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 | B | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 56 | 22 | 13 | 57 | 12 | 12 | 12 | 12 | 12 |
N.S. |
1 | 4.00 | 1.57 | 0.93 | 4.07 | 0.86 | 0.86 | 0.86 | 0.86 | 0.86 |
time (sec) |
N/A | 0.276 | 0.029 | 0.406 | 0.029 | 0.086 | 0.071 | 0.113 | 0.162 | 2.809 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | F | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 0 | 37 | 30 | 34 | 22 | 0 | 35 | 28 |
N.S. |
1 | 0.00 | 0.00 | 1.03 | 0.83 | 0.94 | 0.61 | 0.00 | 0.97 | 0.78 |
time (sec) |
N/A | 0.000 | 0.000 | 1.174 | 0.241 | 0.091 | 0.255 | 0.000 | 0.169 | 2.995 |
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 | 28 | 28 | 28 | 0 | 29 | 44 | 31 | 63 | 29 |
N.S. |
1 | 0.90 | 0.90 | 0.90 | 0.00 | 0.94 | 1.42 | 1.00 | 2.03 | 0.94 |
time (sec) |
N/A | 0.445 | 0.074 | 0.377 | 0.000 | 0.096 | 0.288 | 0.122 | 0.159 | 3.022 |
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 | 18 | 18 | 18 | 18 | 40 | 19 | 19 | 19 | 27 | 21 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 2.22 | 1.06 | 1.06 | 1.06 | 1.50 | 1.17 |
time (sec) |
N/A | 0.206 | 0.027 | 0.415 | 0.031 | 0.085 | 0.076 | 0.117 | 0.161 | 2.838 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | C | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 89 | 80 | 62 | 457 | 82 | 80 | 105 | 124 | 52 |
N.S. |
1 | 3.71 | 3.33 | 2.58 | 19.04 | 3.42 | 3.33 | 4.38 | 5.17 | 2.17 |
time (sec) |
N/A | 0.361 | 0.049 | 3.611 | 0.173 | 0.092 | 0.266 | 0.122 | 0.164 | 2.939 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 26 | 26 | 27 | 25 | 29 | 27 | 29 | 26 | 0 |
N.S. |
1 | 0.96 | 0.96 | 1.00 | 0.93 | 1.07 | 1.00 | 1.07 | 0.96 | 0.00 |
time (sec) |
N/A | 0.558 | 0.105 | 0.585 | 0.063 | 0.080 | 0.075 | 0.123 | 0.164 | 0.000 |
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 | 17 | 17 | 17 | 15 | 14 | 14 | 14 | 0 | 17 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.82 | 0.82 | 0.82 | 0.00 | 1.00 | 0.88 |
time (sec) |
N/A | 0.175 | 0.009 | 0.178 | 0.069 | 0.082 | 0.092 | 0.000 | 0.170 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 72 | 23 | 30 | 0 | 28 | 26 | 0 | 50 | 0 |
N.S. |
1 | 3.00 | 0.96 | 1.25 | 0.00 | 1.17 | 1.08 | 0.00 | 2.08 | 0.00 |
time (sec) |
N/A | 0.672 | 0.196 | 0.907 | 0.000 | 0.095 | 0.212 | 0.000 | 0.167 | 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 | 24 | 28 | 25 | 27 | 27 | 46 | 20 | 27 | 50 | 25 |
N.S. |
1 | 1.17 | 1.04 | 1.12 | 1.12 | 1.92 | 0.83 | 1.12 | 2.08 | 1.04 |
time (sec) |
N/A | 0.327 | 0.020 | 0.085 | 0.027 | 0.075 | 0.069 | 0.116 | 0.160 | 0.058 |
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 | 12 | 12 | 9 | 8 | 8 | 7 | 8 | 9 | 8 |
N.S. |
1 | 1.33 | 1.33 | 1.00 | 0.89 | 0.89 | 0.78 | 0.89 | 1.00 | 0.89 |
time (sec) |
N/A | 0.134 | 0.001 | 0.064 | 0.025 | 0.078 | 0.024 | 0.110 | 0.163 | 2.871 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 125 | 49 | 47 | 74 | 96 | 87 | 80 | 37 | 187 |
N.S. |
1 | 5.00 | 1.96 | 1.88 | 2.96 | 3.84 | 3.48 | 3.20 | 1.48 | 7.48 |
time (sec) |
N/A | 0.598 | 0.025 | 0.639 | 0.029 | 0.093 | 2.588 | 0.119 | 0.163 | 3.465 |
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 | 16 | 0 | 10 | 9 | 8 | 10 | 10 | 10 | 10 | 8 |
N.S. |
1 | 0.00 | 0.62 | 0.56 | 0.50 | 0.62 | 0.62 | 0.62 | 0.62 | 0.50 |
time (sec) |
N/A | 0.000 | 0.027 | 0.263 | 0.065 | 0.087 | 0.066 | 0.115 | 0.163 | 3.144 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 63 | 33 | 37 | 336 | 39 | 379 | 39 | 339 | 49 |
N.S. |
1 | 2.52 | 1.32 | 1.48 | 13.44 | 1.56 | 15.16 | 1.56 | 13.56 | 1.96 |
time (sec) |
N/A | 0.393 | 0.023 | 1.020 | 0.364 | 0.099 | 1.393 | 0.176 | 0.168 | 6.391 |
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 | 35 | 35 | 24 | 49 | 33 | 20 | 34 | 36 | 23 |
N.S. |
1 | 1.30 | 1.30 | 0.89 | 1.81 | 1.22 | 0.74 | 1.26 | 1.33 | 0.85 |
time (sec) |
N/A | 0.218 | 0.018 | 0.276 | 0.028 | 0.108 | 0.074 | 0.122 | 0.165 | 2.952 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 318 | 23 | 454 | 449 | 456 | 0 | 631 | 631 | 461 |
N.S. |
1 | 14.45 | 1.05 | 20.64 | 20.41 | 20.73 | 0.00 | 28.68 | 28.68 | 20.95 |
time (sec) |
N/A | 1.796 | 0.035 | 1.249 | 0.041 | 0.105 | 0.000 | 0.121 | 0.162 | 3.495 |
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 | 174 | 27 | 29 | 45 | 26 | 26 | 39 | 27 | 27 |
N.S. |
1 | 6.21 | 0.96 | 1.04 | 1.61 | 0.93 | 0.93 | 1.39 | 0.96 | 0.96 |
time (sec) |
N/A | 1.070 | 0.200 | 1.527 | 0.150 | 0.091 | 0.099 | 0.121 | 0.163 | 2.980 |
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 | 24 | 24 | 24 | 23 | 23 | 24 | 23 | 31 | 26 |
N.S. |
1 | 1.04 | 1.04 | 1.04 | 1.00 | 1.00 | 1.04 | 1.00 | 1.35 | 1.13 |
time (sec) |
N/A | 0.322 | 0.296 | 0.194 | 0.030 | 0.107 | 0.101 | 0.119 | 1.184 | 3.007 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 55 | 44 | 36 | 52 | 41 | 44 | 0 | 56 | 45 |
N.S. |
1 | 1.96 | 1.57 | 1.29 | 1.86 | 1.46 | 1.57 | 0.00 | 2.00 | 1.61 |
time (sec) |
N/A | 0.449 | 0.509 | 0.524 | 0.148 | 0.084 | 0.094 | 0.000 | 0.167 | 2.949 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 26 | 23 | 56 | 56 | 105 | 56 | 72 | 250 |
N.S. |
1 | 0.00 | 1.37 | 1.21 | 2.95 | 2.95 | 5.53 | 2.95 | 3.79 | 13.16 |
time (sec) |
N/A | 0.000 | 0.158 | 4.417 | 0.295 | 0.095 | 0.125 | 0.175 | 0.168 | 3.174 |
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 | 32 | 35 | 29 | 34 | 32 | 42 | 37 | 34 |
N.S. |
1 | 0.00 | 1.28 | 1.40 | 1.16 | 1.36 | 1.28 | 1.68 | 1.48 | 1.36 |
time (sec) |
N/A | 0.000 | 0.073 | 55.459 | 0.203 | 0.109 | 0.339 | 0.303 | 0.163 | 0.215 |
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 | 22 | 18 | 16 | 15 | 15 | 12 | 15 | 16 | 15 |
N.S. |
1 | 1.10 | 0.90 | 0.80 | 0.75 | 0.75 | 0.60 | 0.75 | 0.80 | 0.75 |
time (sec) |
N/A | 0.186 | 0.006 | 0.239 | 0.025 | 0.097 | 0.054 | 0.109 | 0.170 | 3.040 |
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 | 30 | 0 | 26 | 31 | 34 | 34 | 34 | 44 | 30 | 0 |
N.S. |
1 | 0.00 | 0.87 | 1.03 | 1.13 | 1.13 | 1.13 | 1.47 | 1.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.053 | 1.309 | 0.158 | 0.102 | 12.620 | 0.126 | 0.168 | 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 | 27 | 0 | 31 | 29 | 31 | 31 | 32 | 24 | 37 | 28 |
N.S. |
1 | 0.00 | 1.15 | 1.07 | 1.15 | 1.15 | 1.19 | 0.89 | 1.37 | 1.04 |
time (sec) |
N/A | 0.000 | 0.297 | 2.660 | 0.160 | 0.091 | 0.078 | 0.129 | 0.160 | 2.913 |
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 | 21 | 16 | 15 | 14 | 14 | 15 | 14 | 17 | 14 |
N.S. |
1 | 1.24 | 0.94 | 0.88 | 0.82 | 0.82 | 0.88 | 0.82 | 1.00 | 0.82 |
time (sec) |
N/A | 0.182 | 0.001 | 0.131 | 0.025 | 0.073 | 0.020 | 0.111 | 0.161 | 0.016 |
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 | 32 | 56 | 29 | 28 | 26 | 27 | 26 | 27 | 43 | 26 |
N.S. |
1 | 1.75 | 0.91 | 0.88 | 0.81 | 0.84 | 0.81 | 0.84 | 1.34 | 0.81 |
time (sec) |
N/A | 0.235 | 0.044 | 0.271 | 0.028 | 0.107 | 0.058 | 0.115 | 0.902 | 2.982 |
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 | 21 | 0 | 19 | 20 | 19 | 19 | 17 | 0 | 24 | 17 |
N.S. |
1 | 0.00 | 0.90 | 0.95 | 0.90 | 0.90 | 0.81 | 0.00 | 1.14 | 0.81 |
time (sec) |
N/A | 0.000 | 1.863 | 1.546 | 0.133 | 0.093 | 0.410 | 0.000 | 0.161 | 3.175 |
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 | 19 | 27 | 18 | 16 | 17 | 17 | 22 | 16 | 22 | 17 |
N.S. |
1 | 1.42 | 0.95 | 0.84 | 0.89 | 0.89 | 1.16 | 0.84 | 1.16 | 0.89 |
time (sec) |
N/A | 0.240 | 0.006 | 0.132 | 0.055 | 0.086 | 0.114 | 0.114 | 0.160 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 25 | 40 | 63 | 51 | 39 | 0 | 81 | 67 |
N.S. |
1 | 0.00 | 0.89 | 1.43 | 2.25 | 1.82 | 1.39 | 0.00 | 2.89 | 2.39 |
time (sec) |
N/A | 0.000 | 0.593 | 0.337 | 0.290 | 0.096 | 0.118 | 0.000 | 0.187 | 2.984 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 20 | 28 | 54 | 48 | 29 | 48 | 46 | 45 |
N.S. |
1 | 0.00 | 1.00 | 1.40 | 2.70 | 2.40 | 1.45 | 2.40 | 2.30 | 2.25 |
time (sec) |
N/A | 0.000 | 0.212 | 2.887 | 0.101 | 0.101 | 0.072 | 0.212 | 0.166 | 3.264 |
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 | 23 | 41 | 22 | 22 | 0 | 21 | 24 | 21 | 23 | 20 |
N.S. |
1 | 1.78 | 0.96 | 0.96 | 0.00 | 0.91 | 1.04 | 0.91 | 1.00 | 0.87 |
time (sec) |
N/A | 0.558 | 0.213 | 0.320 | 0.000 | 0.091 | 0.067 | 0.115 | 0.161 | 0.068 |
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 | 30 | 0 | 36 | 35 | 34 | 34 | 36 | 34 | 38 | 48 |
N.S. |
1 | 0.00 | 1.20 | 1.17 | 1.13 | 1.13 | 1.20 | 1.13 | 1.27 | 1.60 |
time (sec) |
N/A | 0.000 | 0.029 | 3.530 | 0.070 | 0.080 | 0.084 | 0.126 | 0.165 | 2.987 |
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 | 11 | 10 | 18 | 10 | 10 | 12 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 1.50 | 0.83 | 0.83 | 1.00 | 0.83 |
time (sec) |
N/A | 0.159 | 0.011 | 0.303 | 0.034 | 0.088 | 0.045 | 0.115 | 0.160 | 0.018 |
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 | 26 | 20 | 24 | 24 | 0 | 34 | 22 | 41 | 45 | 20 |
N.S. |
1 | 0.77 | 0.92 | 0.92 | 0.00 | 1.31 | 0.85 | 1.58 | 1.73 | 0.77 |
time (sec) |
N/A | 0.284 | 0.115 | 0.177 | 0.000 | 0.086 | 0.073 | 0.110 | 0.167 | 2.815 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 23 | 23 | 22 | 22 | 20 | 0 | 23 | 69 |
N.S. |
1 | 0.00 | 0.85 | 0.85 | 0.81 | 0.81 | 0.74 | 0.00 | 0.85 | 2.56 |
time (sec) |
N/A | 0.000 | 0.334 | 1.006 | 0.065 | 0.110 | 0.084 | 0.000 | 0.223 | 3.428 |
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 | 15 | 13 | 13 | 12 | 14 | 14 | 13 | 14 | 12 |
N.S. |
1 | 0.71 | 0.62 | 0.62 | 0.57 | 0.67 | 0.67 | 0.62 | 0.67 | 0.57 |
time (sec) |
N/A | 0.155 | 0.002 | 0.093 | 0.040 | 0.080 | 0.044 | 0.112 | 0.164 | 2.882 |
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 | 14 | 14 | 15 | 14 | 14 | 12 | 14 | 14 | 14 |
N.S. |
1 | 0.56 | 0.56 | 0.60 | 0.56 | 0.56 | 0.48 | 0.56 | 0.56 | 0.56 |
time (sec) |
N/A | 0.317 | 0.089 | 0.396 | 0.055 | 0.096 | 0.064 | 0.112 | 0.161 | 2.864 |
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 | 18 | 16 | 12 | 12 | 12 | 12 | 12 | 14 | 11 |
N.S. |
1 | 1.06 | 0.94 | 0.71 | 0.71 | 0.71 | 0.71 | 0.71 | 0.82 | 0.65 |
time (sec) |
N/A | 0.149 | 0.004 | 0.109 | 0.029 | 0.080 | 0.034 | 0.112 | 0.164 | 0.032 |
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 | 18 | 0 | 19 | 17 | 16 | 16 | 17 | 16 | 20 | 16 |
N.S. |
1 | 0.00 | 1.06 | 0.94 | 0.89 | 0.89 | 0.94 | 0.89 | 1.11 | 0.89 |
time (sec) |
N/A | 0.000 | 0.156 | 0.176 | 0.076 | 0.099 | 0.136 | 0.136 | 0.164 | 3.260 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 49 | 448 | 3013 | 77 | 73 | 326 | 188 | 331 |
N.S. |
1 | 0.00 | 1.75 | 16.00 | 107.61 | 2.75 | 2.61 | 11.64 | 6.71 | 11.82 |
time (sec) |
N/A | 0.000 | 0.236 | 1.934 | 2.801 | 0.093 | 0.876 | 1.490 | 0.173 | 3.557 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 1356 | 31 | 32 | 30 | 50 | 26 | 31 | 54 | 30 |
N.S. |
1 | 46.76 | 1.07 | 1.10 | 1.03 | 1.72 | 0.90 | 1.07 | 1.86 | 1.03 |
time (sec) |
N/A | 5.536 | 0.013 | 0.121 | 0.024 | 0.073 | 0.065 | 0.115 | 0.161 | 0.046 |
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 | 30 | 30 | 27 | 33 | 31 | 24 | 41 | 40 | 26 |
N.S. |
1 | 0.97 | 0.97 | 0.87 | 1.06 | 1.00 | 0.77 | 1.32 | 1.29 | 0.84 |
time (sec) |
N/A | 0.521 | 0.664 | 0.269 | 0.082 | 0.088 | 0.133 | 0.122 | 0.167 | 2.952 |
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 | 32 | 0 | 31 | 32 | 51 | 51 | 29 | 31 | 54 | 31 |
N.S. |
1 | 0.00 | 0.97 | 1.00 | 1.59 | 1.59 | 0.91 | 0.97 | 1.69 | 0.97 |
time (sec) |
N/A | 0.000 | 0.025 | 1.658 | 0.061 | 0.095 | 0.098 | 0.122 | 0.163 | 3.275 |
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 | 26 | 16 | 16 | 16 | 23 | 15 | 14 | 15 | 17 | 15 |
N.S. |
1 | 0.62 | 0.62 | 0.62 | 0.88 | 0.58 | 0.54 | 0.58 | 0.65 | 0.58 |
time (sec) |
N/A | 0.183 | 0.032 | 0.175 | 0.059 | 0.079 | 0.055 | 0.108 | 0.159 | 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 | 23 | 34 | 33 | 28 | 28 | 28 | 29 | 28 | 31 | 29 |
N.S. |
1 | 1.48 | 1.43 | 1.22 | 1.22 | 1.22 | 1.26 | 1.22 | 1.35 | 1.26 |
time (sec) |
N/A | 0.174 | 0.001 | 0.144 | 0.025 | 0.078 | 0.023 | 0.107 | 0.193 | 2.821 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F(-2) | A | A | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 32 | 34 | 0 | 36 | 31 | 149 | 82 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.06 | 0.00 | 1.12 | 0.97 | 4.66 | 2.56 | 0.00 |
time (sec) |
N/A | 0.000 | 0.657 | 2.105 | 0.000 | 0.086 | 0.126 | 0.472 | 0.158 | 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 | 24 | 0 | 25 | 21 | 34 | 61 | 32 | 34 | 40 | 34 |
N.S. |
1 | 0.00 | 1.04 | 0.88 | 1.42 | 2.54 | 1.33 | 1.42 | 1.67 | 1.42 |
time (sec) |
N/A | 0.000 | 1.694 | 1.665 | 0.082 | 0.088 | 0.083 | 0.113 | 0.163 | 0.171 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 41 | 48 | 45 | 45 | 44 | 48 | 50 | 0 |
N.S. |
1 | 0.00 | 1.46 | 1.71 | 1.61 | 1.61 | 1.57 | 1.71 | 1.79 | 0.00 |
time (sec) |
N/A | 0.000 | 3.574 | 0.677 | 0.166 | 0.084 | 0.246 | 0.147 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 48 | 46 | 45 | 53 | 51 | 49 | 54 | 58 | 45 |
N.S. |
1 | 1.92 | 1.84 | 1.80 | 2.12 | 2.04 | 1.96 | 2.16 | 2.32 | 1.80 |
time (sec) |
N/A | 0.335 | 0.150 | 1.258 | 0.056 | 0.088 | 0.078 | 0.109 | 0.158 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | C | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 67 | 40 | 37 | 362 | 73 | 39 | 44 | 48 | 39 |
N.S. |
1 | 2.68 | 1.60 | 1.48 | 14.48 | 2.92 | 1.56 | 1.76 | 1.92 | 1.56 |
time (sec) |
N/A | 0.599 | 7.689 | 1.327 | 0.178 | 0.101 | 0.123 | 0.113 | 0.163 | 0.139 |
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 | 30 | 0 | 34 | 50 | 52 | 47 | 48 | 67 | 65 | 41 |
N.S. |
1 | 0.00 | 1.13 | 1.67 | 1.73 | 1.57 | 1.60 | 2.23 | 2.17 | 1.37 |
time (sec) |
N/A | 0.000 | 2.121 | 0.664 | 0.146 | 0.088 | 0.163 | 0.115 | 0.153 | 0.162 |
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 | 19 | 14 | 11 | 11 | 11 | 10 | 11 | 15 | 10 |
N.S. |
1 | 0.83 | 0.61 | 0.48 | 0.48 | 0.48 | 0.43 | 0.48 | 0.65 | 0.43 |
time (sec) |
N/A | 0.162 | 0.001 | 0.078 | 0.029 | 0.075 | 0.022 | 0.113 | 0.155 | 0.014 |
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 | 25 | 44 | 48 | 38 | 56 | 40 | 41 | 60 | 39 | 36 |
N.S. |
1 | 1.76 | 1.92 | 1.52 | 2.24 | 1.60 | 1.64 | 2.40 | 1.56 | 1.44 |
time (sec) |
N/A | 0.191 | 0.011 | 0.271 | 0.027 | 0.098 | 0.073 | 0.114 | 0.161 | 2.979 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 67 | 54 | 35 | 46 | 48 | 48 | 47 | 24 | 47 |
N.S. |
1 | 2.79 | 2.25 | 1.46 | 1.92 | 2.00 | 2.00 | 1.96 | 1.00 | 1.96 |
time (sec) |
N/A | 0.391 | 0.018 | 0.421 | 0.026 | 0.088 | 0.916 | 0.116 | 0.154 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 19 | 34 | 121 | 32 | 34 | 134 | 30 | 30 |
N.S. |
1 | 0.00 | 1.00 | 1.79 | 6.37 | 1.68 | 1.79 | 7.05 | 1.58 | 1.58 |
time (sec) |
N/A | 0.000 | 0.102 | 1.865 | 0.211 | 0.083 | 0.164 | 0.175 | 0.152 | 3.113 |
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 | 17 | 14 | 13 | 12 | 12 | 14 | 12 | 14 | 12 |
N.S. |
1 | 1.21 | 1.00 | 0.93 | 0.86 | 0.86 | 1.00 | 0.86 | 1.00 | 0.86 |
time (sec) |
N/A | 0.218 | 0.028 | 0.362 | 0.044 | 0.084 | 0.057 | 0.114 | 0.155 | 3.070 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 14 | 14 | 14 | 47 | 13 | 15 | 0 | 51 | 13 |
N.S. |
1 | 0.64 | 0.64 | 0.64 | 2.14 | 0.59 | 0.68 | 0.00 | 2.32 | 0.59 |
time (sec) |
N/A | 0.889 | 0.071 | 13.590 | 0.186 | 0.092 | 5.246 | 0.000 | 0.166 | 2.998 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | C | A | F(-2) | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 47 | 83 | 87 | 33 | 0 | 67 | 89 | 132 |
N.S. |
1 | 0.00 | 1.62 | 2.86 | 3.00 | 1.14 | 0.00 | 2.31 | 3.07 | 4.55 |
time (sec) |
N/A | 0.000 | 0.094 | 7.086 | 0.167 | 0.092 | 0.000 | 0.181 | 0.155 | 3.388 |
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 | 16 | 24 | 23 | 18 | 17 | 14 | 19 | 18 | 14 | 14 |
N.S. |
1 | 1.50 | 1.44 | 1.12 | 1.06 | 0.88 | 1.19 | 1.12 | 0.88 | 0.88 |
time (sec) |
N/A | 0.190 | 0.005 | 0.308 | 0.037 | 0.100 | 0.056 | 0.107 | 0.154 | 3.316 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | A | A | F | B | B |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 31 | 0 | 0 | 25 | 29 | 0 | 50 | 26 |
N.S. |
1 | 0.00 | 1.03 | 0.00 | 0.00 | 0.83 | 0.97 | 0.00 | 1.67 | 0.87 |
time (sec) |
N/A | 0.000 | 0.051 | 0.000 | 0.000 | 0.085 | 0.629 | 0.000 | 0.159 | 3.353 |
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 | 18 | 0 | 19 | 15 | 17 | 49 | 14 | 17 | 19 | 17 |
N.S. |
1 | 0.00 | 1.06 | 0.83 | 0.94 | 2.72 | 0.78 | 0.94 | 1.06 | 0.94 |
time (sec) |
N/A | 0.000 | 0.215 | 0.135 | 0.139 | 0.095 | 0.089 | 0.119 | 0.171 | 3.371 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | C | B | B | F | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 316 | 75 | 106 | 63 | 68 | 0 | 101 | 0 |
N.S. |
1 | 0.00 | 12.64 | 3.00 | 4.24 | 2.52 | 2.72 | 0.00 | 4.04 | 0.00 |
time (sec) |
N/A | 0.000 | 0.452 | 0.062 | 0.067 | 0.091 | 0.207 | 0.000 | 0.183 | 0.000 |
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 | 18 | 0 | 16 | 16 | 15 | 15 | 15 | 0 | 16 | 15 |
N.S. |
1 | 0.00 | 0.89 | 0.89 | 0.83 | 0.83 | 0.83 | 0.00 | 0.89 | 0.83 |
time (sec) |
N/A | 0.000 | 0.038 | 0.658 | 0.072 | 0.084 | 0.151 | 0.000 | 0.151 | 2.897 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | A | A | F(-1) | F | B | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 33 | 247 | 26 | 45 | 0 | 0 | 58 | 48 |
N.S. |
1 | 0.00 | 1.22 | 9.15 | 0.96 | 1.67 | 0.00 | 0.00 | 2.15 | 1.78 |
time (sec) |
N/A | 0.000 | 0.606 | 37.398 | 0.334 | 0.092 | 0.000 | 0.000 | 0.182 | 3.432 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | F(-2) | B | B | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 70 | 98 | 0 | 79 | 600 | 0 | 376 | 0 |
N.S. |
1 | 0.00 | 2.26 | 3.16 | 0.00 | 2.55 | 19.35 | 0.00 | 12.13 | 0.00 |
time (sec) |
N/A | 0.000 | 7.557 | 7.779 | 0.000 | 0.222 | 1.411 | 0.000 | 200.034 | 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 | 20 | 21 | 18 | 15 | 14 | 19 | 15 | 14 | 22 | 14 |
N.S. |
1 | 1.05 | 0.90 | 0.75 | 0.70 | 0.95 | 0.75 | 0.70 | 1.10 | 0.70 |
time (sec) |
N/A | 0.207 | 0.007 | 0.159 | 0.034 | 0.084 | 0.053 | 0.110 | 0.189 | 3.223 |
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 | 33 | 0 | 57 | 50 | 47 | 40 | 37 | 502 | 90 | 38 |
N.S. |
1 | 0.00 | 1.73 | 1.52 | 1.42 | 1.21 | 1.12 | 15.21 | 2.73 | 1.15 |
time (sec) |
N/A | 0.000 | 0.060 | 1.093 | 0.162 | 0.124 | 0.259 | 0.171 | 0.194 | 0.398 |
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 | 40 | 22 | 17 | 26 | 16 | 15 | 16 | 17 | 16 |
N.S. |
1 | 1.43 | 0.79 | 0.61 | 0.93 | 0.57 | 0.54 | 0.57 | 0.61 | 0.57 |
time (sec) |
N/A | 0.201 | 0.059 | 0.343 | 0.028 | 0.087 | 0.065 | 0.110 | 0.190 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 31 | 29 | 29 | 29 | 29 | 28 | 308 | 28 |
N.S. |
1 | 0.00 | 1.03 | 0.97 | 0.97 | 0.97 | 0.97 | 0.93 | 10.27 | 0.93 |
time (sec) |
N/A | 0.000 | 1.863 | 0.368 | 0.072 | 0.095 | 0.093 | 0.123 | 0.200 | 3.269 |
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 | 19 | 19 | 19 | 17 | 15 | 19 | 14 | 15 | 15 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.79 | 1.00 | 0.74 | 0.79 | 0.79 | 0.84 |
time (sec) |
N/A | 0.140 | 0.001 | 0.378 | 0.029 | 0.076 | 0.037 | 0.117 | 0.179 | 0.048 |
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 | 23 | 22 | 19 | 18 | 19 | 19 | 18 | 22 | 20 |
N.S. |
1 | 0.74 | 0.71 | 0.61 | 0.58 | 0.61 | 0.61 | 0.58 | 0.71 | 0.65 |
time (sec) |
N/A | 0.189 | 0.003 | 0.212 | 0.025 | 0.081 | 0.061 | 0.116 | 0.194 | 2.891 |
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 | 23 | 21 | 20 | 43 | 19 | 34 | 24 | 20 |
N.S. |
1 | 0.00 | 0.92 | 0.84 | 0.80 | 1.72 | 0.76 | 1.36 | 0.96 | 0.80 |
time (sec) |
N/A | 0.000 | 0.072 | 0.404 | 0.112 | 0.096 | 0.112 | 0.114 | 0.190 | 2.938 |
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 | 30 | 0 | 31 | 32 | 44 | 48 | 29 | 49 | 51 | 0 |
N.S. |
1 | 0.00 | 1.03 | 1.07 | 1.47 | 1.60 | 0.97 | 1.63 | 1.70 | 0.00 |
time (sec) |
N/A | 0.000 | 7.063 | 10.999 | 0.094 | 0.099 | 0.123 | 0.118 | 0.191 | 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 | 19 | 11 | 11 | 11 | 10 | 12 | 7 | 10 | 13 | 10 |
N.S. |
1 | 0.58 | 0.58 | 0.58 | 0.53 | 0.63 | 0.37 | 0.53 | 0.68 | 0.53 |
time (sec) |
N/A | 0.146 | 0.002 | 0.078 | 0.033 | 0.070 | 0.033 | 0.105 | 0.200 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 86 | 73 | 87 | 91 | 55 | 51 | 55 | 86 | 22 |
N.S. |
1 | 2.97 | 2.52 | 3.00 | 3.14 | 1.90 | 1.76 | 1.90 | 2.97 | 0.76 |
time (sec) |
N/A | 0.508 | 0.038 | 6.447 | 0.030 | 0.093 | 0.091 | 0.119 | 0.189 | 3.144 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | A | A | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 143 | 35 | 68 | 34 | 32 | 0 | 35 | 40 |
N.S. |
1 | 0.00 | 4.21 | 1.03 | 2.00 | 1.00 | 0.94 | 0.00 | 1.03 | 1.18 |
time (sec) |
N/A | 0.000 | 0.183 | 4.220 | 0.095 | 0.090 | 0.338 | 0.000 | 0.190 | 3.099 |
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 | 11 | 12 | 11 | 11 | 10 | 11 | 11 | 11 |
N.S. |
1 | 1.00 | 1.10 | 1.20 | 1.10 | 1.10 | 1.00 | 1.10 | 1.10 | 1.10 |
time (sec) |
N/A | 0.132 | 0.000 | 0.070 | 0.025 | 0.066 | 0.019 | 0.110 | 0.191 | 0.024 |
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 | 16 | 34 | 27 | 16 | 0 | 15 | 14 | 15 | 30 | 11 |
N.S. |
1 | 2.12 | 1.69 | 1.00 | 0.00 | 0.94 | 0.88 | 0.94 | 1.88 | 0.69 |
time (sec) |
N/A | 0.353 | 0.014 | 0.413 | 0.000 | 0.086 | 0.095 | 0.116 | 0.194 | 2.770 |
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 | 33 | 26 | 26 | 23 | 60 | 28 | 27 | 24 | 28 | 24 |
N.S. |
1 | 0.79 | 0.79 | 0.70 | 1.82 | 0.85 | 0.82 | 0.73 | 0.85 | 0.73 |
time (sec) |
N/A | 0.778 | 0.115 | 0.358 | 0.273 | 0.084 | 0.147 | 0.134 | 0.197 | 2.913 |
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 | 31 | 46 | 50 | 31 | 90 | 33 | 24 | 38 | 39 | 34 |
N.S. |
1 | 1.48 | 1.61 | 1.00 | 2.90 | 1.06 | 0.77 | 1.23 | 1.26 | 1.10 |
time (sec) |
N/A | 0.453 | 0.087 | 0.395 | 0.159 | 0.094 | 0.223 | 0.114 | 0.213 | 3.298 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | A | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 3869 | 25 | 49 | 42 | 19 | 53 | 75 | 368 |
N.S. |
1 | 0.00 | 138.18 | 0.89 | 1.75 | 1.50 | 0.68 | 1.89 | 2.68 | 13.14 |
time (sec) |
N/A | 0.000 | 66.520 | 1.636 | 0.155 | 0.097 | 0.476 | 0.116 | 0.200 | 3.484 |
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 | 23 | 28 | 27 | 20 | 37 | 26 | 15 | 44 | 24 | 23 |
N.S. |
1 | 1.22 | 1.17 | 0.87 | 1.61 | 1.13 | 0.65 | 1.91 | 1.04 | 1.00 |
time (sec) |
N/A | 0.366 | 0.026 | 0.335 | 0.064 | 0.077 | 0.060 | 0.106 | 0.190 | 2.835 |
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 | 29 | 32 | 23 | 45 | 20 | 19 | 26 | 24 | 22 |
N.S. |
1 | 1.32 | 1.45 | 1.05 | 2.05 | 0.91 | 0.86 | 1.18 | 1.09 | 1.00 |
time (sec) |
N/A | 0.548 | 0.072 | 0.213 | 0.155 | 0.081 | 0.057 | 0.112 | 0.198 | 2.930 |
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 | 19 | 19 | 13 | 11 | 10 | 12 | 10 | 12 | 20 | 10 |
N.S. |
1 | 1.00 | 0.68 | 0.58 | 0.53 | 0.63 | 0.53 | 0.63 | 1.05 | 0.53 |
time (sec) |
N/A | 0.173 | 0.010 | 0.139 | 0.035 | 0.091 | 0.053 | 0.114 | 0.195 | 0.036 |
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 | 26 | 0 | 26 | 25 | 26 | 43 | 24 | 0 | 55 | 26 |
N.S. |
1 | 0.00 | 1.00 | 0.96 | 1.00 | 1.65 | 0.92 | 0.00 | 2.12 | 1.00 |
time (sec) |
N/A | 0.000 | 0.569 | 0.559 | 0.225 | 0.089 | 27.710 | 0.000 | 0.209 | 0.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 26 | 48 | 27 | 47 | 44 | 47 | 47 | 160 |
N.S. |
1 | 0.00 | 1.18 | 2.18 | 1.23 | 2.14 | 2.00 | 2.14 | 2.14 | 7.27 |
time (sec) |
N/A | 0.000 | 0.037 | 2.349 | 0.084 | 0.081 | 0.101 | 0.313 | 0.197 | 3.106 |
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 | 19 | 13 | 13 | 10 | 9 | 10 | 10 | 9 | 12 | 10 |
N.S. |
1 | 0.68 | 0.68 | 0.53 | 0.47 | 0.53 | 0.53 | 0.47 | 0.63 | 0.53 |
time (sec) |
N/A | 0.155 | 0.001 | 0.059 | 0.037 | 0.069 | 0.037 | 0.107 | 0.192 | 0.014 |
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 | 28 | 31 | 29 | 24 | 23 | 24 | 24 | 0 | 28 | 25 |
N.S. |
1 | 1.11 | 1.04 | 0.86 | 0.82 | 0.86 | 0.86 | 0.00 | 1.00 | 0.89 |
time (sec) |
N/A | 0.743 | 0.129 | 1.286 | 0.100 | 0.086 | 0.521 | 0.000 | 0.216 | 3.018 |
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 | 9 | 8 | 7 | 6 | 8 | 5 | 6 | 6 | 6 |
N.S. |
1 | 0.39 | 0.35 | 0.30 | 0.26 | 0.35 | 0.22 | 0.26 | 0.26 | 0.26 |
time (sec) |
N/A | 0.123 | 0.000 | 0.026 | 0.026 | 0.064 | 0.021 | 0.110 | 0.188 | 0.001 |
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 | 30 | 0 | 20 | 20 | 20 | 20 | 15 | 20 | 26 | 19 |
N.S. |
1 | 0.00 | 0.67 | 0.67 | 0.67 | 0.67 | 0.50 | 0.67 | 0.87 | 0.63 |
time (sec) |
N/A | 0.000 | 0.405 | 0.136 | 0.064 | 0.089 | 0.056 | 0.112 | 0.189 | 0.064 |
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 | 9 | 22 | 9 | 10 | 11 | 9 | 7 | 9 | 9 | 9 |
N.S. |
1 | 2.44 | 1.00 | 1.11 | 1.22 | 1.00 | 0.78 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.333 | 0.040 | 0.208 | 0.069 | 0.079 | 0.046 | 0.110 | 0.196 | 2.919 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 29 | 38 | 29 | 28 | 28 | 27 | 28 | 29 | 0 |
N.S. |
1 | 1.12 | 1.46 | 1.12 | 1.08 | 1.08 | 1.04 | 1.08 | 1.12 | 0.00 |
time (sec) |
N/A | 0.522 | 0.030 | 0.535 | 0.153 | 0.091 | 0.105 | 0.133 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 31 | 28 | 5288 | 34 | 31 | 34 | 29 | 35 |
N.S. |
1 | 0.00 | 0.97 | 0.88 | 165.25 | 1.06 | 0.97 | 1.06 | 0.91 | 1.09 |
time (sec) |
N/A | 0.000 | 0.242 | 1.320 | 0.207 | 0.113 | 5.563 | 0.114 | 0.187 | 3.164 |
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 | 37 | 27 | 30 | 31 | 31 | 32 | 32 | 49 | 1785 |
N.S. |
1 | 1.61 | 1.17 | 1.30 | 1.35 | 1.35 | 1.39 | 1.39 | 2.13 | 77.61 |
time (sec) |
N/A | 0.659 | 0.008 | 0.105 | 0.030 | 0.088 | 0.937 | 0.134 | 0.210 | 3.197 |
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 | 27 | 27 | 27 | 27 | 26 | 30 | 27 | 0 | 31 | 26 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.96 | 1.11 | 1.00 | 0.00 | 1.15 | 0.96 |
time (sec) |
N/A | 0.729 | 0.042 | 38.140 | 0.173 | 0.098 | 21.511 | 0.000 | 0.222 | 3.122 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 31 | 24 | 23 | 34 | 24 | 0 | 40 | 32 | 0 |
N.S. |
1 | 1.29 | 1.00 | 0.96 | 1.42 | 1.00 | 0.00 | 1.67 | 1.33 | 0.00 |
time (sec) |
N/A | 10.713 | 0.106 | 0.046 | 0.095 | 0.092 | 0.000 | 0.177 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 37 | 30 | 30 | 26 | 46 | 27 | 56 | 107 | 0 |
N.S. |
1 | 1.48 | 1.20 | 1.20 | 1.04 | 1.84 | 1.08 | 2.24 | 4.28 | 0.00 |
time (sec) |
N/A | 0.964 | 0.470 | 0.988 | 0.190 | 0.096 | 0.155 | 0.142 | 0.198 | 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 | 33 | 0 | 34 | 29 | 26 | 26 | 31 | 47 | 39 | 18 |
N.S. |
1 | 0.00 | 1.03 | 0.88 | 0.79 | 0.79 | 0.94 | 1.42 | 1.18 | 0.55 |
time (sec) |
N/A | 0.000 | 0.060 | 0.168 | 0.040 | 0.093 | 0.099 | 0.106 | 0.196 | 2.829 |
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 | 47 | 29 | 24 | 39 | 23 | 31 | 23 | 25 | 23 |
N.S. |
1 | 1.96 | 1.21 | 1.00 | 1.62 | 0.96 | 1.29 | 0.96 | 1.04 | 0.96 |
time (sec) |
N/A | 0.233 | 0.017 | 0.661 | 0.029 | 0.088 | 0.068 | 0.109 | 0.192 | 0.031 |
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 | 10 | 10 | 8 | 7 | 7 | 7 | 7 | 8 | 7 |
N.S. |
1 | 0.59 | 0.59 | 0.47 | 0.41 | 0.41 | 0.41 | 0.41 | 0.47 | 0.41 |
time (sec) |
N/A | 0.130 | 0.000 | 0.051 | 0.032 | 0.075 | 0.020 | 0.108 | 0.193 | 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 | 27 | 31 | 19 | 16 | 19 | 20 | 15 | 20 | 22 | 14 |
N.S. |
1 | 1.15 | 0.70 | 0.59 | 0.70 | 0.74 | 0.56 | 0.74 | 0.81 | 0.52 |
time (sec) |
N/A | 0.200 | 0.007 | 0.260 | 0.028 | 0.082 | 0.065 | 0.120 | 0.190 | 0.048 |