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(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 74 | 120 | 98 | 73 | 75 | 0 | 90 | 136 | 70 |
N.S. |
1 | 0.89 | 1.45 | 1.18 | 0.88 | 0.90 | 0.00 | 1.08 | 1.64 | 0.84 |
time (sec) |
N/A | 0.252 | 0.281 | 1.259 | 0.026 | 0.077 | 0.000 | 0.163 | 0.149 | 0.084 |
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 | 66 | 59 | 88 | 81 | 58 | 60 | 0 | 68 | 106 | 55 |
N.S. |
1 | 0.89 | 1.33 | 1.23 | 0.88 | 0.91 | 0.00 | 1.03 | 1.61 | 0.83 |
time (sec) |
N/A | 0.249 | 0.172 | 1.050 | 0.029 | 0.074 | 0.000 | 0.174 | 0.153 | 12.506 |
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 | 44 | 40 | 53 | 62 | 40 | 42 | 0 | 45 | 125 | 39 |
N.S. |
1 | 0.91 | 1.20 | 1.41 | 0.91 | 0.95 | 0.00 | 1.02 | 2.84 | 0.89 |
time (sec) |
N/A | 0.230 | 0.127 | 0.914 | 0.027 | 0.076 | 0.000 | 0.132 | 0.151 | 0.069 |
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 | 24 | 23 | 35 | 25 | 25 | 27 | 0 | 25 | 34 | 25 |
N.S. |
1 | 0.96 | 1.46 | 1.04 | 1.04 | 1.12 | 0.00 | 1.04 | 1.42 | 1.04 |
time (sec) |
N/A | 0.211 | 0.028 | 0.337 | 0.025 | 0.077 | 0.000 | 0.156 | 0.150 | 0.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 26 | 58 | 38 | 44 | 60 | 0 | 50 | 59 | 29 |
N.S. |
1 | 0.96 | 2.15 | 1.41 | 1.63 | 2.22 | 0.00 | 1.85 | 2.19 | 1.07 |
time (sec) |
N/A | 0.206 | 0.149 | 0.299 | 0.028 | 0.080 | 0.000 | 0.135 | 0.148 | 0.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 60 | 236 | 90 | 76 | 124 | 0 | 90 | 138 | 62 |
N.S. |
1 | 1.13 | 4.45 | 1.70 | 1.43 | 2.34 | 0.00 | 1.70 | 2.60 | 1.17 |
time (sec) |
N/A | 0.242 | 0.450 | 0.810 | 0.034 | 0.084 | 0.000 | 0.133 | 0.153 | 12.534 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 97 | 198 | 120 | 101 | 178 | 0 | 112 | 160 | 86 |
N.S. |
1 | 1.20 | 2.44 | 1.48 | 1.25 | 2.20 | 0.00 | 1.38 | 1.98 | 1.06 |
time (sec) |
N/A | 0.279 | 1.471 | 0.925 | 0.029 | 0.084 | 0.000 | 0.182 | 0.186 | 12.518 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 124 | 78 | 89 | 111 | 86 | 0 | 104 | 132 | 105 |
N.S. |
1 | 1.27 | 0.80 | 0.91 | 1.13 | 0.88 | 0.00 | 1.06 | 1.35 | 1.07 |
time (sec) |
N/A | 0.349 | 0.424 | 1.180 | 0.105 | 0.082 | 0.000 | 0.191 | 0.159 | 13.063 |
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 | 70 | 90 | 54 | 71 | 82 | 68 | 0 | 82 | 102 | 79 |
N.S. |
1 | 1.29 | 0.77 | 1.01 | 1.17 | 0.97 | 0.00 | 1.17 | 1.46 | 1.13 |
time (sec) |
N/A | 0.259 | 0.397 | 0.975 | 0.107 | 0.079 | 0.000 | 0.134 | 0.158 | 12.625 |
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 | 42 | 55 | 54 | 46 | 47 | 50 | 0 | 47 | 61 | 35 |
N.S. |
1 | 1.31 | 1.29 | 1.10 | 1.12 | 1.19 | 0.00 | 1.12 | 1.45 | 0.83 |
time (sec) |
N/A | 0.230 | 0.107 | 0.451 | 0.110 | 0.072 | 0.000 | 0.148 | 0.153 | 12.539 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 16 | 15 | 31 | 0 | 15 | 31 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.00 | 2.07 | 0.00 | 1.00 | 2.07 | 1.13 |
time (sec) |
N/A | 0.150 | 0.003 | 0.719 | 0.027 | 0.073 | 0.000 | 0.108 | 0.154 | 12.513 |
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 | 26 | 24 | 36 | 43 | 26 | 39 | 0 | 26 | 48 | 28 |
N.S. |
1 | 0.92 | 1.38 | 1.65 | 1.00 | 1.50 | 0.00 | 1.00 | 1.85 | 1.08 |
time (sec) |
N/A | 0.230 | 0.228 | 0.800 | 0.032 | 0.066 | 0.000 | 0.142 | 0.151 | 12.540 |
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 | 46 | 41 | 84 | 73 | 43 | 66 | 0 | 50 | 72 | 46 |
N.S. |
1 | 0.89 | 1.83 | 1.59 | 0.93 | 1.43 | 0.00 | 1.09 | 1.57 | 1.00 |
time (sec) |
N/A | 0.238 | 0.194 | 1.357 | 0.034 | 0.065 | 0.000 | 0.154 | 0.155 | 12.603 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 60 | 128 | 89 | 64 | 91 | 0 | 76 | 94 | 60 |
N.S. |
1 | 0.88 | 1.88 | 1.31 | 0.94 | 1.34 | 0.00 | 1.12 | 1.38 | 0.88 |
time (sec) |
N/A | 0.252 | 0.209 | 1.500 | 0.037 | 0.074 | 0.000 | 0.172 | 0.206 | 12.717 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 86 | 118 | 155 | 89 | 90 | 0 | 115 | 261 | 87 |
N.S. |
1 | 0.89 | 1.22 | 1.60 | 0.92 | 0.93 | 0.00 | 1.19 | 2.69 | 0.90 |
time (sec) |
N/A | 0.292 | 1.108 | 1.397 | 0.031 | 0.084 | 0.000 | 0.153 | 0.166 | 12.425 |
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 | 72 | 65 | 83 | 69 | 67 | 67 | 0 | 77 | 474 | 66 |
N.S. |
1 | 0.90 | 1.15 | 0.96 | 0.93 | 0.93 | 0.00 | 1.07 | 6.58 | 0.92 |
time (sec) |
N/A | 0.264 | 0.833 | 1.123 | 0.032 | 0.077 | 0.000 | 0.181 | 0.162 | 12.506 |
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 | 46 | 41 | 75 | 42 | 42 | 44 | 0 | 43 | 138 | 45 |
N.S. |
1 | 0.89 | 1.63 | 0.91 | 0.91 | 0.96 | 0.00 | 0.93 | 3.00 | 0.98 |
time (sec) |
N/A | 0.231 | 0.080 | 0.474 | 0.035 | 0.076 | 0.000 | 0.129 | 0.160 | 0.058 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 48 | 108 | 94 | 82 | 101 | 0 | 95 | 266 | 53 |
N.S. |
1 | 0.92 | 2.08 | 1.81 | 1.58 | 1.94 | 0.00 | 1.83 | 5.12 | 1.02 |
time (sec) |
N/A | 0.257 | 0.839 | 0.521 | 0.032 | 0.082 | 0.000 | 0.124 | 0.160 | 0.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 117 | 1021 | 163 | 126 | 193 | 0 | 147 | 408 | 96 |
N.S. |
1 | 1.46 | 12.76 | 2.04 | 1.58 | 2.41 | 0.00 | 1.84 | 5.10 | 1.20 |
time (sec) |
N/A | 0.308 | 7.037 | 1.213 | 0.028 | 0.083 | 0.000 | 0.124 | 0.159 | 12.535 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 162 | 218 | 211 | 165 | 286 | 0 | 191 | 446 | 135 |
N.S. |
1 | 1.34 | 1.80 | 1.74 | 1.36 | 2.36 | 0.00 | 1.58 | 3.69 | 1.12 |
time (sec) |
N/A | 0.354 | 1.962 | 1.499 | 0.038 | 0.089 | 0.000 | 0.185 | 0.161 | 12.602 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 168 | 499 | 165 | 164 | 131 | 0 | 183 | 353 | 163 |
N.S. |
1 | 1.19 | 3.54 | 1.17 | 1.16 | 0.93 | 0.00 | 1.30 | 2.50 | 1.16 |
time (sec) |
N/A | 0.476 | 1.766 | 1.770 | 0.112 | 0.094 | 0.000 | 0.295 | 0.184 | 12.944 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 129 | 153 | 100 | 120 | 107 | 0 | 123 | 275 | 116 |
N.S. |
1 | 1.19 | 1.42 | 0.93 | 1.11 | 0.99 | 0.00 | 1.14 | 2.55 | 1.07 |
time (sec) |
N/A | 0.337 | 1.670 | 1.469 | 0.102 | 0.082 | 0.000 | 0.191 | 0.170 | 12.524 |
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 | 65 | 76 | 126 | 71 | 67 | 81 | 0 | 67 | 167 | 94 |
N.S. |
1 | 1.17 | 1.94 | 1.09 | 1.03 | 1.25 | 0.00 | 1.03 | 2.57 | 1.45 |
time (sec) |
N/A | 0.266 | 1.351 | 0.746 | 0.112 | 0.079 | 0.000 | 0.150 | 0.159 | 12.652 |
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 | 40 | 44 | 41 | 46 | 44 | 58 | 0 | 49 | 106 | 42 |
N.S. |
1 | 1.10 | 1.02 | 1.15 | 1.10 | 1.45 | 0.00 | 1.22 | 2.65 | 1.05 |
time (sec) |
N/A | 0.220 | 0.316 | 1.294 | 0.026 | 0.082 | 0.000 | 0.164 | 0.160 | 12.436 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 45 | 109 | 96 | 54 | 71 | 0 | 60 | 124 | 56 |
N.S. |
1 | 0.90 | 2.18 | 1.92 | 1.08 | 1.42 | 0.00 | 1.20 | 2.48 | 1.12 |
time (sec) |
N/A | 0.257 | 1.354 | 0.959 | 0.030 | 0.072 | 0.000 | 0.191 | 0.156 | 12.479 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 68 | 151 | 130 | 80 | 101 | 0 | 98 | 145 | 85 |
N.S. |
1 | 0.89 | 1.99 | 1.71 | 1.05 | 1.33 | 0.00 | 1.29 | 1.91 | 1.12 |
time (sec) |
N/A | 0.274 | 3.480 | 1.539 | 0.032 | 0.073 | 0.000 | 0.242 | 0.155 | 12.545 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 92 | 353 | 154 | 107 | 139 | 0 | 141 | 200 | 108 |
N.S. |
1 | 0.89 | 3.43 | 1.50 | 1.04 | 1.35 | 0.00 | 1.37 | 1.94 | 1.05 |
time (sec) |
N/A | 0.301 | 1.868 | 1.839 | 0.030 | 0.073 | 0.000 | 0.193 | 0.156 | 12.817 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 91 | 425 | 115 | 102 | 229 | 0 | 146 | 315 | 123 |
N.S. |
1 | 0.93 | 4.34 | 1.17 | 1.04 | 2.34 | 0.00 | 1.49 | 3.21 | 1.26 |
time (sec) |
N/A | 0.301 | 2.825 | 1.688 | 0.116 | 0.105 | 0.000 | 0.138 | 0.183 | 12.458 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 69 | 376 | 67 | 63 | 154 | 0 | 85 | 182 | 76 |
N.S. |
1 | 0.97 | 5.30 | 0.94 | 0.89 | 2.17 | 0.00 | 1.20 | 2.56 | 1.07 |
time (sec) |
N/A | 0.253 | 1.077 | 0.915 | 0.112 | 0.094 | 0.000 | 0.137 | 0.221 | 0.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 46 | 329 | 44 | 40 | 118 | 0 | 42 | 76 | 39 |
N.S. |
1 | 0.98 | 7.00 | 0.94 | 0.85 | 2.51 | 0.00 | 0.89 | 1.62 | 0.83 |
time (sec) |
N/A | 0.222 | 0.459 | 0.418 | 0.106 | 0.093 | 0.000 | 0.140 | 0.156 | 12.398 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 54 | 239 | 71 | 64 | 156 | 0 | 73 | 84 | 123 |
N.S. |
1 | 0.98 | 4.35 | 1.29 | 1.16 | 2.84 | 0.00 | 1.33 | 1.53 | 2.24 |
time (sec) |
N/A | 0.241 | 1.013 | 0.421 | 0.111 | 0.102 | 0.000 | 0.167 | 0.158 | 0.199 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 99 | 371 | 115 | 128 | 327 | 0 | 140 | 162 | 392 |
N.S. |
1 | 1.15 | 4.31 | 1.34 | 1.49 | 3.80 | 0.00 | 1.63 | 1.88 | 4.56 |
time (sec) |
N/A | 0.279 | 1.792 | 0.557 | 0.112 | 0.123 | 0.000 | 0.149 | 0.161 | 12.987 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | B | F | B | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 155 | 549 | 181 | 231 | 693 | 0 | 233 | 268 | 870 |
N.S. |
1 | 1.20 | 4.26 | 1.40 | 1.79 | 5.37 | 0.00 | 1.81 | 2.08 | 6.74 |
time (sec) |
N/A | 0.339 | 4.677 | 0.728 | 0.117 | 0.148 | 0.000 | 0.138 | 0.168 | 15.937 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 199 | 357 | 170 | 209 | 428 | 0 | 237 | 384 | 1448 |
N.S. |
1 | 1.20 | 2.15 | 1.02 | 1.26 | 2.58 | 0.00 | 1.43 | 2.31 | 8.72 |
time (sec) |
N/A | 0.442 | 3.374 | 2.303 | 0.110 | 0.120 | 0.000 | 0.174 | 0.196 | 13.844 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 141 | 303 | 119 | 137 | 332 | 0 | 152 | 230 | 494 |
N.S. |
1 | 1.21 | 2.59 | 1.02 | 1.17 | 2.84 | 0.00 | 1.30 | 1.97 | 4.22 |
time (sec) |
N/A | 0.337 | 1.341 | 1.210 | 0.124 | 0.107 | 0.000 | 0.159 | 0.176 | 12.753 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 91 | 245 | 78 | 77 | 257 | 0 | 92 | 104 | 111 |
N.S. |
1 | 1.20 | 3.22 | 1.03 | 1.01 | 3.38 | 0.00 | 1.21 | 1.37 | 1.46 |
time (sec) |
N/A | 0.276 | 0.549 | 0.697 | 0.116 | 0.110 | 0.000 | 0.172 | 0.204 | 12.666 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 182 | 46 | 44 | 231 | 0 | 65 | 85 | 460 |
N.S. |
1 | 1.00 | 4.04 | 1.02 | 0.98 | 5.13 | 0.00 | 1.44 | 1.89 | 10.22 |
time (sec) |
N/A | 0.258 | 1.384 | 0.332 | 0.110 | 0.098 | 0.000 | 0.149 | 0.157 | 12.657 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 52 | 189 | 52 | 50 | 271 | 0 | 71 | 120 | 46 |
N.S. |
1 | 0.96 | 3.50 | 0.96 | 0.93 | 5.02 | 0.00 | 1.31 | 2.22 | 0.85 |
time (sec) |
N/A | 0.241 | 0.920 | 0.449 | 0.111 | 0.105 | 0.000 | 0.191 | 0.158 | 12.507 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 77 | 226 | 69 | 82 | 397 | 0 | 103 | 204 | 80 |
N.S. |
1 | 1.01 | 2.97 | 0.91 | 1.08 | 5.22 | 0.00 | 1.36 | 2.68 | 1.05 |
time (sec) |
N/A | 0.261 | 1.974 | 0.587 | 0.115 | 0.110 | 0.000 | 0.150 | 0.164 | 12.418 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 97 | 318 | 93 | 137 | 587 | 0 | 173 | 329 | 112 |
N.S. |
1 | 0.92 | 3.03 | 0.89 | 1.30 | 5.59 | 0.00 | 1.65 | 3.13 | 1.07 |
time (sec) |
N/A | 0.328 | 1.671 | 0.764 | 0.102 | 0.112 | 0.000 | 0.244 | 0.189 | 12.944 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 136 | 454 | 159 | 148 | 405 | 0 | 206 | 782 | 195 |
N.S. |
1 | 0.95 | 3.17 | 1.11 | 1.03 | 2.83 | 0.00 | 1.44 | 5.47 | 1.36 |
time (sec) |
N/A | 0.339 | 5.330 | 3.409 | 0.106 | 0.114 | 0.000 | 0.117 | 0.254 | 0.152 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 107 | 403 | 102 | 104 | 297 | 0 | 133 | 523 | 130 |
N.S. |
1 | 0.94 | 3.54 | 0.89 | 0.91 | 2.61 | 0.00 | 1.17 | 4.59 | 1.14 |
time (sec) |
N/A | 0.325 | 2.911 | 1.915 | 0.115 | 0.114 | 0.000 | 0.114 | 0.234 | 0.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 83 | 393 | 69 | 70 | 201 | 0 | 72 | 525 | 72 |
N.S. |
1 | 0.99 | 4.68 | 0.82 | 0.83 | 2.39 | 0.00 | 0.86 | 6.25 | 0.86 |
time (sec) |
N/A | 0.239 | 2.482 | 0.869 | 0.110 | 0.099 | 0.000 | 0.147 | 0.170 | 12.363 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 106 | 384 | 103 | 138 | 390 | 0 | 150 | 530 | 2188 |
N.S. |
1 | 1.07 | 3.88 | 1.04 | 1.39 | 3.94 | 0.00 | 1.52 | 5.35 | 22.10 |
time (sec) |
N/A | 0.285 | 1.636 | 0.643 | 0.107 | 0.141 | 0.000 | 0.176 | 0.171 | 13.660 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 157 | 468 | 148 | 231 | 698 | 0 | 235 | 770 | 1845 |
N.S. |
1 | 1.07 | 3.18 | 1.01 | 1.57 | 4.75 | 0.00 | 1.60 | 5.24 | 12.55 |
time (sec) |
N/A | 0.348 | 2.203 | 0.793 | 0.107 | 0.161 | 0.000 | 0.195 | 0.207 | 13.478 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 221 | 450 | 213 | 369 | 1202 | 0 | 325 | 895 | 4338 |
N.S. |
1 | 1.12 | 2.28 | 1.08 | 1.87 | 6.10 | 0.00 | 1.65 | 4.54 | 22.02 |
time (sec) |
N/A | 0.414 | 2.659 | 1.059 | 0.125 | 0.200 | 0.000 | 0.201 | 0.231 | 17.136 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 267 | 298 | 2468 | 204 | 302 | 674 | 0 | 294 | 967 | 1461 |
N.S. |
1 | 1.12 | 9.24 | 0.76 | 1.13 | 2.52 | 0.00 | 1.10 | 3.62 | 5.47 |
time (sec) |
N/A | 0.556 | 20.020 | 4.392 | 0.117 | 0.145 | 0.000 | 0.171 | 0.280 | 14.623 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 213 | 1105 | 147 | 205 | 522 | 0 | 193 | 664 | 435 |
N.S. |
1 | 1.12 | 5.79 | 0.77 | 1.07 | 2.73 | 0.00 | 1.01 | 3.48 | 2.28 |
time (sec) |
N/A | 0.421 | 11.371 | 2.537 | 0.111 | 0.125 | 0.000 | 0.179 | 0.252 | 13.653 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 145 | 699 | 109 | 126 | 441 | 0 | 149 | 663 | 816 |
N.S. |
1 | 1.12 | 5.38 | 0.84 | 0.97 | 3.39 | 0.00 | 1.15 | 5.10 | 6.28 |
time (sec) |
N/A | 0.331 | 8.846 | 1.408 | 0.112 | 0.120 | 0.000 | 0.194 | 0.186 | 13.015 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 111 | 240 | 90 | 106 | 435 | 0 | 114 | 562 | 2056 |
N.S. |
1 | 1.21 | 2.61 | 0.98 | 1.15 | 4.73 | 0.00 | 1.24 | 6.11 | 22.35 |
time (sec) |
N/A | 0.265 | 2.707 | 0.494 | 0.114 | 0.125 | 0.000 | 0.168 | 0.169 | 14.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 92 | 242 | 78 | 117 | 407 | 0 | 127 | 427 | 91 |
N.S. |
1 | 1.01 | 2.66 | 0.86 | 1.29 | 4.47 | 0.00 | 1.40 | 4.69 | 1.00 |
time (sec) |
N/A | 0.265 | 2.246 | 0.650 | 0.115 | 0.114 | 0.000 | 0.162 | 0.192 | 12.501 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 125 | 303 | 106 | 193 | 663 | 0 | 185 | 735 | 141 |
N.S. |
1 | 1.02 | 2.46 | 0.86 | 1.57 | 5.39 | 0.00 | 1.50 | 5.98 | 1.15 |
time (sec) |
N/A | 0.385 | 4.873 | 0.882 | 0.115 | 0.147 | 0.000 | 0.225 | 0.215 | 13.421 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 195 | 777 | 124 | 268 | 987 | 0 | 254 | 927 | 198 |
N.S. |
1 | 1.32 | 5.25 | 0.84 | 1.81 | 6.67 | 0.00 | 1.72 | 6.26 | 1.34 |
time (sec) |
N/A | 0.478 | 3.178 | 1.129 | 0.115 | 0.147 | 0.000 | 0.261 | 0.250 | 14.375 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 214 | 1641 | 190 | 204 | 579 | 0 | 254 | 1391 | 255 |
N.S. |
1 | 1.07 | 8.20 | 0.95 | 1.02 | 2.90 | 0.00 | 1.27 | 6.96 | 1.28 |
time (sec) |
N/A | 0.532 | 9.004 | 7.334 | 0.111 | 0.142 | 0.000 | 0.221 | 0.412 | 12.510 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 152 | 1153 | 125 | 149 | 439 | 0 | 165 | 1390 | 172 |
N.S. |
1 | 0.99 | 7.49 | 0.81 | 0.97 | 2.85 | 0.00 | 1.07 | 9.03 | 1.12 |
time (sec) |
N/A | 0.449 | 7.606 | 4.056 | 0.122 | 0.122 | 0.000 | 0.122 | 0.290 | 0.151 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 120 | 656 | 83 | 103 | 299 | 0 | 89 | 1410 | 105 |
N.S. |
1 | 1.03 | 5.66 | 0.72 | 0.89 | 2.58 | 0.00 | 0.77 | 12.16 | 0.91 |
time (sec) |
N/A | 0.262 | 4.566 | 2.148 | 0.110 | 0.111 | 0.000 | 0.124 | 0.221 | 0.138 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 173 | 447 | 156 | 261 | 779 | 0 | 245 | 1447 | 3557 |
N.S. |
1 | 1.12 | 2.90 | 1.01 | 1.69 | 5.06 | 0.00 | 1.59 | 9.40 | 23.10 |
time (sec) |
N/A | 0.378 | 2.672 | 1.178 | 0.114 | 0.203 | 0.000 | 0.161 | 0.227 | 15.792 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 237 | 532 | 198 | 399 | 1332 | 0 | 329 | 1863 | 2728 |
N.S. |
1 | 1.11 | 2.50 | 0.93 | 1.87 | 6.25 | 0.00 | 1.54 | 8.75 | 12.81 |
time (sec) |
N/A | 0.458 | 3.705 | 1.339 | 0.114 | 0.244 | 0.000 | 0.194 | 0.285 | 14.206 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 284 | 549 | 259 | 528 | 1833 | 0 | 462 | 1988 | 5613 |
N.S. |
1 | 1.11 | 2.14 | 1.01 | 2.05 | 7.13 | 0.00 | 1.80 | 7.74 | 21.84 |
time (sec) |
N/A | 0.522 | 4.511 | 1.724 | 0.115 | 0.275 | 0.000 | 0.239 | 0.359 | 17.132 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 314 | 346 | 1639 | 247 | 418 | 930 | 0 | 351 | 1719 | 2117 |
N.S. |
1 | 1.10 | 5.22 | 0.79 | 1.33 | 2.96 | 0.00 | 1.12 | 5.47 | 6.74 |
time (sec) |
N/A | 0.634 | 15.999 | 8.401 | 0.115 | 0.180 | 0.000 | 0.227 | 0.477 | 15.567 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 238 | 261 | 2469 | 193 | 299 | 803 | 0 | 306 | 1736 | 1317 |
N.S. |
1 | 1.10 | 10.37 | 0.81 | 1.26 | 3.37 | 0.00 | 1.29 | 7.29 | 5.53 |
time (sec) |
N/A | 0.480 | 20.024 | 4.609 | 0.141 | 0.163 | 0.000 | 0.204 | 0.352 | 15.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 216 | 1915 | 155 | 272 | 815 | 0 | 208 | 1738 | 2628 |
N.S. |
1 | 1.17 | 10.41 | 0.84 | 1.48 | 4.43 | 0.00 | 1.13 | 9.45 | 14.28 |
time (sec) |
N/A | 0.403 | 14.057 | 3.026 | 0.114 | 0.156 | 0.000 | 0.246 | 0.257 | 15.713 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 175 | 332 | 147 | 231 | 819 | 0 | 196 | 1496 | 3271 |
N.S. |
1 | 1.22 | 2.31 | 1.02 | 1.60 | 5.69 | 0.00 | 1.36 | 10.39 | 22.72 |
time (sec) |
N/A | 0.333 | 5.519 | 1.152 | 0.115 | 0.141 | 0.000 | 0.215 | 0.216 | 16.389 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 132 | 749 | 97 | 219 | 615 | 0 | 177 | 922 | 146 |
N.S. |
1 | 1.06 | 6.04 | 0.78 | 1.77 | 4.96 | 0.00 | 1.43 | 7.44 | 1.18 |
time (sec) |
N/A | 0.291 | 6.148 | 1.185 | 0.116 | 0.130 | 0.000 | 0.326 | 0.262 | 13.177 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 166 | 994 | 140 | 323 | 1009 | 0 | 264 | 1367 | 207 |
N.S. |
1 | 1.01 | 6.06 | 0.85 | 1.97 | 6.15 | 0.00 | 1.61 | 8.34 | 1.26 |
time (sec) |
N/A | 0.468 | 3.848 | 1.311 | 0.122 | 0.163 | 0.000 | 0.263 | 0.286 | 14.656 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 249 | 479 | 180 | 434 | 1423 | 0 | 367 | 1865 | 267 |
N.S. |
1 | 1.20 | 2.30 | 0.87 | 2.09 | 6.84 | 0.00 | 1.76 | 8.97 | 1.28 |
time (sec) |
N/A | 0.586 | 4.881 | 1.816 | 0.132 | 0.175 | 0.000 | 0.361 | 0.321 | 15.135 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 143 | 152 | 326 | 171 | 306 | 0 | 1281 | 24 | 0 |
N.S. |
1 | 1.03 | 1.09 | 2.35 | 1.23 | 2.20 | 0.00 | 9.22 | 0.17 | 0.00 |
time (sec) |
N/A | 0.322 | 0.620 | 5.246 | 0.116 | 0.234 | 0.000 | 0.577 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 95 | 120 | 236 | 116 | 243 | 0 | 85 | 24 | 0 |
N.S. |
1 | 0.95 | 1.20 | 2.36 | 1.16 | 2.43 | 0.00 | 0.85 | 0.24 | 0.00 |
time (sec) |
N/A | 0.287 | 0.255 | 4.056 | 0.113 | 0.218 | 0.000 | 0.210 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 64 | 99 | 93 | 88 | 193 | 0 | 55 | 22 | 87 |
N.S. |
1 | 0.97 | 1.50 | 1.41 | 1.33 | 2.92 | 0.00 | 0.83 | 0.33 | 1.32 |
time (sec) |
N/A | 0.244 | 0.094 | 0.240 | 0.114 | 0.208 | 0.000 | 0.176 | 0.162 | 12.862 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 80 | 119 | 554 | 0 | 536 | 0 | 405 | 22 | 0 |
N.S. |
1 | 0.98 | 1.45 | 6.76 | 0.00 | 6.54 | 0.00 | 4.94 | 0.27 | 0.00 |
time (sec) |
N/A | 0.290 | 0.091 | 3.984 | 0.000 | 0.161 | 0.000 | 0.543 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 131 | 163 | 1244 | 0 | 907 | 0 | 578 | 24 | 0 |
N.S. |
1 | 1.06 | 1.31 | 10.03 | 0.00 | 7.31 | 0.00 | 4.66 | 0.19 | 0.00 |
time (sec) |
N/A | 0.327 | 0.299 | 4.069 | 0.000 | 0.227 | 0.000 | 0.633 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 207 | 209 | 2007 | 0 | 1516 | 0 | 867 | 24 | 0 |
N.S. |
1 | 1.13 | 1.14 | 10.97 | 0.00 | 8.28 | 0.00 | 4.74 | 0.13 | 0.00 |
time (sec) |
N/A | 0.423 | 1.074 | 4.122 | 0.000 | 0.453 | 0.000 | 0.958 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 240 | 270 | 0 | 831 | 0 | 1715 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.12 | 0.00 | 3.46 | 0.00 | 7.15 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.524 | 0.000 | 35.727 | 0.000 | 2.485 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 197 | 0 | 645 | 0 | 1565 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.09 | 0.00 | 3.56 | 0.00 | 8.65 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.392 | 0.000 | 21.786 | 0.000 | 0.863 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 127 | 432 | 481 | 0 | 1417 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.03 | 3.51 | 3.91 | 0.00 | 11.52 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.314 | 3.327 | 18.800 | 0.000 | 0.402 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | C | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 77 | 284 | 351 | 3227 | 1227 | 0 | 0 | 15 | 0 |
N.S. |
1 | 0.97 | 3.59 | 4.44 | 40.85 | 15.53 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.236 | 1.373 | 17.822 | 0.631 | 0.298 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 66 | 61 | 324 | 50 | 306 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.97 | 0.90 | 4.76 | 0.74 | 4.50 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.254 | 0.176 | 17.876 | 0.035 | 0.135 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 100 | 285 | 589 | 82 | 436 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.95 | 2.71 | 5.61 | 0.78 | 4.15 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.281 | 5.574 | 18.878 | 0.032 | 0.272 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 157 | 422 | 903 | 143 | 656 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.05 | 2.83 | 6.06 | 0.96 | 4.40 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.325 | 6.943 | 19.313 | 0.038 | 1.117 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 175 | 188 | 498 | 277 | 362 | 0 | 1952 | 61 | 0 |
N.S. |
1 | 0.89 | 0.96 | 2.54 | 1.41 | 1.85 | 0.00 | 9.96 | 0.31 | 0.00 |
time (sec) |
N/A | 0.330 | 0.984 | 16.865 | 0.115 | 0.334 | 0.000 | 1.763 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 144 | 164 | 399 | 250 | 289 | 0 | 146 | 61 | 0 |
N.S. |
1 | 0.89 | 1.01 | 2.46 | 1.54 | 1.78 | 0.00 | 0.90 | 0.38 | 0.00 |
time (sec) |
N/A | 0.323 | 0.524 | 9.302 | 0.113 | 0.313 | 0.000 | 0.396 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 98 | 73 | 121 | 142 | 242 | 0 | 87 | 57 | 61 |
N.S. |
1 | 0.98 | 0.73 | 1.21 | 1.42 | 2.42 | 0.00 | 0.87 | 0.57 | 0.61 |
time (sec) |
N/A | 0.255 | 0.475 | 0.219 | 0.109 | 0.238 | 0.000 | 0.196 | 0.226 | 14.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 119 | 171 | 1466 | 0 | 755 | 0 | 0 | 57 | 0 |
N.S. |
1 | 0.98 | 1.40 | 12.02 | 0.00 | 6.19 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.335 | 0.424 | 8.936 | 0.000 | 0.224 | 0.000 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 162 | 202 | 2037 | 0 | 1024 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.01 | 1.25 | 12.65 | 0.00 | 6.36 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.384 | 1.062 | 9.216 | 0.000 | 0.240 | 0.000 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 218 | 226 | 262 | 2890 | 0 | 1551 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.04 | 1.20 | 13.26 | 0.00 | 7.11 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.490 | 2.553 | 9.266 | 0.000 | 0.278 | 0.000 | 0.000 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 298 | 311 | 0 | 1172 | 0 | 1855 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.04 | 0.00 | 3.93 | 0.00 | 6.22 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.606 | 0.000 | 37.056 | 0.000 | 9.540 | 0.000 | 0.000 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 221 | 225 | 961 | 0 | 1667 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.02 | 1.04 | 4.43 | 0.00 | 7.68 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.469 | 3.126 | 36.352 | 0.000 | 2.919 | 0.000 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 159 | 493 | 825 | 0 | 1535 | 0 | 0 | 61 | 0 |
N.S. |
1 | 0.99 | 3.06 | 5.12 | 0.00 | 9.53 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.364 | 3.439 | 23.526 | 0.000 | 0.937 | 0.000 | 0.000 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 116 | 527 | 673 | 0 | 1457 | 0 | 0 | 44 | 0 |
N.S. |
1 | 0.98 | 4.47 | 5.70 | 0.00 | 12.35 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.280 | 3.167 | 20.885 | 0.000 | 0.439 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 103 | 64 | 616 | 98 | 370 | 0 | 0 | 61 | 0 |
N.S. |
1 | 0.98 | 0.61 | 5.87 | 0.93 | 3.52 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.279 | 0.184 | 20.866 | 0.032 | 0.287 | 0.000 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 154 | 163 | 654 | 243 | 472 | 0 | 0 | 61 | 0 |
N.S. |
1 | 0.90 | 0.95 | 3.80 | 1.41 | 2.74 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.324 | 5.555 | 21.831 | 0.040 | 1.243 | 0.000 | 0.000 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 209 | 188 | 512 | 999 | 273 | 682 | 0 | 0 | 61 | 0 |
N.S. |
1 | 0.90 | 2.45 | 4.78 | 1.31 | 3.26 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.361 | 8.643 | 23.002 | 0.037 | 5.777 | 0.000 | 0.000 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 126 | 93 | 89 | 162 | 87 | 0 | 928 | 38 | 0 |
N.S. |
1 | 1.02 | 0.76 | 0.72 | 1.32 | 0.71 | 0.00 | 7.54 | 0.31 | 0.00 |
time (sec) |
N/A | 0.312 | 0.775 | 2.409 | 0.035 | 0.101 | 0.000 | 0.669 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 72 | 64 | 58 | 83 | 57 | 0 | 59 | 38 | 0 |
N.S. |
1 | 0.97 | 0.86 | 0.78 | 1.12 | 0.77 | 0.00 | 0.80 | 0.51 | 0.00 |
time (sec) |
N/A | 0.272 | 0.156 | 2.125 | 0.035 | 0.089 | 0.000 | 0.319 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 48 | 31 | 28 | 37 | 0 | 31 | 36 | 46 |
N.S. |
1 | 1.00 | 1.60 | 1.03 | 0.93 | 1.23 | 0.00 | 1.03 | 1.20 | 1.53 |
time (sec) |
N/A | 0.224 | 0.086 | 0.398 | 0.026 | 0.082 | 0.000 | 0.179 | 0.172 | 13.296 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 86 | 247 | 0 | 149 | 0 | 49 | 36 | 0 |
N.S. |
1 | 1.00 | 2.00 | 5.74 | 0.00 | 3.47 | 0.00 | 1.14 | 0.84 | 0.00 |
time (sec) |
N/A | 0.250 | 0.082 | 1.326 | 0.000 | 0.137 | 0.000 | 0.192 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 93 | 140 | 567 | 0 | 314 | 0 | 480 | 38 | 0 |
N.S. |
1 | 1.07 | 1.61 | 6.52 | 0.00 | 3.61 | 0.00 | 5.52 | 0.44 | 0.00 |
time (sec) |
N/A | 0.287 | 0.631 | 1.409 | 0.000 | 0.149 | 0.000 | 0.474 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 157 | 78 | 975 | 0 | 500 | 0 | 785 | 38 | 0 |
N.S. |
1 | 1.14 | 0.57 | 7.07 | 0.00 | 3.62 | 0.00 | 5.69 | 0.28 | 0.00 |
time (sec) |
N/A | 0.348 | 0.120 | 1.443 | 0.000 | 0.179 | 0.000 | 0.771 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 215 | 163 | 633 | 0 | 639 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.11 | 0.84 | 3.28 | 0.00 | 3.31 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.442 | 1.000 | 19.707 | 0.000 | 1.077 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 148 | 145 | 463 | 0 | 565 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.10 | 1.07 | 3.43 | 0.00 | 4.19 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.326 | 0.278 | 9.355 | 0.000 | 0.368 | 0.000 | 0.000 | 0.164 | 0.000 |