 0.75 | 0.45 | 0.76 | 0.00 | 1.72 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.485 | 0.062 | 0.144 | 0.000 | 0.290 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 181 | 137 | 95 | 154 | 0 | 364 | 0 | 0 | 0 |
N.S. |
1 | 0.76 | 0.52 | 0.85 | 0.00 | 2.01 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.453 | 0.059 | 0.099 | 0.000 | 0.297 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 107 | 87 | 136 | 0 | 330 | 0 | 0 | 0 |
N.S. |
1 | 0.63 | 0.51 | 0.80 | 0.00 | 1.93 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.425 | 0.047 | 0.108 | 0.000 | 0.293 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 128 | 84 | 70 | 108 | 0 | 266 | 0 | 0 | 0 |
N.S. |
1 | 0.66 | 0.55 | 0.84 | 0.00 | 2.08 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.412 | 0.035 | 0.108 | 0.000 | 0.293 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 84 | 65 | 65 | 89 | 0 | 249 | 0 | 0 | 0 |
N.S. |
1 | 0.77 | 0.77 | 1.06 | 0.00 | 2.96 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.390 | 0.034 | 0.101 | 0.000 | 0.277 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 157 | 116 | 105 | 168 | 0 | 447 | 0 | 0 | 0 |
N.S. |
1 | 0.74 | 0.67 | 1.07 | 0.00 | 2.85 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.428 | 0.043 | 0.122 | 0.000 | 0.320 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 198 | 147 | 126 | 276 | 0 | 526 | 0 | 0 | 0 |
N.S. |
1 | 0.74 | 0.64 | 1.39 | 0.00 | 2.66 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.488 | 0.105 | 0.116 | 0.000 | 0.321 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 249 | 187 | 139 | 365 | 0 | 600 | 0 | 0 | 0 |
N.S. |
1 | 0.75 | 0.56 | 1.47 | 0.00 | 2.41 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.505 | 0.126 | 0.125 | 0.000 | 0.324 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | C | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 145 | 145 | 91 | 155 | 0 | 234 | 2222 | 0 | 0 |
N.S. |
1 | 1.00 | 0.63 | 1.07 | 0.00 | 1.61 | 15.32 | 0.00 | 0.00 |
time (sec) |
N/A | 0.375 | 0.111 | 0.139 | 0.000 | 0.263 | 14.766 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | C | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 120 | 123 | 83 | 144 | 0 | 212 | 740 | 0 | 0 |
N.S. |
1 | 1.02 | 0.69 | 1.20 | 0.00 | 1.77 | 6.17 | 0.00 | 0.00 |
time (sec) |
N/A | 0.366 | 0.066 | 0.123 | 0.000 | 0.265 | 12.001 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | C | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 96 | 102 | 75 | 108 | 0 | 182 | 144 | 0 | 0 |
N.S. |
1 | 1.06 | 0.78 | 1.12 | 0.00 | 1.90 | 1.50 | 0.00 | 0.00 |
time (sec) |
N/A | 0.358 | 0.060 | 0.120 | 0.000 | 0.263 | 3.734 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | C | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 71 | 79 | 57 | 103 | 0 | 136 | 173 | 0 | 0 |
N.S. |
1 | 1.11 | 0.80 | 1.45 | 0.00 | 1.92 | 2.44 | 0.00 | 0.00 |
time (sec) |
N/A | 0.342 | 0.044 | 0.116 | 0.000 | 0.264 | 13.318 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 57 | 51 | 99 | 0 | 125 | 0 | 97 | 0 |
N.S. |
1 | 1.12 | 1.00 | 1.94 | 0.00 | 2.45 | 0.00 | 1.90 | 0.00 |
time (sec) |
N/A | 0.318 | 0.023 | 0.102 | 0.000 | 0.263 | 0.000 | 0.300 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 71 | 82 | 44 | 152 | 0 | 175 | 0 | 171 | 0 |
N.S. |
1 | 1.15 | 0.62 | 2.14 | 0.00 | 2.46 | 0.00 | 2.41 | 0.00 |
time (sec) |
N/A | 0.322 | 0.020 | 0.125 | 0.000 | 0.272 | 0.000 | 0.366 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 96 | 109 | 55 | 203 | 0 | 238 | 0 | 246 | 0 |
N.S. |
1 | 1.14 | 0.57 | 2.11 | 0.00 | 2.48 | 0.00 | 2.56 | 0.00 |
time (sec) |
N/A | 0.353 | 0.024 | 0.119 | 0.000 | 0.272 | 0.000 | 0.426 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 136 | 59 | 249 | 0 | 294 | 0 | 317 | 0 |
N.S. |
1 | 1.14 | 0.50 | 2.09 | 0.00 | 2.47 | 0.00 | 2.66 | 0.00 |
time (sec) |
N/A | 0.392 | 0.024 | 0.157 | 0.000 | 0.261 | 0.000 | 0.495 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 146 | 163 | 46 | 293 | 0 | 346 | 0 | 392 | 0 |
N.S. |
1 | 1.12 | 0.32 | 2.01 | 0.00 | 2.37 | 0.00 | 2.68 | 0.00 |
time (sec) |
N/A | 0.393 | 0.032 | 0.125 | 0.000 | 0.269 | 0.000 | 0.604 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 223 | 159 | 85 | 172 | 0 | 386 | 0 | 0 | 0 |
N.S. |
1 | 0.71 | 0.38 | 0.77 | 0.00 | 1.73 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.459 | 0.048 | 0.137 | 0.000 | 0.303 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 217 | 131 | 77 | 154 | 0 | 364 | 0 | 0 | 0 |
N.S. |
1 | 0.60 | 0.35 | 0.71 | 0.00 | 1.68 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.451 | 0.045 | 0.115 | 0.000 | 0.282 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 176 | 109 | 66 | 136 | 0 | 330 | 0 | 0 | 0 |
N.S. |
1 | 0.62 | 0.38 | 0.77 | 0.00 | 1.88 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.455 | 0.035 | 0.113 | 0.000 | 0.288 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 85 | 42 | 109 | 0 | 268 | 0 | 0 | 0 |
N.S. |
1 | 0.67 | 0.33 | 0.86 | 0.00 | 2.11 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.428 | 0.023 | 0.152 | 0.000 | 0.308 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 155 | 110 | 105 | 165 | 0 | 442 | 0 | 0 | 0 |
N.S. |
1 | 0.71 | 0.68 | 1.06 | 0.00 | 2.85 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.430 | 0.044 | 0.117 | 0.000 | 0.314 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 195 | 139 | 120 | 276 | 0 | 513 | 0 | 0 | 0 |
N.S. |
1 | 0.71 | 0.62 | 1.42 | 0.00 | 2.63 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.450 | 0.112 | 0.132 | 0.000 | 0.315 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 249 | 182 | 139 | 364 | 0 | 600 | 0 | 0 | 0 |
N.S. |
1 | 0.73 | 0.56 | 1.46 | 0.00 | 2.41 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.491 | 0.140 | 0.125 | 0.000 | 0.332 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 293 | 219 | 147 | 416 | 0 | 668 | 0 | 0 | 0 |
N.S. |
1 | 0.75 | 0.50 | 1.42 | 0.00 | 2.28 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.527 | 0.129 | 0.131 | 0.000 | 0.336 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 225 | 169 | 108 | 172 | 0 | 386 | 0 | 0 | 0 |
N.S. |
1 | 0.75 | 0.48 | 0.76 | 0.00 | 1.72 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.471 | 2.351 | 0.112 | 0.000 | 0.281 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 179 | 137 | 95 | 154 | 0 | 364 | 0 | 0 | 0 |
N.S. |
1 | 0.77 | 0.53 | 0.86 | 0.00 | 2.03 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.448 | 0.073 | 0.107 | 0.000 | 0.295 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 105 | 87 | 136 | 0 | 330 | 0 | 0 | 0 |
N.S. |
1 | 0.77 | 0.64 | 0.99 | 0.00 | 2.41 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.423 | 0.049 | 0.112 | 0.000 | 0.278 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 126 | 87 | 71 | 109 | 0 | 268 | 0 | 0 | 0 |
N.S. |
1 | 0.69 | 0.56 | 0.87 | 0.00 | 2.13 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.403 | 0.038 | 0.108 | 0.000 | 0.303 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 67 | 67 | 91 | 0 | 250 | 0 | 0 | 0 |
N.S. |
1 | 0.74 | 0.74 | 1.01 | 0.00 | 2.78 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.395 | 0.040 | 0.110 | 0.000 | 0.277 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 69 | 69 | 92 | 0 | 254 | 0 | 0 | 0 |
N.S. |
1 | 0.78 | 0.78 | 1.05 | 0.00 | 2.89 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.390 | 0.034 | 0.106 | 0.000 | 0.296 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 159 | 116 | 107 | 168 | 0 | 453 | 0 | 0 | 0 |
N.S. |
1 | 0.73 | 0.67 | 1.06 | 0.00 | 2.85 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.454 | 0.048 | 0.118 | 0.000 | 0.319 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 208 | 150 | 127 | 276 | 0 | 528 | 0 | 0 | 0 |
N.S. |
1 | 0.72 | 0.61 | 1.33 | 0.00 | 2.54 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.475 | 0.121 | 0.135 | 0.000 | 0.328 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 252 | 187 | 139 | 367 | 0 | 600 | 0 | 0 | 0 |
N.S. |
1 | 0.74 | 0.55 | 1.46 | 0.00 | 2.38 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.509 | 0.149 | 0.140 | 0.000 | 0.331 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 189 | 193 | 133 | 232 | 0 | 342 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.70 | 1.23 | 0.00 | 1.81 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.480 | 0.254 | 0.141 | 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 | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 164 | 171 | 125 | 224 | 0 | 320 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.76 | 1.37 | 0.00 | 1.95 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.444 | 0.132 | 0.141 | 0.000 | 0.271 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 139 | 149 | 116 | 214 | 0 | 282 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.83 | 1.54 | 0.00 | 2.03 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.420 | 0.078 | 0.126 | 0.000 | 0.267 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 127 | 96 | 195 | 0 | 231 | 0 | 0 | 0 |
N.S. |
1 | 1.12 | 0.85 | 1.73 | 0.00 | 2.04 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.401 | 0.064 | 0.141 | 0.000 | 0.273 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 93 | 107 | 93 | 170 | 0 | 217 | 0 | 0 | 0 |
N.S. |
1 | 1.15 | 1.00 | 1.83 | 0.00 | 2.33 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.382 | 0.040 | 0.112 | 0.000 | 0.257 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 96 | 104 | 96 | 136 | 0 | 232 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 1.00 | 1.42 | 0.00 | 2.42 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.372 | 0.037 | 0.108 | 0.000 | 0.262 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 95 | 115 | 95 | 136 | 0 | 231 | 0 | 0 | 0 |
N.S. |
1 | 1.21 | 1.00 | 1.43 | 0.00 | 2.43 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.369 | 0.042 | 0.112 | 0.000 | 0.278 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 131 | 67 | 229 | 0 | 284 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 0.56 | 1.92 | 0.00 | 2.39 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.433 | 0.040 | 0.121 | 0.000 | 0.273 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 148 | 161 | 77 | 273 | 0 | 356 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 0.52 | 1.84 | 0.00 | 2.41 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.428 | 0.056 | 0.119 | 0.000 | 0.273 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 173 | 191 | 82 | 317 | 0 | 428 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 0.47 | 1.83 | 0.00 | 2.47 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.459 | 0.045 | 0.119 | 0.000 | 0.268 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 267 | 188 | 285 | 227 | 0 | 408 | 0 | 0 | 0 |
N.S. |
1 | 0.70 | 1.07 | 0.85 | 0.00 | 1.53 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.506 | 5.437 | 0.141 | 0.000 | 0.286 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 225 | 164 | 200 | 209 | 0 | 386 | 0 | 0 | 0 |
N.S. |
1 | 0.73 | 0.89 | 0.93 | 0.00 | 1.72 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.475 | 3.277 | 0.135 | 0.000 | 0.281 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 181 | 132 | 97 | 191 | 0 | 352 | 0 | 0 | 0 |
N.S. |
1 | 0.73 | 0.54 | 1.06 | 0.00 | 1.94 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.454 | 0.064 | 0.119 | 0.000 | 0.309 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 133 | 100 | 80 | 164 | 0 | 298 | 0 | 0 | 0 |
N.S. |
1 | 0.75 | 0.60 | 1.23 | 0.00 | 2.24 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.421 | 0.047 | 0.128 | 0.000 | 0.297 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 123 | 82 | 82 | 140 | 0 | 282 | 0 | 0 | 0 |
N.S. |
1 | 0.67 | 0.67 | 1.14 | 0.00 | 2.29 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.396 | 0.042 | 0.138 | 0.000 | 0.292 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 88 | 86 | 143 | 0 | 286 | 0 | 0 | 0 |
N.S. |
1 | 0.69 | 0.68 | 1.13 | 0.00 | 2.25 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.420 | 0.049 | 0.116 | 0.000 | 0.283 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 131 | 94 | 44 | 143 | 0 | 294 | 0 | 0 | 0 |
N.S. |
1 | 0.72 | 0.34 | 1.09 | 0.00 | 2.24 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.433 | 0.036 | 0.118 | 0.000 | 0.291 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 199 | 139 | 162 | 279 | 0 | 492 | 0 | 0 | 0 |
N.S. |
1 | 0.70 | 0.81 | 1.40 | 0.00 | 2.47 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.457 | 0.106 | 0.129 | 0.000 | 0.332 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 251 | 177 | 234 | 315 | 0 | 596 | 0 | 0 | 0 |
N.S. |
1 | 0.71 | 0.93 | 1.25 | 0.00 | 2.37 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.486 | 0.417 | 0.147 | 0.000 | 0.331 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 105 | 99 | 92 | 165 | 0 | 120 | 0 | 217 | 138 |
N.S. |
1 | 0.94 | 0.88 | 1.57 | 0.00 | 1.14 | 0.00 | 2.07 | 1.31 |
time (sec) |
N/A | 0.499 | 0.039 | 0.198 | 0.000 | 0.257 | 0.000 | 0.292 | 3.530 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 56 | 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 |
time (sec) |
N/A | 0.466 | 0.022 | 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 | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 179 | 121 | 88 | 125 | 0 | 292 | 0 | 0 | 0 |
N.S. |
1 | 0.68 | 0.49 | 0.70 | 0.00 | 1.63 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.513 | 0.040 | 0.120 | 0.000 | 0.288 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 135 | 92 | 80 | 105 | 0 | 272 | 0 | 0 | 0 |
N.S. |
1 | 0.68 | 0.59 | 0.78 | 0.00 | 2.01 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.448 | 0.040 | 0.198 | 0.000 | 0.291 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 65 | 65 | 89 | 0 | 249 | 0 | 0 | 0 |
N.S. |
1 | 0.76 | 0.76 | 1.05 | 0.00 | 2.93 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.383 | 0.021 | 0.000 | 0.000 | 0.280 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 67 | 62 | 90 | 0 | 236 | 0 | 0 | 0 |
N.S. |
1 | 0.78 | 0.72 | 1.05 | 0.00 | 2.74 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.464 | 0.029 | 0.128 | 0.000 | 0.273 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 41 | 40 | 0 | 47 | 0 | 0 | 44 |
N.S. |
1 | 1.00 | 1.00 | 0.98 | 0.00 | 1.15 | 0.00 | 0.00 | 1.07 |
time (sec) |
N/A | 0.452 | 0.026 | 0.115 | 0.000 | 0.244 | 0.000 | 0.000 | 3.832 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 84 | 69 | 47 | 46 | 0 | 58 | 0 | 0 | 52 |
N.S. |
1 | 0.82 | 0.56 | 0.55 | 0.00 | 0.69 | 0.00 | 0.00 | 0.62 |
time (sec) |
N/A | 0.463 | 0.021 | 0.102 | 0.000 | 0.256 | 0.000 | 0.000 | 3.729 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 128 | 93 | 55 | 54 | 0 | 66 | 0 | 0 | 60 |
N.S. |
1 | 0.73 | 0.43 | 0.42 | 0.00 | 0.52 | 0.00 | 0.00 | 0.47 |
time (sec) |
N/A | 0.501 | 0.026 | 0.109 | 0.000 | 0.247 | 0.000 | 0.000 | 3.742 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 172 | 117 | 63 | 62 | 0 | 74 | 0 | 0 | 68 |
N.S. |
1 | 0.68 | 0.37 | 0.36 | 0.00 | 0.43 | 0.00 | 0.00 | 0.40 |
time (sec) |
N/A | 0.487 | 0.027 | 0.108 | 0.000 | 0.283 | 0.000 | 0.000 | 3.723 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 130 | 156 | 50 | 127 | 0 | 179 | 0 | 142 | 111 |
N.S. |
1 | 1.20 | 0.38 | 0.98 | 0.00 | 1.38 | 0.00 | 1.09 | 0.85 |
time (sec) |
N/A | 0.545 | 0.028 | 0.118 | 0.000 | 0.259 | 0.000 | 0.304 | 3.975 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 105 | 123 | 50 | 119 | 0 | 163 | 0 | 127 | 90 |
N.S. |
1 | 1.17 | 0.48 | 1.13 | 0.00 | 1.55 | 0.00 | 1.21 | 0.86 |
time (sec) |
N/A | 0.533 | 0.028 | 0.105 | 0.000 | 0.272 | 0.000 | 0.300 | 3.913 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 90 | 77 | 111 | 0 | 147 | 0 | 112 | 0 |
N.S. |
1 | 1.12 | 0.96 | 1.39 | 0.00 | 1.84 | 0.00 | 1.40 | 0.00 |
time (sec) |
N/A | 0.437 | 0.062 | 0.109 | 0.000 | 0.260 | 0.000 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 57 | 51 | 99 | 0 | 125 | 0 | 97 | 0 |
N.S. |
1 | 1.12 | 1.00 | 1.94 | 0.00 | 2.45 | 0.00 | 1.90 | 0.00 |
time (sec) |
N/A | 0.314 | 0.020 | 0.000 | 0.000 | 0.261 | 0.000 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | B | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 57 | 47 | 98 | 0 | 111 | 95 | 0 | 0 |
N.S. |
1 | 1.21 | 1.00 | 2.09 | 0.00 | 2.36 | 2.02 | 0.00 | 0.00 |
time (sec) |
N/A | 0.488 | 0.028 | 0.122 | 0.000 | 0.255 | 3.809 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 54 | 28 | 27 | 0 | 28 | 0 | 0 | 24 |
N.S. |
1 | 1.29 | 0.67 | 0.64 | 0.00 | 0.67 | 0.00 | 0.00 | 0.57 |
time (sec) |
N/A | 0.493 | 0.026 | 0.107 | 0.000 | 0.262 | 0.000 | 0.000 | 3.449 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 69 | 77 | 36 | 35 | 0 | 36 | 0 | 0 | 32 |
N.S. |
1 | 1.12 | 0.52 | 0.51 | 0.00 | 0.52 | 0.00 | 0.00 | 0.46 |
time (sec) |
N/A | 0.521 | 0.035 | 0.127 | 0.000 | 0.253 | 0.000 | 0.000 | 3.488 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 96 | 104 | 44 | 43 | 0 | 44 | 0 | 0 | 77 |
N.S. |
1 | 1.08 | 0.46 | 0.45 | 0.00 | 0.46 | 0.00 | 0.00 | 0.80 |
time (sec) |
N/A | 0.528 | 0.049 | 0.120 | 0.000 | 0.262 | 0.000 | 0.000 | 3.491 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 129 | 52 | 51 | 0 | 52 | 0 | 0 | 98 |
N.S. |
1 | 1.07 | 0.43 | 0.42 | 0.00 | 0.43 | 0.00 | 0.00 | 0.81 |
time (sec) |
N/A | 0.556 | 0.044 | 0.128 | 0.000 | 0.245 | 0.000 | 0.000 | 3.449 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 292 | 197 | 129 | 247 | 0 | 500 | 0 | 0 | 0 |
N.S. |
1 | 0.67 | 0.44 | 0.85 | 0.00 | 1.71 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.550 | 0.082 | 0.128 | 0.000 | 0.328 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 248 | 168 | 121 | 219 | 0 | 484 | 0 | 0 | 0 |
N.S. |
1 | 0.68 | 0.49 | 0.88 | 0.00 | 1.95 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.562 | 0.065 | 0.132 | 0.000 | 0.329 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 204 | 139 | 113 | 191 | 0 | 468 | 0 | 0 | 0 |
N.S. |
1 | 0.68 | 0.55 | 0.94 | 0.00 | 2.29 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.505 | 0.060 | 0.132 | 0.000 | 0.337 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 155 | 110 | 105 | 165 | 0 | 442 | 0 | 0 | 0 |
N.S. |
1 | 0.71 | 0.68 | 1.06 | 0.00 | 2.85 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.430 | 0.022 | 0.112 | 0.000 | 0.318 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 154 | 108 | 105 | 166 | 0 | 429 | 0 | 0 | 0 |
N.S. |
1 | 0.70 | 0.68 | 1.08 | 0.00 | 2.79 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.496 | 0.033 | 0.117 | 0.000 | 0.325 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 147 | 108 | 93 | 150 | 0 | 309 | 0 | 0 | 0 |
N.S. |
1 | 0.73 | 0.63 | 1.02 | 0.00 | 2.10 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.474 | 0.043 | 0.125 | 0.000 | 0.294 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 191 | 129 | 101 | 181 | 0 | 337 | 0 | 0 | 0 |
N.S. |
1 | 0.68 | 0.53 | 0.95 | 0.00 | 1.76 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.500 | 0.054 | 0.125 | 0.000 | 0.281 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 237 | 154 | 109 | 209 | 0 | 353 | 0 | 0 | 0 |
N.S. |
1 | 0.65 | 0.46 | 0.88 | 0.00 | 1.49 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.536 | 0.051 | 0.125 | 0.000 | 0.290 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 281 | 182 | 117 | 232 | 0 | 369 | 0 | 0 | 0 |
N.S. |
1 | 0.65 | 0.42 | 0.83 | 0.00 | 1.31 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.575 | 0.064 | 0.122 | 0.000 | 0.295 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 116 | 104 | 87 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.90 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.503 | 0.050 | 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 | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 182 | 121 | 88 | 125 | 0 | 292 | 0 | 0 | 0 |
N.S. |
1 | 0.66 | 0.48 | 0.69 | 0.00 | 1.60 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.525 | 0.064 | 0.129 | 0.000 | 0.293 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 138 | 92 | 80 | 107 | 0 | 276 | 0 | 0 | 0 |
N.S. |
1 | 0.67 | 0.58 | 0.78 | 0.00 | 2.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.445 | 0.038 | 0.120 | 0.000 | 0.280 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 67 | 67 | 91 | 0 | 250 | 0 | 0 | 0 |
N.S. |
1 | 0.74 | 0.74 | 1.01 | 0.00 | 2.78 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.383 | 0.026 | 0.121 | 0.000 | 0.287 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 67 | 60 | 91 | 0 | 235 | 0 | 0 | 0 |
N.S. |
1 | 0.75 | 0.67 | 1.02 | 0.00 | 2.64 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.486 | 0.029 | 0.129 | 0.000 | 0.267 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 84 | 69 | 47 | 46 | 0 | 48 | 0 | 0 | 60 |
N.S. |
1 | 0.82 | 0.56 | 0.55 | 0.00 | 0.57 | 0.00 | 0.00 | 0.71 |
time (sec) |
N/A | 0.462 | 0.025 | 0.125 | 0.000 | 0.259 | 0.000 | 0.000 | 3.780 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 128 | 93 | 55 | 54 | 0 | 58 | 0 | 0 | 79 |
N.S. |
1 | 0.73 | 0.43 | 0.42 | 0.00 | 0.45 | 0.00 | 0.00 | 0.62 |
time (sec) |
N/A | 0.480 | 0.025 | 0.173 | 0.000 | 0.258 | 0.000 | 0.000 | 3.827 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 172 | 117 | 63 | 62 | 0 | 66 | 0 | 0 | 86 |
N.S. |
1 | 0.68 | 0.37 | 0.36 | 0.00 | 0.38 | 0.00 | 0.00 | 0.50 |
time (sec) |
N/A | 0.474 | 0.027 | 0.128 | 0.000 | 0.257 | 0.000 | 0.000 | 3.995 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 172 | 206 | 116 | 198 | 0 | 274 | 0 | 0 | 0 |
N.S. |
1 | 1.20 | 0.67 | 1.15 | 0.00 | 1.59 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.644 | 0.108 | 0.113 | 0.000 | 0.272 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 147 | 173 | 108 | 190 | 0 | 256 | 0 | 0 | 0 |
N.S. |
1 | 1.18 | 0.73 | 1.29 | 0.00 | 1.74 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.613 | 0.084 | 0.137 | 0.000 | 0.270 | 0.000 | 0.000 | 0.000 |