Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 20 | 20 | 21 | 18 | 20 | 17 | 18 | 20 | 20 |
N.S. |
1 | 0.74 | 0.74 | 0.78 | 0.67 | 0.74 | 0.63 | 0.67 | 0.74 | 0.74 |
time (sec) |
N/A | 0.489 | 0.015 | 1.658 | 0.080 | 0.095 | 0.113 | 0.220 | 0.171 | 3.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | A | A | F(-1) | A | B | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 26 | 820 | 36 | 33 | 0 | 37 | 34 | 0 |
N.S. |
1 | 0.00 | 0.84 | 26.45 | 1.16 | 1.06 | 0.00 | 1.19 | 1.10 | 0.00 |
time (sec) |
N/A | 0.000 | 0.116 | 0.836 | 0.303 | 0.102 | 0.000 | 2.738 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 26 | 20 | 25 | 44 | 24 | 25 | 58 | 19 |
N.S. |
1 | 0.00 | 1.13 | 0.87 | 1.09 | 1.91 | 1.04 | 1.09 | 2.52 | 0.83 |
time (sec) |
N/A | 0.000 | 0.024 | 0.205 | 0.081 | 0.091 | 0.118 | 0.131 | 0.184 | 2.554 |
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 | 20 | 19 | 18 | 18 | 19 | 18 | 27 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.90 | 0.90 | 0.95 | 0.90 | 1.35 | 1.05 |
time (sec) |
N/A | 0.499 | 0.280 | 0.126 | 0.135 | 0.099 | 0.109 | 0.127 | 0.188 | 0.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 22 | 30 | 21 | 39 | 27 | 24 | 32 | 26 |
N.S. |
1 | 0.00 | 0.88 | 1.20 | 0.84 | 1.56 | 1.08 | 0.96 | 1.28 | 1.04 |
time (sec) |
N/A | 0.000 | 0.073 | 0.487 | 0.097 | 0.096 | 0.287 | 0.194 | 0.179 | 2.719 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 28 | 74 | 24 | 24 | 24 | 24 | 28 | 310 |
N.S. |
1 | 0.00 | 1.00 | 2.64 | 0.86 | 0.86 | 0.86 | 0.86 | 1.00 | 11.07 |
time (sec) |
N/A | 0.000 | 0.100 | 0.130 | 0.105 | 0.103 | 0.273 | 0.223 | 0.192 | 3.176 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | B | B | B | B | F | B | B |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 58 | 0 | 134 | 138 | 147 | 133 | 0 | 277 | 63 |
N.S. |
1 | 1.66 | 0.00 | 3.83 | 3.94 | 4.20 | 3.80 | 0.00 | 7.91 | 1.80 |
time (sec) |
N/A | 1.474 | 0.000 | 2.790 | 0.199 | 0.093 | 0.363 | 0.000 | 0.197 | 3.404 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 25 | 26 | 27 | 22 | 24 | 24 | 0 | 25 | 19 |
N.S. |
1 | 1.19 | 1.24 | 1.29 | 1.05 | 1.14 | 1.14 | 0.00 | 1.19 | 0.90 |
time (sec) |
N/A | 0.244 | 0.041 | 0.184 | 0.128 | 0.092 | 0.098 | 0.000 | 0.182 | 2.654 |
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 | 12 | 11 | 11 | 8 | 11 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 1.00 | 1.00 | 0.73 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.259 | 0.003 | 0.174 | 0.033 | 0.091 | 0.045 | 0.124 | 0.176 | 2.458 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 146 | 28 | 30 | 83 | 27 | 29 | 33 | 30 | 23 |
N.S. |
1 | 6.35 | 1.22 | 1.30 | 3.61 | 1.17 | 1.26 | 1.43 | 1.30 | 1.00 |
time (sec) |
N/A | 0.471 | 0.022 | 0.110 | 0.099 | 0.102 | 0.071 | 0.119 | 0.182 | 2.595 |
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 | 25 | 21 | 21 | 20 | 36 | 42 | 27 | 36 | 45 | 39 |
N.S. |
1 | 0.84 | 0.84 | 0.80 | 1.44 | 1.68 | 1.08 | 1.44 | 1.80 | 1.56 |
time (sec) |
N/A | 0.405 | 0.126 | 0.503 | 0.297 | 0.095 | 0.167 | 0.159 | 1.250 | 3.231 |
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 | 14 | 14 | 14 | 13 | 18 | 10 | 14 | 19 | 13 |
N.S. |
1 | 0.70 | 0.70 | 0.70 | 0.65 | 0.90 | 0.50 | 0.70 | 0.95 | 0.65 |
time (sec) |
N/A | 0.161 | 0.001 | 0.031 | 0.037 | 0.094 | 0.041 | 0.124 | 0.171 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 19 | 18 | 17 | 21 | 17 | 17 | 17 | 17 |
N.S. |
1 | 0.00 | 0.83 | 0.78 | 0.74 | 0.91 | 0.74 | 0.74 | 0.74 | 0.74 |
time (sec) |
N/A | 0.000 | 0.157 | 0.216 | 0.082 | 0.091 | 0.049 | 0.140 | 0.171 | 2.697 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 16 | 12 | 16 | 20 | 17 | 8 | 15 | 18 | 11 |
N.S. |
1 | 0.73 | 0.55 | 0.73 | 0.91 | 0.77 | 0.36 | 0.68 | 0.82 | 0.50 |
time (sec) |
N/A | 0.197 | 0.066 | 0.079 | 0.082 | 0.091 | 0.048 | 0.124 | 0.169 | 2.480 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 22 | 19 | 31 | 18 | 20 | 18 | 27 | 28 |
N.S. |
1 | 0.00 | 0.79 | 0.68 | 1.11 | 0.64 | 0.71 | 0.64 | 0.96 | 1.00 |
time (sec) |
N/A | 0.000 | 10.661 | 0.319 | 0.098 | 0.070 | 0.121 | 0.131 | 0.182 | 2.585 |
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 | 22 | 23 | 23 | 20 | 18 | 24 | 20 | 19 | 24 | 19 |
N.S. |
1 | 1.05 | 1.05 | 0.91 | 0.82 | 1.09 | 0.91 | 0.86 | 1.09 | 0.86 |
time (sec) |
N/A | 0.307 | 0.005 | 0.048 | 0.036 | 0.076 | 0.044 | 0.120 | 0.169 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 20 | 20 | 28 | 20 | 24 | 28 | 18 | 20 |
N.S. |
1 | 0.00 | 0.95 | 0.95 | 1.33 | 0.95 | 1.14 | 1.33 | 0.86 | 0.95 |
time (sec) |
N/A | 0.000 | 0.134 | 0.224 | 0.583 | 0.088 | 0.085 | 0.130 | 0.178 | 2.577 |
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 | 14 | 14 | 14 | 14 | 13 | 13 | 8 | 13 | 14 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.93 | 0.93 | 0.57 | 0.93 | 1.00 | 0.93 |
time (sec) |
N/A | 1.531 | 0.123 | 0.073 | 0.067 | 0.082 | 0.138 | 0.131 | 0.177 | 2.703 |
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 | 22 | 25 | 23 | 21 | 20 | 20 | 22 | 20 | 26 | 23 |
N.S. |
1 | 1.14 | 1.05 | 0.95 | 0.91 | 0.91 | 1.00 | 0.91 | 1.18 | 1.05 |
time (sec) |
N/A | 0.516 | 0.083 | 0.120 | 0.033 | 0.089 | 0.119 | 0.125 | 0.180 | 2.801 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 723 | 30 | 30 | 36 | 29 | 24 | 29 | 31 | 31 |
N.S. |
1 | 25.82 | 1.07 | 1.07 | 1.29 | 1.04 | 0.86 | 1.04 | 1.11 | 1.11 |
time (sec) |
N/A | 14.471 | 0.046 | 1.488 | 0.155 | 0.086 | 0.439 | 0.163 | 0.170 | 0.255 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 14 | 13 | 22 | 13 | 10 | 13 | 14 | 12 |
N.S. |
1 | 1.00 | 0.74 | 0.68 | 1.16 | 0.68 | 0.53 | 0.68 | 0.74 | 0.63 |
time (sec) |
N/A | 0.288 | 0.040 | 0.071 | 0.063 | 0.091 | 0.044 | 0.117 | 0.170 | 2.736 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 31 | 24 | 28 | 23 | 17 | 242 | 33 | 21 |
N.S. |
1 | 0.00 | 1.35 | 1.04 | 1.22 | 1.00 | 0.74 | 10.52 | 1.43 | 0.91 |
time (sec) |
N/A | 0.000 | 0.696 | 0.319 | 0.092 | 0.089 | 0.090 | 0.130 | 0.161 | 0.188 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 44 | 21 | 26 | 20 | 22 | 20 | 20 | 0 |
N.S. |
1 | 0.00 | 1.91 | 0.91 | 1.13 | 0.87 | 0.96 | 0.87 | 0.87 | 0.00 |
time (sec) |
N/A | 0.000 | 0.900 | 0.472 | 0.161 | 0.089 | 0.189 | 0.140 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 56 | 58 | 56 | 96 | 37 | 85 | 65 | 66 | 42 |
N.S. |
1 | 1.93 | 2.00 | 1.93 | 3.31 | 1.28 | 2.93 | 2.24 | 2.28 | 1.45 |
time (sec) |
N/A | 0.330 | 0.014 | 0.542 | 0.047 | 0.101 | 0.127 | 0.121 | 0.165 | 3.139 |
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 | 13 | 13 | 13 | 12 | 16 | 15 | 12 | 11 | 16 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 1.23 | 1.15 | 0.92 | 0.85 | 1.23 | 0.85 |
time (sec) |
N/A | 0.143 | 0.001 | 0.070 | 0.037 | 0.090 | 0.022 | 0.125 | 0.168 | 0.057 |
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 | 15 | 14 | 14 | 15 | 14 | 14 | 14 | 16 | 28 | 14 |
N.S. |
1 | 0.93 | 0.93 | 1.00 | 0.93 | 0.93 | 0.93 | 1.07 | 1.87 | 0.93 |
time (sec) |
N/A | 0.226 | 0.005 | 0.059 | 0.108 | 0.072 | 0.049 | 0.129 | 0.172 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 32 | 32 | 25 | 24 | 39 | 24 | 17 | 54 | 17 |
N.S. |
1 | 2.13 | 2.13 | 1.67 | 1.60 | 2.60 | 1.60 | 1.13 | 3.60 | 1.13 |
time (sec) |
N/A | 0.271 | 0.014 | 0.128 | 0.035 | 0.096 | 0.117 | 0.125 | 0.174 | 2.925 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 35 | 17 | 16 | 47 | 15 | 57 | 142 | 16 |
N.S. |
1 | 0.00 | 1.59 | 0.77 | 0.73 | 2.14 | 0.68 | 2.59 | 6.45 | 0.73 |
time (sec) |
N/A | 0.000 | 0.311 | 1.027 | 0.297 | 0.088 | 0.217 | 0.279 | 0.191 | 3.186 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 20 | 20 | 21 | 22 | 19 | 15 | 19 | 21 | 18 |
N.S. |
1 | 0.67 | 0.67 | 0.70 | 0.73 | 0.63 | 0.50 | 0.63 | 0.70 | 0.60 |
time (sec) |
N/A | 0.343 | 0.018 | 0.097 | 0.063 | 0.086 | 0.075 | 0.129 | 0.173 | 2.789 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 120 | 25 | 36 | 40 | 35 | 34 | 0 | 38 | 31 |
N.S. |
1 | 4.44 | 0.93 | 1.33 | 1.48 | 1.30 | 1.26 | 0.00 | 1.41 | 1.15 |
time (sec) |
N/A | 1.251 | 0.110 | 0.655 | 0.123 | 0.109 | 0.193 | 0.000 | 0.181 | 2.985 |
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 | 17 | 12 | 12 | 9 | 9 | 12 | 8 | 12 | 10 | 11 |
N.S. |
1 | 0.71 | 0.71 | 0.53 | 0.53 | 0.71 | 0.47 | 0.71 | 0.59 | 0.65 |
time (sec) |
N/A | 0.189 | 0.000 | 0.018 | 0.028 | 0.072 | 0.022 | 0.122 | 0.200 | 0.002 |
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 | 14 | 14 | 14 | 13 | 12 | 12 | 12 | 12 | 13 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.86 | 0.86 | 0.86 | 0.86 | 0.93 | 0.86 |
time (sec) |
N/A | 0.228 | 0.000 | 0.043 | 0.041 | 0.083 | 0.022 | 0.118 | 0.190 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | A | A | A | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 0 | 27 | 53 | 22 | 19 | 26 | 27 | 56 |
N.S. |
1 | 0.00 | 0.00 | 1.12 | 2.21 | 0.92 | 0.79 | 1.08 | 1.12 | 2.33 |
time (sec) |
N/A | 0.000 | 0.000 | 2.010 | 0.217 | 0.090 | 0.339 | 0.204 | 0.196 | 3.126 |
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 | 20 | 12 | 21 | 17 | 15 | 17 | 17 | 14 | 9 |
N.S. |
1 | 1.67 | 1.00 | 1.75 | 1.42 | 1.25 | 1.42 | 1.42 | 1.17 | 0.75 |
time (sec) |
N/A | 0.156 | 0.004 | 0.161 | 0.026 | 0.082 | 0.263 | 0.126 | 0.205 | 2.654 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 66 | 21 | 23 | 17 | 24 | 26 | 24 | 27 | 19 |
N.S. |
1 | 3.14 | 1.00 | 1.10 | 0.81 | 1.14 | 1.24 | 1.14 | 1.29 | 0.90 |
time (sec) |
N/A | 0.338 | 0.176 | 0.394 | 0.096 | 0.097 | 0.180 | 0.147 | 0.189 | 3.125 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 23 | 23 | 136 | 157 | 168 | 239 | 262 | 148 |
N.S. |
1 | 0.00 | 0.96 | 0.96 | 5.67 | 6.54 | 7.00 | 9.96 | 10.92 | 6.17 |
time (sec) |
N/A | 0.000 | 1.346 | 0.065 | 0.133 | 0.097 | 0.438 | 1.133 | 200.015 | 3.529 |
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 | 25 | 46 | 22 | 24 | 40 | 24 | 29 | 32 | 43 | 28 |
N.S. |
1 | 1.84 | 0.88 | 0.96 | 1.60 | 0.96 | 1.16 | 1.28 | 1.72 | 1.12 |
time (sec) |
N/A | 0.408 | 0.393 | 0.182 | 0.207 | 0.081 | 0.144 | 0.133 | 0.151 | 2.975 |
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 | 28 | 23 | 23 | 22 | 21 | 21 | 19 | 21 | 27 | 21 |
N.S. |
1 | 0.82 | 0.82 | 0.79 | 0.75 | 0.75 | 0.68 | 0.75 | 0.96 | 0.75 |
time (sec) |
N/A | 1.157 | 0.147 | 0.115 | 0.080 | 0.090 | 0.105 | 0.122 | 0.147 | 0.271 |
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 | 8 | 9 | 8 | 8 | 10 | 9 | 9 | 8 |
N.S. |
1 | 1.00 | 0.89 | 1.00 | 0.89 | 0.89 | 1.11 | 1.00 | 1.00 | 0.89 |
time (sec) |
N/A | 0.218 | 0.043 | 0.036 | 0.030 | 0.080 | 0.083 | 0.104 | 0.151 | 2.900 |
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 | 25 | 17 | 15 | 12 | 11 | 17 | 12 | 12 | 17 | 11 |
N.S. |
1 | 0.68 | 0.60 | 0.48 | 0.44 | 0.68 | 0.48 | 0.48 | 0.68 | 0.44 |
time (sec) |
N/A | 0.169 | 0.001 | 0.023 | 0.029 | 0.075 | 0.038 | 0.107 | 0.150 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | B | B | B | B | F | F | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 0 | 70 | 68 | 84 | 65 | 0 | 178 | 73 |
N.S. |
1 | 0.00 | 0.00 | 2.26 | 2.19 | 2.71 | 2.10 | 0.00 | 5.74 | 2.35 |
time (sec) |
N/A | 0.000 | 0.000 | 132.877 | 1.383 | 0.116 | 6.000 | 0.000 | 200.030 | 3.508 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 30 | 27 | 25 | 29 | 24 | 27 | 30 | 24 |
N.S. |
1 | 0.00 | 0.97 | 0.87 | 0.81 | 0.94 | 0.77 | 0.87 | 0.97 | 0.77 |
time (sec) |
N/A | 0.000 | 0.366 | 5.145 | 0.083 | 0.094 | 0.172 | 0.138 | 6.279 | 3.117 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 0 | 13 | 14 | 13 | 13 | 12 | 13 | 13 | 13 |
N.S. |
1 | 0.00 | 1.08 | 1.17 | 1.08 | 1.08 | 1.00 | 1.08 | 1.08 | 1.08 |
time (sec) |
N/A | 0.000 | 0.034 | 0.077 | 0.067 | 0.086 | 0.086 | 0.115 | 0.284 | 2.837 |
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 | 18 | 17 | 24 | 17 | 16 | 22 | 14 | 16 | 35 | 16 |
N.S. |
1 | 0.94 | 1.33 | 0.94 | 0.89 | 1.22 | 0.78 | 0.89 | 1.94 | 0.89 |
time (sec) |
N/A | 0.260 | 0.030 | 0.080 | 0.033 | 0.087 | 0.043 | 0.112 | 0.244 | 0.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 47 | 54 | 0 | 43 | 48 | 66 | 55 | 49 |
N.S. |
1 | 0.00 | 1.34 | 1.54 | 0.00 | 1.23 | 1.37 | 1.89 | 1.57 | 1.40 |
time (sec) |
N/A | 0.000 | 4.571 | 1.174 | 0.000 | 0.088 | 0.138 | 0.112 | 0.201 | 2.905 |
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 | 10 | 10 | 8 | 9 | 7 | 8 | 9 | 8 | 7 |
N.S. |
1 | 0.83 | 0.83 | 0.67 | 0.75 | 0.58 | 0.67 | 0.75 | 0.67 | 0.58 |
time (sec) |
N/A | 0.231 | 0.001 | 0.031 | 0.025 | 0.090 | 0.024 | 0.116 | 0.224 | 0.121 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 57 | 29 | 30 | 115 | 35 | 34 | 80 | 37 | 34 |
N.S. |
1 | 1.97 | 1.00 | 1.03 | 3.97 | 1.21 | 1.17 | 2.76 | 1.28 | 1.17 |
time (sec) |
N/A | 0.597 | 0.019 | 0.124 | 0.194 | 0.090 | 0.082 | 0.112 | 0.266 | 0.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 30 | 17 | 30 | 0 | 29 | 44 | 64 | 32 | 16 |
N.S. |
1 | 1.76 | 1.00 | 1.76 | 0.00 | 1.71 | 2.59 | 3.76 | 1.88 | 0.94 |
time (sec) |
N/A | 0.334 | 0.015 | 0.208 | 0.000 | 0.084 | 0.156 | 0.109 | 0.247 | 2.887 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 27 | 25 | 0 | 24 | 26 | 24 | 45 | 24 |
N.S. |
1 | 0.00 | 1.23 | 1.14 | 0.00 | 1.09 | 1.18 | 1.09 | 2.05 | 1.09 |
time (sec) |
N/A | 0.000 | 0.444 | 0.132 | 0.000 | 0.091 | 0.123 | 0.148 | 0.207 | 0.108 |
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 | 16 | 16 | 16 | 15 | 15 | 14 | 15 | 21 | 16 |
N.S. |
1 | 0.80 | 0.80 | 0.80 | 0.75 | 0.75 | 0.70 | 0.75 | 1.05 | 0.80 |
time (sec) |
N/A | 0.293 | 0.021 | 0.058 | 0.032 | 0.090 | 0.045 | 0.103 | 0.192 | 2.734 |
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 | 21 | 26 | 27 | 20 | 24 | 24 | 26 | 24 | 19 | 19 |
N.S. |
1 | 1.24 | 1.29 | 0.95 | 1.14 | 1.14 | 1.24 | 1.14 | 0.90 | 0.90 |
time (sec) |
N/A | 0.171 | 0.001 | 0.040 | 0.034 | 0.078 | 0.020 | 0.105 | 0.257 | 0.034 |
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 | 26 | 35 | 24 | 24 | 24 | 38 | 20 | 22 | 56 | 22 |
N.S. |
1 | 1.35 | 0.92 | 0.92 | 0.92 | 1.46 | 0.77 | 0.85 | 2.15 | 0.85 |
time (sec) |
N/A | 0.800 | 0.092 | 0.393 | 0.099 | 0.094 | 0.116 | 0.126 | 0.273 | 2.888 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 27 | 25 | 24 | 157 | 26 | 0 | 29 | 26 |
N.S. |
1 | 0.00 | 0.84 | 0.78 | 0.75 | 4.91 | 0.81 | 0.00 | 0.91 | 0.81 |
time (sec) |
N/A | 0.000 | 0.085 | 0.158 | 0.562 | 0.107 | 0.608 | 0.000 | 0.392 | 3.301 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 17 | 17 | 25 | 19 | 15 | 0 | 118 | 15 |
N.S. |
1 | 0.00 | 0.89 | 0.89 | 1.32 | 1.00 | 0.79 | 0.00 | 6.21 | 0.79 |
time (sec) |
N/A | 0.000 | 1.835 | 1.029 | 0.254 | 0.089 | 0.255 | 0.000 | 0.244 | 2.831 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 295 | 25 | 31 | 1272 | 42 | 31 | 55 | 61 | 29 |
N.S. |
1 | 10.54 | 0.89 | 1.11 | 45.43 | 1.50 | 1.11 | 1.96 | 2.18 | 1.04 |
time (sec) |
N/A | 3.031 | 2.938 | 1.901 | 0.244 | 0.088 | 0.137 | 0.148 | 0.290 | 0.804 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 33 | 36 | 60 | 55 | 32 | 284 | 67 | 0 |
N.S. |
1 | 0.00 | 1.22 | 1.33 | 2.22 | 2.04 | 1.19 | 10.52 | 2.48 | 0.00 |
time (sec) |
N/A | 0.000 | 0.128 | 0.032 | 0.125 | 0.100 | 0.136 | 0.195 | 0.268 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 0 | 17 | 28 | 26 | 31 | 20 | 353 | 22 |
N.S. |
1 | 0.00 | 0.00 | 0.74 | 1.22 | 1.13 | 1.35 | 0.87 | 15.35 | 0.96 |
time (sec) |
N/A | 0.000 | 0.000 | 1.811 | 0.162 | 0.103 | 0.428 | 0.147 | 0.400 | 3.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 54 | 29 | 21 | 0 | 20 | 22 | 20 | 23 | 22 |
N.S. |
1 | 1.74 | 0.94 | 0.68 | 0.00 | 0.65 | 0.71 | 0.65 | 0.74 | 0.71 |
time (sec) |
N/A | 0.487 | 0.114 | 0.142 | 0.000 | 0.113 | 0.084 | 0.121 | 0.306 | 2.697 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | A | B | B | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 48 | 73 | 49 | 49 | 46 | 72 | 0 | 0 |
N.S. |
1 | 0.00 | 1.55 | 2.35 | 1.58 | 1.58 | 1.48 | 2.32 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 10.065 | 0.288 | 0.100 | 0.100 | 0.371 | 0.586 | 0.434 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 40 | 69 | 74 | 74 | 112 | 758 | 202 | 175 |
N.S. |
1 | 0.00 | 1.38 | 2.38 | 2.55 | 2.55 | 3.86 | 26.14 | 6.97 | 6.03 |
time (sec) |
N/A | 0.000 | 5.951 | 2.128 | 1.210 | 0.086 | 0.207 | 6.976 | 200.030 | 2.845 |
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 | 24 | 25 | 24 | 32 | 162 | 29 | 29 | 31 | 99 | 29 |
N.S. |
1 | 1.04 | 1.00 | 1.33 | 6.75 | 1.21 | 1.21 | 1.29 | 4.12 | 1.21 |
time (sec) |
N/A | 0.615 | 0.049 | 2.172 | 0.193 | 0.093 | 0.124 | 0.139 | 0.190 | 3.138 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 21 | 15 | 25 | 25 | 14 | 25 | 31 | 16 |
N.S. |
1 | 0.00 | 1.00 | 0.71 | 1.19 | 1.19 | 0.67 | 1.19 | 1.48 | 0.76 |
time (sec) |
N/A | 0.000 | 0.731 | 0.115 | 0.075 | 0.086 | 0.060 | 0.126 | 0.187 | 2.645 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 47 | 51 | 35 | 0 | 37 | 31 | 122 | 49 | 42 |
N.S. |
1 | 1.47 | 1.59 | 1.09 | 0.00 | 1.16 | 0.97 | 3.81 | 1.53 | 1.31 |
time (sec) |
N/A | 3.352 | 0.244 | 1.115 | 0.000 | 0.092 | 0.144 | 0.143 | 0.175 | 0.227 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 42 | 38 | 43 | 79 | 68 | 78 | 39 | 108 | 42 |
N.S. |
1 | 1.35 | 1.23 | 1.39 | 2.55 | 2.19 | 2.52 | 1.26 | 3.48 | 1.35 |
time (sec) |
N/A | 0.430 | 0.029 | 0.270 | 0.034 | 0.087 | 0.975 | 0.124 | 0.178 | 2.771 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 98 | 50 | 17 | 245 | 20 | 20 | 202 | 27 | 21 |
N.S. |
1 | 5.16 | 2.63 | 0.89 | 12.89 | 1.05 | 1.05 | 10.63 | 1.42 | 1.11 |
time (sec) |
N/A | 0.324 | 0.021 | 0.184 | 0.039 | 0.073 | 0.072 | 0.120 | 0.178 | 0.089 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 426 | 28 | 265 | 716 | 39 | 49 | 217 | 64 | 24 |
N.S. |
1 | 15.78 | 1.04 | 9.81 | 26.52 | 1.44 | 1.81 | 8.04 | 2.37 | 0.89 |
time (sec) |
N/A | 8.107 | 0.130 | 0.033 | 0.216 | 0.102 | 0.199 | 2.654 | 0.184 | 3.369 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 22 | 20 | 19 | 19 | 19 | 19 | 30 | 72 |
N.S. |
1 | 0.00 | 0.92 | 0.83 | 0.79 | 0.79 | 0.79 | 0.79 | 1.25 | 3.00 |
time (sec) |
N/A | 0.000 | 0.288 | 0.369 | 0.067 | 0.089 | 0.079 | 0.174 | 0.184 | 2.876 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 31 | 31 | 25 | 33 | 50 | 26 | 45 | 35 | 28 |
N.S. |
1 | 1.19 | 1.19 | 0.96 | 1.27 | 1.92 | 1.00 | 1.73 | 1.35 | 1.08 |
time (sec) |
N/A | 0.510 | 0.044 | 0.075 | 0.074 | 0.107 | 0.112 | 0.131 | 0.185 | 0.206 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 23 | 28 | 44 | 36 | 53 | 36 | 38 | 31 |
N.S. |
1 | 0.00 | 0.92 | 1.12 | 1.76 | 1.44 | 2.12 | 1.44 | 1.52 | 1.24 |
time (sec) |
N/A | 0.000 | 0.193 | 17.468 | 0.176 | 0.088 | 0.131 | 0.142 | 0.195 | 2.875 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 32 | 34 | 33 | 26 | 34 | 33 | 33 | 33 |
N.S. |
1 | 0.00 | 1.68 | 1.79 | 1.74 | 1.37 | 1.79 | 1.74 | 1.74 | 1.74 |
time (sec) |
N/A | 0.000 | 0.092 | 0.171 | 0.159 | 0.089 | 0.158 | 0.129 | 0.182 | 2.879 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 34 | 33 | 54 | 28 | 26 | 0 | 50 | 134 |
N.S. |
1 | 0.00 | 1.10 | 1.06 | 1.74 | 0.90 | 0.84 | 0.00 | 1.61 | 4.32 |
time (sec) |
N/A | 0.000 | 0.091 | 23.148 | 0.179 | 0.108 | 0.651 | 0.000 | 0.204 | 3.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 43 | 40 | 36 | 41 | 37 | 36 | 43 | 40 |
N.S. |
1 | 0.00 | 1.39 | 1.29 | 1.16 | 1.32 | 1.19 | 1.16 | 1.39 | 1.29 |
time (sec) |
N/A | 0.000 | 0.049 | 57.142 | 0.135 | 0.088 | 0.431 | 0.951 | 0.192 | 3.749 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 33 | 31 | 30 | 30 | 27 | 0 | 33 | 30 |
N.S. |
1 | 0.00 | 1.06 | 1.00 | 0.97 | 0.97 | 0.87 | 0.00 | 1.06 | 0.97 |
time (sec) |
N/A | 0.000 | 0.267 | 0.050 | 0.171 | 0.113 | 6.666 | 0.000 | 0.211 | 3.605 |
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 | 17 | 14 | 12 | 13 | 13 | 11 | 12 | 13 | 15 | 11 |
N.S. |
1 | 0.82 | 0.71 | 0.76 | 0.76 | 0.65 | 0.71 | 0.76 | 0.88 | 0.65 |
time (sec) |
N/A | 0.183 | 0.009 | 0.060 | 0.027 | 0.099 | 0.052 | 0.118 | 0.189 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 19 | 19 | 77 | 26 | 17 | 181 | 20 | 19 |
N.S. |
1 | 1.00 | 1.06 | 1.06 | 4.28 | 1.44 | 0.94 | 10.06 | 1.11 | 1.06 |
time (sec) |
N/A | 0.292 | 0.021 | 0.230 | 0.094 | 0.082 | 0.084 | 0.158 | 0.181 | 2.742 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 26 | 22 | 29 | 30 | 26 | 22 | 31 | 27 | 43 |
N.S. |
1 | 0.72 | 0.61 | 0.81 | 0.83 | 0.72 | 0.61 | 0.86 | 0.75 | 1.19 |
time (sec) |
N/A | 0.564 | 0.019 | 0.561 | 0.175 | 0.094 | 0.089 | 0.192 | 0.180 | 3.061 |
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 | 15 | 17 | 16 | 17 | 17 | 22 | 14 | 16 | 20 | 17 |
N.S. |
1 | 1.13 | 1.07 | 1.13 | 1.13 | 1.47 | 0.93 | 1.07 | 1.33 | 1.13 |
time (sec) |
N/A | 0.188 | 0.002 | 0.037 | 0.044 | 0.075 | 0.036 | 0.122 | 0.190 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | C | F(-2) | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 0 | 25 | 0 | 0 | 22 | 23 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.86 | 0.00 | 0.00 | 0.76 | 0.79 | 0.00 |
time (sec) |
N/A | 1.142 | 0.085 | 0.000 | 0.383 | 0.000 | 0.000 | 0.170 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 50 | 51 | 45 | 49 | 29 | 30 | 48 | 32 |
N.S. |
1 | 0.00 | 1.79 | 1.82 | 1.61 | 1.75 | 1.04 | 1.07 | 1.71 | 1.14 |
time (sec) |
N/A | 0.000 | 0.043 | 17.873 | 0.082 | 0.091 | 0.168 | 0.429 | 21.177 | 2.839 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 27 | 29 | 27 | 28 | 26 | 0 | 28 | 199 |
N.S. |
1 | 0.00 | 0.96 | 1.04 | 0.96 | 1.00 | 0.93 | 0.00 | 1.00 | 7.11 |
time (sec) |
N/A | 0.000 | 0.062 | 0.125 | 0.180 | 0.093 | 0.189 | 0.000 | 0.246 | 3.604 |
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 | 13 | 11 | 11 | 10 | 9 | 9 | 7 | 11 | 9 | 8 |
N.S. |
1 | 0.85 | 0.85 | 0.77 | 0.69 | 0.69 | 0.54 | 0.85 | 0.69 | 0.62 |
time (sec) |
N/A | 0.241 | 0.003 | 0.042 | 0.024 | 0.077 | 0.041 | 0.122 | 0.202 | 2.610 |
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 | 27 | 23 | 22 | 24 | 22 | 22 | 21 | 27 | 21 |
N.S. |
1 | 1.17 | 1.00 | 0.96 | 1.04 | 0.96 | 0.96 | 0.91 | 1.17 | 0.91 |
time (sec) |
N/A | 0.330 | 0.002 | 0.077 | 0.031 | 0.076 | 0.111 | 0.124 | 0.192 | 2.602 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 43 | 50 | 0 | 60 | 49 | 98 | 65 | 81 |
N.S. |
1 | 0.00 | 1.23 | 1.43 | 0.00 | 1.71 | 1.40 | 2.80 | 1.86 | 2.31 |
time (sec) |
N/A | 0.000 | 0.068 | 1.808 | 0.000 | 0.086 | 0.149 | 0.182 | 0.197 | 2.883 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F(-1) | B | B | B | B | F | B |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 25 | 0 | 114 | 114 | 110 | 114 | 280 | 114 |
N.S. |
1 | 0.00 | 1.00 | 0.00 | 4.56 | 4.56 | 4.40 | 4.56 | 11.20 | 4.56 |
time (sec) |
N/A | 0.000 | 5.789 | 0.000 | 0.193 | 0.090 | 0.188 | 0.900 | 200.033 | 2.909 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 83 | 71 | 34 | 45 | 35 | 27 | 0 | 33 | 31 |
N.S. |
1 | 3.46 | 2.96 | 1.42 | 1.88 | 1.46 | 1.12 | 0.00 | 1.38 | 1.29 |
time (sec) |
N/A | 0.746 | 0.044 | 0.359 | 0.084 | 0.087 | 0.085 | 0.000 | 0.198 | 2.707 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 29 | 22 | 21 | 21 | 17 | 26 | 21 | 194 |
N.S. |
1 | 0.00 | 1.53 | 1.16 | 1.11 | 1.11 | 0.89 | 1.37 | 1.11 | 10.21 |
time (sec) |
N/A | 0.000 | 0.292 | 2.102 | 0.158 | 0.084 | 0.093 | 0.169 | 0.192 | 3.102 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 136 | 27 | 36 | 47 | 37 | 36 | 38 | 44 | 0 |
N.S. |
1 | 5.67 | 1.12 | 1.50 | 1.96 | 1.54 | 1.50 | 1.58 | 1.83 | 0.00 |
time (sec) |
N/A | 2.624 | 5.093 | 18.314 | 0.179 | 0.092 | 0.407 | 0.139 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 24 | 25 | 23 | 47 | 19 | 0 | 29 | 24 |
N.S. |
1 | 0.00 | 0.96 | 1.00 | 0.92 | 1.88 | 0.76 | 0.00 | 1.16 | 0.96 |
time (sec) |
N/A | 0.000 | 0.196 | 0.339 | 0.327 | 0.096 | 0.182 | 0.000 | 0.238 | 2.777 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 26 | 24 | 24 | 37 | 20 | 0 | 28 | 24 |
N.S. |
1 | 0.00 | 1.04 | 0.96 | 0.96 | 1.48 | 0.80 | 0.00 | 1.12 | 0.96 |
time (sec) |
N/A | 0.000 | 0.142 | 0.124 | 0.503 | 0.079 | 5.911 | 0.000 | 8.176 | 3.265 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 65 | 26 | 33 | 0 | 23 | 31 | 20 | 29 | 20 |
N.S. |
1 | 2.50 | 1.00 | 1.27 | 0.00 | 0.88 | 1.19 | 0.77 | 1.12 | 0.77 |
time (sec) |
N/A | 0.385 | 0.050 | 0.386 | 0.000 | 0.098 | 0.245 | 0.122 | 0.192 | 2.700 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 59 | 49 | 36 | 33 | 33 | 41 | 33 | 57 | 38 |
N.S. |
1 | 3.11 | 2.58 | 1.89 | 1.74 | 1.74 | 2.16 | 1.74 | 3.00 | 2.00 |
time (sec) |
N/A | 0.315 | 0.228 | 0.256 | 0.039 | 0.080 | 0.075 | 0.122 | 0.220 | 0.090 |
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 | 10 | 10 | 11 | 12 | 13 | 7 | 17 | 13 | 10 |
N.S. |
1 | 0.91 | 0.91 | 1.00 | 1.09 | 1.18 | 0.64 | 1.55 | 1.18 | 0.91 |
time (sec) |
N/A | 0.148 | 0.002 | 0.021 | 0.029 | 0.080 | 0.030 | 0.119 | 0.202 | 0.023 |
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 | 22 | 32 | 29 | 32 | 41 | 38 | 31 | 31 | 61 | 28 |
N.S. |
1 | 1.45 | 1.32 | 1.45 | 1.86 | 1.73 | 1.41 | 1.41 | 2.77 | 1.27 |
time (sec) |
N/A | 0.295 | 0.529 | 0.169 | 0.032 | 0.092 | 0.055 | 0.118 | 0.190 | 2.560 |
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 | 21 | 20 | 20 | 21 | 20 | 20 | 17 | 21 | 20 | 20 |
N.S. |
1 | 0.95 | 0.95 | 1.00 | 0.95 | 0.95 | 0.81 | 1.00 | 0.95 | 0.95 |
time (sec) |
N/A | 0.251 | 0.006 | 0.043 | 0.034 | 0.087 | 0.055 | 0.124 | 0.202 | 2.578 |
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 | 23 | 21 | 24 | 22 | 22 | 22 | 26 | 26 | 23 |
N.S. |
1 | 1.15 | 1.05 | 1.20 | 1.10 | 1.10 | 1.10 | 1.30 | 1.30 | 1.15 |
time (sec) |
N/A | 0.444 | 0.078 | 0.165 | 0.154 | 0.081 | 0.151 | 0.134 | 0.212 | 4.820 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 24 | 33 | 28 | 32 | 31 | 35 | 35 | 0 |
N.S. |
1 | 0.00 | 0.77 | 1.06 | 0.90 | 1.03 | 1.00 | 1.13 | 1.13 | 0.00 |
time (sec) |
N/A | 0.000 | 0.222 | 0.630 | 0.155 | 0.096 | 0.095 | 0.292 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 30 | 22 | 20 | 31 | 19 | 17 | 24 | 21 | 19 |
N.S. |
1 | 1.50 | 1.10 | 1.00 | 1.55 | 0.95 | 0.85 | 1.20 | 1.05 | 0.95 |
time (sec) |
N/A | 0.267 | 0.061 | 0.073 | 0.068 | 0.086 | 0.055 | 0.116 | 0.184 | 0.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | A | B | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 50 | 69 | 123 | 104 | 44 | 1618 | 0 | 0 |
N.S. |
1 | 0.00 | 1.43 | 1.97 | 3.51 | 2.97 | 1.26 | 46.23 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.161 | 0.132 | 0.249 | 0.100 | 0.218 | 1.224 | 0.303 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | B | B | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 54 | 433 | 97 | 66 | 31 | 53 | 54 | 0 |
N.S. |
1 | 0.00 | 1.69 | 13.53 | 3.03 | 2.06 | 0.97 | 1.66 | 1.69 | 0.00 |
time (sec) |
N/A | 0.000 | 0.704 | 0.025 | 0.130 | 0.097 | 0.644 | 0.578 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 28 | 29 | 54 | 30 | 63 | 65 | 50 | 24 |
N.S. |
1 | 0.00 | 0.93 | 0.97 | 1.80 | 1.00 | 2.10 | 2.17 | 1.67 | 0.80 |
time (sec) |
N/A | 0.000 | 0.106 | 0.961 | 0.160 | 0.092 | 0.089 | 0.300 | 0.189 | 3.121 |