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 | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 177 | 273 | 239 | 0 | 134 | 0 | 134 | 104 | 0 |
N.S. |
1 | 1.03 | 1.59 | 1.39 | 0.00 | 0.78 | 0.00 | 0.78 | 0.60 | 0.00 |
time (sec) |
N/A | 0.660 | 0.907 | 0.105 | 0.000 | 0.102 | 0.000 | 0.177 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 154 | 232 | 192 | 0 | 124 | 0 | 124 | 88 | 0 |
N.S. |
1 | 1.03 | 1.56 | 1.29 | 0.00 | 0.83 | 0.00 | 0.83 | 0.59 | 0.00 |
time (sec) |
N/A | 0.583 | 0.872 | 0.050 | 0.000 | 0.100 | 0.000 | 0.168 | 0.154 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 127 | 190 | 175 | 0 | 114 | 0 | 114 | 72 | 0 |
N.S. |
1 | 1.00 | 1.50 | 1.38 | 0.00 | 0.90 | 0.00 | 0.90 | 0.57 | 0.00 |
time (sec) |
N/A | 0.515 | 0.707 | 0.047 | 0.000 | 0.083 | 0.000 | 0.182 | 0.159 | 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 | 95 | 98 | 85 | 80 | 0 | 101 | 0 | 101 | 55 | 0 |
N.S. |
1 | 1.03 | 0.89 | 0.84 | 0.00 | 1.06 | 0.00 | 1.06 | 0.58 | 0.00 |
time (sec) |
N/A | 0.434 | 0.065 | 0.043 | 0.000 | 0.093 | 0.000 | 0.140 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 23 | 19 | 21 | 23 | 19 | 21 | 20 | 21 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.10 | 0.90 | 1.00 | 0.95 | 1.00 |
time (sec) |
N/A | 0.279 | 0.545 | 0.011 | 0.097 | 0.074 | 32.266 | 0.144 | 0.150 | 26.113 |
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 | 76 | 79 | 142 | 132 | 0 | 115 | 0 | 92 | 99 | 0 |
N.S. |
1 | 1.04 | 1.87 | 1.74 | 0.00 | 1.51 | 0.00 | 1.21 | 1.30 | 0.00 |
time (sec) |
N/A | 0.541 | 0.675 | 0.046 | 0.000 | 0.088 | 0.000 | 0.151 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 95 | 186 | 0 | 138 | 0 | 130 | 84 | 0 |
N.S. |
1 | 1.00 | 0.94 | 1.84 | 0.00 | 1.37 | 0.00 | 1.29 | 0.83 | 0.00 |
time (sec) |
N/A | 0.567 | 0.600 | 0.056 | 0.000 | 0.086 | 0.000 | 0.189 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 192 | 216 | 0 | 0 | 110 | 0 | 110 | 81 | 0 |
N.S. |
1 | 1.03 | 1.16 | 0.00 | 0.00 | 0.59 | 0.00 | 0.59 | 0.43 | 0.00 |
time (sec) |
N/A | 0.672 | 1.562 | 0.000 | 0.000 | 0.096 | 0.000 | 0.148 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 163 | 198 | 0 | 0 | 100 | 0 | 100 | 63 | 0 |
N.S. |
1 | 1.03 | 1.25 | 0.00 | 0.00 | 0.63 | 0.00 | 0.63 | 0.40 | 0.00 |
time (sec) |
N/A | 0.626 | 1.139 | 0.000 | 0.000 | 0.083 | 0.000 | 0.153 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 130 | 172 | 0 | 0 | 85 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.10 | 1.46 | 0.00 | 0.00 | 0.72 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.584 | 0.962 | 0.000 | 0.000 | 0.112 | 0.000 | 0.000 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 116 | 180 | 0 | 0 | 84 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.02 | 1.58 | 0.00 | 0.00 | 0.74 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.514 | 0.756 | 0.000 | 0.000 | 0.088 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 150 | 280 | 0 | 0 | 108 | 0 | 181 | 73 | 0 |
N.S. |
1 | 0.99 | 1.85 | 0.00 | 0.00 | 0.72 | 0.00 | 1.20 | 0.48 | 0.00 |
time (sec) |
N/A | 0.632 | 1.090 | 0.000 | 0.000 | 0.085 | 0.000 | 0.227 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 97 | 93 | 84 | 82 | 88 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.04 | 1.00 | 0.90 | 0.88 | 0.95 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.577 | 0.013 | 0.184 | 0.036 | 0.075 | 0.000 | 0.000 | 0.141 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 79 | 77 | 69 | 67 | 73 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.03 | 1.00 | 0.90 | 0.87 | 0.95 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.467 | 0.011 | 0.123 | 0.034 | 0.086 | 0.000 | 0.000 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 59 | 52 | 50 | 56 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.85 | 0.95 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.352 | 0.008 | 0.091 | 0.035 | 0.084 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 46 | 38 | 28 | 34 | 40 | 0 | 0 | 35 | 35 |
N.S. |
1 | 1.21 | 1.00 | 0.74 | 0.89 | 1.05 | 0.00 | 0.00 | 0.92 | 0.92 |
time (sec) |
N/A | 0.302 | 0.006 | 0.216 | 0.035 | 0.071 | 0.000 | 0.000 | 0.144 | 26.487 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 11 | 13 | 13 | 10 | 13 | 14 | 13 |
N.S. |
1 | 1.00 | 1.17 | 0.92 | 1.08 | 1.08 | 0.83 | 1.08 | 1.17 | 1.08 |
time (sec) |
N/A | 0.219 | 0.074 | 0.030 | 0.075 | 0.071 | 0.381 | 0.130 | 0.142 | 26.749 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 162 | 132 | 601 | 189 | 128 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.23 | 1.00 | 4.55 | 1.43 | 0.97 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.703 | 0.023 | 2.146 | 0.064 | 0.079 | 0.000 | 0.000 | 0.143 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 113 | 98 | 430 | 153 | 93 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.15 | 1.00 | 4.39 | 1.56 | 0.95 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.486 | 0.012 | 0.963 | 0.062 | 0.089 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 63 | 262 | 117 | 58 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 1.00 | 4.16 | 1.86 | 0.92 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.328 | 0.010 | 0.476 | 0.055 | 0.076 | 0.000 | 0.000 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 31 | 32 | 76 | 31 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 2.45 | 1.00 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.202 | 0.005 | 0.391 | 0.052 | 0.080 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 21 | 23 | 19 | 22 | 23 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.05 | 1.15 | 0.95 | 1.10 | 1.15 | 1.10 |
time (sec) |
N/A | 0.255 | 0.312 | 0.019 | 0.141 | 0.080 | 1.772 | 0.166 | 0.143 | 26.418 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 223 | 193 | 1276 | 204 | 245 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.16 | 1.00 | 6.61 | 1.06 | 1.27 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.892 | 0.021 | 2.123 | 0.062 | 0.079 | 0.000 | 0.000 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 171 | 156 | 916 | 165 | 205 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.10 | 1.00 | 5.87 | 1.06 | 1.31 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.646 | 0.017 | 0.965 | 0.061 | 0.077 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 118 | 558 | 126 | 169 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 1.00 | 4.73 | 1.07 | 1.43 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.458 | 0.015 | 0.470 | 0.059 | 0.080 | 0.000 | 0.000 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 101 | 75 | 69 | 82 | 106 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.35 | 1.00 | 0.92 | 1.09 | 1.41 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.436 | 0.010 | 0.487 | 0.054 | 0.085 | 0.000 | 0.000 | 0.143 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 21 | 23 | 19 | 22 | 23 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.05 | 1.15 | 0.95 | 1.10 | 1.15 | 1.10 |
time (sec) |
N/A | 0.245 | 0.293 | 0.017 | 0.149 | 0.073 | 1.861 | 0.177 | 0.149 | 25.984 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 51 | 39 | 96 | 82 | 106 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.31 | 1.00 | 2.46 | 2.10 | 2.72 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.255 | 0.022 | 0.435 | 0.056 | 0.093 | 0.000 | 0.000 | 0.143 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 5 | 5 | 5 | 6 | 5 | 5 | 5 | 22 | 5 | 5 |
N.S. |
1 | 1.00 | 1.00 | 1.20 | 1.00 | 1.00 | 1.00 | 4.40 | 1.00 | 1.00 |
time (sec) |
N/A | 0.178 | 0.031 | 0.042 | 0.029 | 0.067 | 0.045 | 0.110 | 0.141 | 26.327 |
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 | 12 | 12 | 12 | 9 | 8 | 8 | 10 | 8 | 11 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 0.67 | 0.67 | 0.83 | 0.67 | 0.92 | 1.08 |
time (sec) |
N/A | 0.182 | 0.009 | 0.124 | 0.024 | 0.092 | 0.354 | 0.112 | 0.151 | 25.852 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 10 | 9 | 8 | 31 | 39 | 31 | 32 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.80 | 3.10 | 3.90 | 3.10 | 3.20 | 2.60 |
time (sec) |
N/A | 0.174 | 0.008 | 0.318 | 0.024 | 0.069 | 0.121 | 0.134 | 0.146 | 26.964 |
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 | 8 | 8 | 8 | 7 | 6 | 6 | 7 | 6 | 5 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.75 | 0.75 | 0.88 | 0.75 | 0.62 | 0.75 |
time (sec) |
N/A | 0.169 | 0.005 | 0.066 | 0.024 | 0.064 | 0.168 | 0.107 | 0.143 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 3 | 3 | 3 | 4 | 3 | 3 | 15 | 3 | 3 | 3 |
N.S. |
1 | 1.00 | 1.00 | 1.33 | 1.00 | 1.00 | 5.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.176 | 0.038 | 0.222 | 0.102 | 0.071 | 0.064 | 0.114 | 0.152 | 26.605 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 42 | 13 | 16 | 16 | 0 | 0 | 22 | 12 |
N.S. |
1 | 1.00 | 3.00 | 0.93 | 1.14 | 1.14 | 0.00 | 0.00 | 1.57 | 0.86 |
time (sec) |
N/A | 0.196 | 0.048 | 0.056 | 0.029 | 0.065 | 0.000 | 0.000 | 0.147 | 27.005 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 25 | 8 | 7 | 21 | 0 | 7 | 27 | 7 |
N.S. |
1 | 1.00 | 2.27 | 0.73 | 0.64 | 1.91 | 0.00 | 0.64 | 2.45 | 0.64 |
time (sec) |
N/A | 0.198 | 0.030 | 0.058 | 0.103 | 0.066 | 0.000 | 0.109 | 0.147 | 26.580 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 7 | 7 | 18 | 6 | 5 | 16 | 0 | 16 | 22 | 5 |
N.S. |
1 | 1.00 | 2.57 | 0.86 | 0.71 | 2.29 | 0.00 | 2.29 | 3.14 | 0.71 |
time (sec) |
N/A | 0.180 | 0.107 | 0.052 | 0.103 | 0.065 | 0.000 | 0.125 | 0.161 | 26.875 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 113 | 106 | 23 | 97 | 71 | 17 | 0 | 79 | 120 |
N.S. |
1 | 1.02 | 0.95 | 0.21 | 0.87 | 0.64 | 0.15 | 0.00 | 0.71 | 1.08 |
time (sec) |
N/A | 0.353 | 0.152 | 0.125 | 0.107 | 0.075 | 0.117 | 0.000 | 0.167 | 33.760 |
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 | 11 | 11 | 11 | 10 | 9 | 9 | 8 | 9 | 9 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.82 | 0.82 | 0.73 | 0.82 | 0.82 | 0.82 |
time (sec) |
N/A | 0.205 | 0.009 | 0.062 | 0.024 | 0.083 | 0.061 | 0.272 | 0.146 | 26.434 |
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 | 9 | 9 | 9 | 10 | 9 | 11 | 7 | 9 | 9 | 9 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 1.00 | 1.22 | 0.78 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.173 | 0.013 | 0.165 | 0.028 | 0.098 | 0.100 | 0.127 | 0.150 | 27.374 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 16 | 13 | 12 | 13 | 156 | 12 | 13 | 12 |
N.S. |
1 | 1.00 | 0.94 | 0.76 | 0.71 | 0.76 | 9.18 | 0.71 | 0.76 | 0.71 |
time (sec) |
N/A | 0.214 | 0.047 | 0.227 | 0.031 | 0.076 | 0.950 | 0.109 | 0.145 | 26.733 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 13 | 12 | 12 | 10 | 27 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.00 | 1.00 | 0.83 | 2.25 | 1.00 | 1.00 |
time (sec) |
N/A | 0.214 | 0.073 | 0.059 | 0.032 | 0.068 | 0.046 | 0.107 | 0.144 | 25.789 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 29 | 24 | 23 | 23 | 27 | 23 | 22 | 22 |
N.S. |
1 | 1.00 | 1.38 | 1.14 | 1.10 | 1.10 | 1.29 | 1.10 | 1.05 | 1.05 |
time (sec) |
N/A | 0.215 | 0.026 | 0.122 | 0.024 | 0.069 | 0.093 | 0.127 | 0.150 | 25.773 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 47 | 31 | 31 | 30 | 36 | 27 | 37 | 47 | 26 |
N.S. |
1 | 1.12 | 0.74 | 0.74 | 0.71 | 0.86 | 0.64 | 0.88 | 1.12 | 0.62 |
time (sec) |
N/A | 0.232 | 0.042 | 0.062 | 0.102 | 0.073 | 0.470 | 0.114 | 0.150 | 25.692 |
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 | 24 | 24 | 20 | 19 | 20 | 26 | 17 | 34 | 34 | 18 |
N.S. |
1 | 1.00 | 0.83 | 0.79 | 0.83 | 1.08 | 0.71 | 1.42 | 1.42 | 0.75 |
time (sec) |
N/A | 0.225 | 0.046 | 0.053 | 0.024 | 0.070 | 0.059 | 0.148 | 0.145 | 25.598 |
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 | 23 | 23 | 16 | 18 | 17 | 12 | 20 | 17 | 11 | 13 |
N.S. |
1 | 1.00 | 0.70 | 0.78 | 0.74 | 0.52 | 0.87 | 0.74 | 0.48 | 0.57 |
time (sec) |
N/A | 0.220 | 0.052 | 0.086 | 0.029 | 0.061 | 0.968 | 0.137 | 0.159 | 25.754 |
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 | 29 | 29 | 20 | 22 | 21 | 16 | 22 | 21 | 15 | 15 |
N.S. |
1 | 1.00 | 0.69 | 0.76 | 0.72 | 0.55 | 0.76 | 0.72 | 0.52 | 0.52 |
time (sec) |
N/A | 0.238 | 0.049 | 0.093 | 0.025 | 0.060 | 1.153 | 0.108 | 0.147 | 25.724 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 30 | 29 | 29 | 32 | 268 | 29 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.36 | 1.32 | 1.32 | 1.45 | 12.18 | 1.32 | 0.82 |
time (sec) |
N/A | 0.229 | 0.180 | 0.076 | 0.025 | 0.065 | 0.605 | 0.336 | 0.154 | 26.073 |
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 | 27 | 27 | 22 | 20 | 32 | 32 | 32 | 20 | 33 | 18 |
N.S. |
1 | 1.00 | 0.81 | 0.74 | 1.19 | 1.19 | 1.19 | 0.74 | 1.22 | 0.67 |
time (sec) |
N/A | 0.255 | 0.055 | 0.082 | 0.029 | 0.063 | 0.092 | 0.120 | 0.152 | 26.089 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 30 | 0 | 38 | 0 | 48 | 27 | 27 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 0.00 | 1.41 | 0.00 | 1.78 | 1.00 | 1.00 |
time (sec) |
N/A | 0.191 | 0.025 | 1.453 | 0.000 | 0.073 | 0.000 | 0.119 | 0.148 | 27.667 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 32 | 0 | 27 | 0 | 24 | 27 | 27 |
N.S. |
1 | 1.00 | 1.00 | 1.19 | 0.00 | 1.00 | 0.00 | 0.89 | 1.00 | 1.00 |
time (sec) |
N/A | 0.197 | 0.011 | 0.864 | 0.000 | 0.068 | 0.000 | 0.297 | 0.143 | 27.973 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 21 | 20 | 13 | 0 | 27 | 13 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.80 | 0.52 | 0.00 | 1.08 | 0.52 | 0.84 |
time (sec) |
N/A | 0.182 | 0.013 | 1.321 | 0.038 | 0.107 | 0.000 | 0.114 | 0.157 | 27.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 34 | 0 | 33 | 0 | 35 | 30 | 29 |
N.S. |
1 | 1.00 | 1.00 | 1.17 | 0.00 | 1.14 | 0.00 | 1.21 | 1.03 | 1.00 |
time (sec) |
N/A | 0.200 | 0.011 | 0.250 | 0.000 | 0.103 | 0.000 | 0.111 | 0.155 | 26.988 |
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 | 31 | 31 | 21 | 29 | 5 | 5 | 3 | 5 | 5 | 5 |
N.S. |
1 | 1.00 | 0.68 | 0.94 | 0.16 | 0.16 | 0.10 | 0.16 | 0.16 | 0.16 |
time (sec) |
N/A | 0.211 | 0.020 | 0.027 | 0.027 | 0.062 | 0.047 | 0.111 | 0.186 | 27.597 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 34 | 30 | 80 | 57 | 30 | 0 | 102 | 11 | 0 |
N.S. |
1 | 0.97 | 0.86 | 2.29 | 1.63 | 0.86 | 0.00 | 2.91 | 0.31 | 0.00 |
time (sec) |
N/A | 0.393 | 0.062 | 1.527 | 0.066 | 0.079 | 0.000 | 0.115 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 50 | 132 | 79 | 52 | 0 | 123 | 13 | 0 |
N.S. |
1 | 1.00 | 0.76 | 2.00 | 1.20 | 0.79 | 0.00 | 1.86 | 0.20 | 0.00 |
time (sec) |
N/A | 0.306 | 0.094 | 13.274 | 0.101 | 0.082 | 0.000 | 0.125 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 85 | 66 | 162 | 110 | 64 | 0 | 454 | 13 | 0 |
N.S. |
1 | 0.96 | 0.74 | 1.82 | 1.24 | 0.72 | 0.00 | 5.10 | 0.15 | 0.00 |
time (sec) |
N/A | 0.785 | 0.124 | 267.454 | 0.078 | 0.109 | 0.000 | 0.121 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 33 | 30 | 79 | 55 | 30 | 0 | 108 | 106 | 0 |
N.S. |
1 | 0.94 | 0.86 | 2.26 | 1.57 | 0.86 | 0.00 | 3.09 | 3.03 | 0.00 |
time (sec) |
N/A | 0.399 | 0.054 | 1.138 | 0.067 | 0.094 | 0.000 | 0.116 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 65 | 50 | 132 | 76 | 54 | 0 | 122 | 13 | 0 |
N.S. |
1 | 0.98 | 0.76 | 2.00 | 1.15 | 0.82 | 0.00 | 1.85 | 0.20 | 0.00 |
time (sec) |
N/A | 0.322 | 0.114 | 9.576 | 0.100 | 0.091 | 0.000 | 0.116 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 84 | 66 | 162 | 109 | 64 | 0 | 495 | 13 | 0 |
N.S. |
1 | 0.95 | 0.75 | 1.84 | 1.24 | 0.73 | 0.00 | 5.62 | 0.15 | 0.00 |
time (sec) |
N/A | 0.695 | 0.188 | 220.082 | 0.085 | 0.096 | 0.000 | 0.129 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 5 | 5 | 5 | 6 | 5 | 5 | 5 | 5 | 79 | 5 |
N.S. |
1 | 1.00 | 1.00 | 1.20 | 1.00 | 1.00 | 1.00 | 1.00 | 15.80 | 1.00 |
time (sec) |
N/A | 0.188 | 0.044 | 2.895 | 0.056 | 0.075 | 3.972 | 0.112 | 0.163 | 27.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 54 | 42 | 87 | 87 | 104 | 0 | 0 | 7 | 0 |
N.S. |
1 | 1.15 | 0.89 | 1.85 | 1.85 | 2.21 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.355 | 0.044 | 0.543 | 0.220 | 0.123 | 0.000 | 0.000 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 59 | 43 | 86 | 89 | 109 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.31 | 0.96 | 1.91 | 1.98 | 2.42 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.363 | 0.025 | 0.478 | 0.194 | 0.097 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 59 | 52 | 0 | 91 | 115 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.13 | 1.00 | 0.00 | 1.75 | 2.21 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.356 | 0.038 | 0.000 | 0.244 | 0.099 | 0.000 | 0.000 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 54 | 47 | 115 | 60 | 104 | 0 | 0 | 7 | 37 |
N.S. |
1 | 1.15 | 1.00 | 2.45 | 1.28 | 2.21 | 0.00 | 0.00 | 0.15 | 0.79 |
time (sec) |
N/A | 0.331 | 0.017 | 0.500 | 0.203 | 0.097 | 0.000 | 0.000 | 0.144 | 0.102 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 59 | 43 | 115 | 62 | 106 | 0 | 0 | 9 | 39 |
N.S. |
1 | 1.31 | 0.96 | 2.56 | 1.38 | 2.36 | 0.00 | 0.00 | 0.20 | 0.87 |
time (sec) |
N/A | 0.359 | 0.027 | 0.493 | 0.236 | 0.095 | 0.000 | 0.000 | 0.153 | 0.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 59 | 52 | 0 | 65 | 115 | 0 | 0 | 9 | 41 |
N.S. |
1 | 1.13 | 1.00 | 0.00 | 1.25 | 2.21 | 0.00 | 0.00 | 0.17 | 0.79 |
time (sec) |
N/A | 0.359 | 0.034 | 0.000 | 0.295 | 0.097 | 0.000 | 0.000 | 0.155 | 26.741 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 54 | 75 | 85 | 42 | 184 | 0 | 0 | 7 | 39 |
N.S. |
1 | 1.06 | 1.47 | 1.67 | 0.82 | 3.61 | 0.00 | 0.00 | 0.14 | 0.76 |
time (sec) |
N/A | 0.354 | 0.026 | 0.485 | 0.134 | 0.090 | 0.000 | 0.000 | 0.149 | 0.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 56 | 75 | 82 | 44 | 184 | 0 | 0 | 9 | 41 |
N.S. |
1 | 1.14 | 1.53 | 1.67 | 0.90 | 3.76 | 0.00 | 0.00 | 0.18 | 0.84 |
time (sec) |
N/A | 0.360 | 0.020 | 0.491 | 0.108 | 0.088 | 0.000 | 0.000 | 0.164 | 0.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | F | F | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 57 | 81 | 2196 | 48 | 195 | 0 | 0 | 9 | 44 |
N.S. |
1 | 1.02 | 1.45 | 39.21 | 0.86 | 3.48 | 0.00 | 0.00 | 0.16 | 0.79 |
time (sec) |
N/A | 0.357 | 0.018 | 2.892 | 0.110 | 0.090 | 0.000 | 0.000 | 0.148 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 54 | 75 | 86 | 43 | 147 | 0 | 0 | 7 | 0 |
N.S. |
1 | 1.06 | 1.47 | 1.69 | 0.84 | 2.88 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.347 | 0.019 | 0.497 | 0.108 | 0.099 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 56 | 75 | 82 | 44 | 148 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.14 | 1.53 | 1.67 | 0.90 | 3.02 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.360 | 0.020 | 0.478 | 0.108 | 0.095 | 0.000 | 0.000 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | F | F | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 57 | 81 | 2197 | 49 | 158 | 0 | 0 | 9 | 44 |
N.S. |
1 | 1.02 | 1.45 | 39.23 | 0.88 | 2.82 | 0.00 | 0.00 | 0.16 | 0.79 |
time (sec) |
N/A | 0.362 | 0.023 | 2.672 | 0.109 | 0.122 | 0.000 | 0.000 | 0.148 | 0.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 54 | 46 | 108 | 60 | 106 | 0 | 0 | 7 | 39 |
N.S. |
1 | 1.17 | 1.00 | 2.35 | 1.30 | 2.30 | 0.00 | 0.00 | 0.15 | 0.85 |
time (sec) |
N/A | 0.344 | 0.018 | 0.537 | 0.209 | 0.093 | 0.000 | 0.000 | 0.150 | 0.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 59 | 43 | 117 | 61 | 102 | 0 | 0 | 9 | 39 |
N.S. |
1 | 1.31 | 0.96 | 2.60 | 1.36 | 2.27 | 0.00 | 0.00 | 0.20 | 0.87 |
time (sec) |
N/A | 0.358 | 0.028 | 0.462 | 0.183 | 0.093 | 0.000 | 0.000 | 0.158 | 26.676 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 60 | 51 | 0 | 65 | 117 | 0 | 0 | 9 | 43 |
N.S. |
1 | 1.18 | 1.00 | 0.00 | 1.27 | 2.29 | 0.00 | 0.00 | 0.18 | 0.84 |
time (sec) |
N/A | 0.347 | 0.032 | 0.000 | 0.298 | 0.094 | 0.000 | 0.000 | 0.146 | 26.549 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 54 | 41 | 83 | 87 | 106 | 0 | 0 | 7 | 0 |
N.S. |
1 | 1.17 | 0.89 | 1.80 | 1.89 | 2.30 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.342 | 0.028 | 0.457 | 0.240 | 0.091 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 59 | 42 | 88 | 87 | 107 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.31 | 0.93 | 1.96 | 1.93 | 2.38 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.356 | 0.025 | 0.424 | 0.194 | 0.092 | 0.000 | 0.000 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 60 | 51 | 0 | 91 | 117 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.18 | 1.00 | 0.00 | 1.78 | 2.29 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.357 | 0.031 | 0.000 | 0.254 | 0.095 | 0.000 | 0.000 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 13 | 111 | 17 | 17 | 0 | 13 | 14 | 0 |
N.S. |
1 | 1.00 | 0.62 | 5.29 | 0.81 | 0.81 | 0.00 | 0.62 | 0.67 | 0.00 |
time (sec) |
N/A | 0.220 | 0.008 | 1.909 | 0.031 | 0.083 | 0.000 | 0.115 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 6 | 6 | 6 | 8 | 7 | 7 | 0 | 24 | 19 | 6 |
N.S. |
1 | 1.00 | 1.00 | 1.33 | 1.17 | 1.17 | 0.00 | 4.00 | 3.17 | 1.00 |
time (sec) |
N/A | 0.193 | 0.042 | 0.425 | 0.026 | 0.075 | 0.000 | 0.113 | 0.162 | 26.657 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 25 | 35 | 6 | 6 | 0 | 6 | 6 | 6 |
N.S. |
1 | 1.00 | 0.68 | 0.95 | 0.16 | 0.16 | 0.00 | 0.16 | 0.16 | 0.16 |
time (sec) |
N/A | 0.239 | 0.059 | 1.145 | 0.030 | 0.067 | 0.000 | 0.126 | 0.150 | 26.971 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 20 | 94 | 22 | 15 | 12 | 38 | 35 |
N.S. |
1 | 1.00 | 1.00 | 1.67 | 7.83 | 1.83 | 1.25 | 1.00 | 3.17 | 2.92 |
time (sec) |
N/A | 0.228 | 0.022 | 0.566 | 0.107 | 0.075 | 10.259 | 0.123 | 0.158 | 27.665 |
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 | 9 | 9 | 9 | 8 | 7 | 7 | 0 | 7 | 21 | 7 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.78 | 0.78 | 0.00 | 0.78 | 2.33 | 0.78 |
time (sec) |
N/A | 0.203 | 0.008 | 0.362 | 0.029 | 0.080 | 0.000 | 0.128 | 0.153 | 27.098 |
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 | 20 | 20 | 15 | 17 | 16 | 24 | 17 | 16 | 13 | 11 |
N.S. |
1 | 1.00 | 0.75 | 0.85 | 0.80 | 1.20 | 0.85 | 0.80 | 0.65 | 0.55 |
time (sec) |
N/A | 0.249 | 0.025 | 0.437 | 0.027 | 0.091 | 0.611 | 0.117 | 0.152 | 27.970 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 33 | 66 | 42 | 65 | 0 | 0 | 29 | 29 |
N.S. |
1 | 1.00 | 0.66 | 1.32 | 0.84 | 1.30 | 0.00 | 0.00 | 0.58 | 0.58 |
time (sec) |
N/A | 0.257 | 0.015 | 7.545 | 0.050 | 0.090 | 0.000 | 0.000 | 0.162 | 27.458 |
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 | 6 | 6 | 6 | 7 | 6 | 6 | 0 | 7 | 25 | 6 |
N.S. |
1 | 1.00 | 1.00 | 1.17 | 1.00 | 1.00 | 0.00 | 1.17 | 4.17 | 1.00 |
time (sec) |
N/A | 0.206 | 0.015 | 0.310 | 0.030 | 0.074 | 0.000 | 0.116 | 0.163 | 27.687 |
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 | 9 | 9 | 9 | 8 | 7 | 7 | 8 | 7 | 26 | 7 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.78 | 0.78 | 0.89 | 0.78 | 2.89 | 0.78 |
time (sec) |
N/A | 0.198 | 0.007 | 0.450 | 0.030 | 0.075 | 1.496 | 0.103 | 0.156 | 28.737 |
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 | 10 | 10 | 10 | 11 | 10 | 10 | 10 | 10 | 10 | 9 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 0.90 |
time (sec) |
N/A | 0.203 | 0.013 | 0.274 | 0.033 | 0.076 | 0.216 | 0.112 | 0.160 | 28.506 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 43 | 29 | 108 | 27 | 223 | 27 | 46 | 0 |
N.S. |
1 | 1.00 | 3.07 | 2.07 | 7.71 | 1.93 | 15.93 | 1.93 | 3.29 | 0.00 |
time (sec) |
N/A | 0.225 | 0.015 | 0.494 | 0.033 | 0.094 | 0.847 | 0.114 | 0.150 | 0.000 |
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 | 11 | 11 | 11 | 9 | 11 | 11 | 10 | 11 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 1.00 | 1.00 | 0.91 | 1.00 | 0.73 | 0.73 |
time (sec) |
N/A | 0.206 | 0.001 | 0.319 | 0.027 | 0.074 | 0.209 | 0.114 | 0.152 | 27.798 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 77 | 59 | 194 | 104 | 120 | 0 | 0 | 10 | 0 |
N.S. |
1 | 1.04 | 0.80 | 2.62 | 1.41 | 1.62 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.378 | 0.073 | 1.125 | 0.285 | 0.097 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 42 | 47 | 45 | 179 | 43 | 456 | 41 | 90 | 0 |
N.S. |
1 | 1.05 | 1.18 | 1.12 | 4.48 | 1.08 | 11.40 | 1.02 | 2.25 | 0.00 |
time (sec) |
N/A | 0.321 | 0.053 | 0.654 | 0.035 | 0.086 | 2.894 | 0.117 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 95 | 88 | 0 | 139 | 0 | 0 | 0 | 6 | 0 |
N.S. |
1 | 1.20 | 1.11 | 0.00 | 1.76 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.518 | 0.063 | 0.000 | 0.042 | 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 | B | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 37 | 81 | 19 | 17 | 19 | 36 | 57 |
N.S. |
1 | 1.00 | 1.00 | 2.47 | 5.40 | 1.27 | 1.13 | 1.27 | 2.40 | 3.80 |
time (sec) |
N/A | 0.236 | 0.028 | 0.496 | 0.111 | 0.076 | 9.567 | 0.123 | 0.162 | 28.618 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 33 | 30 | 58 | 36 | 134 | 0 | 53 | 57 | 0 |
N.S. |
1 | 0.94 | 0.86 | 1.66 | 1.03 | 3.83 | 0.00 | 1.51 | 1.63 | 0.00 |
time (sec) |
N/A | 0.394 | 0.076 | 0.512 | 0.086 | 0.075 | 0.000 | 0.114 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 65 | 50 | 99 | 67 | 313 | 0 | 70 | 94 | 0 |
N.S. |
1 | 0.98 | 0.76 | 1.50 | 1.02 | 4.74 | 0.00 | 1.06 | 1.42 | 0.00 |
time (sec) |
N/A | 0.353 | 0.118 | 1.922 | 0.086 | 0.077 | 0.000 | 0.119 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 85 | 67 | 120 | 110 | 587 | 0 | 103 | 124 | 0 |
N.S. |
1 | 0.96 | 0.75 | 1.35 | 1.24 | 6.60 | 0.00 | 1.16 | 1.39 | 0.00 |
time (sec) |
N/A | 0.776 | 0.126 | 17.254 | 0.107 | 0.087 | 0.000 | 0.126 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 41 | 30 | 58 | 37 | 134 | 0 | 56 | 58 | 0 |
N.S. |
1 | 1.17 | 0.86 | 1.66 | 1.06 | 3.83 | 0.00 | 1.60 | 1.66 | 0.00 |
time (sec) |
N/A | 0.398 | 0.061 | 0.459 | 0.083 | 0.073 | 0.000 | 0.110 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 65 | 50 | 99 | 67 | 305 | 0 | 71 | 94 | 0 |
N.S. |
1 | 0.98 | 0.76 | 1.50 | 1.02 | 4.62 | 0.00 | 1.08 | 1.42 | 0.00 |
time (sec) |
N/A | 0.323 | 0.097 | 1.825 | 0.085 | 0.091 | 0.000 | 0.132 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 84 | 66 | 120 | 111 | 587 | 0 | 106 | 125 | 0 |
N.S. |
1 | 0.95 | 0.75 | 1.36 | 1.26 | 6.67 | 0.00 | 1.20 | 1.42 | 0.00 |
time (sec) |
N/A | 0.703 | 0.192 | 26.044 | 0.110 | 0.082 | 0.000 | 0.115 | 0.163 | 0.000 |