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 | F | A | C | B | B | B | F(-2) | B | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 32 | 578 | 500 | 62 | 61 | 0 | 129 | 94 |
N.S. |
1 | 0.00 | 1.33 | 24.08 | 20.83 | 2.58 | 2.54 | 0.00 | 5.38 | 3.92 |
time (sec) |
N/A | 0.000 | 0.250 | 0.071 | 5.314 | 0.074 | 3.723 | 0.000 | 0.523 | 1.668 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | A | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 0 | 23 | 28 | 29 | 15 | 27 | 28 | 15 | 15 |
N.S. |
1 | 0.00 | 1.77 | 2.15 | 2.23 | 1.15 | 2.08 | 2.15 | 1.15 | 1.15 |
time (sec) |
N/A | 0.000 | 0.222 | 2.474 | 0.061 | 0.070 | 0.286 | 0.152 | 0.221 | 0.775 |
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 | 29 | 24 | 32 | 25 | 24 | 29 | 81 | 26 |
N.S. |
1 | 0.00 | 0.97 | 0.80 | 1.07 | 0.83 | 0.80 | 0.97 | 2.70 | 0.87 |
time (sec) |
N/A | 0.000 | 7.448 | 0.548 | 1.300 | 0.073 | 0.126 | 0.138 | 0.291 | 0.099 |
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 | 31 | 0 | 28 | 82 | 33 | 43 | 34 | 36 | 39 | 42 |
N.S. |
1 | 0.00 | 0.90 | 2.65 | 1.06 | 1.39 | 1.10 | 1.16 | 1.26 | 1.35 |
time (sec) |
N/A | 0.000 | 0.081 | 1.136 | 0.166 | 0.066 | 0.245 | 0.153 | 0.227 | 0.703 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 57 | 22 | 29 | 0 | 28 | 29 | 19 | 22 | 62 |
N.S. |
1 | 2.59 | 1.00 | 1.32 | 0.00 | 1.27 | 1.32 | 0.86 | 1.00 | 2.82 |
time (sec) |
N/A | 2.751 | 0.452 | 7.631 | 0.000 | 0.070 | 0.323 | 0.201 | 0.237 | 0.678 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | B | F | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 0 | 24 | 30 | 23 | 22 | 73 | 95 | 21 |
N.S. |
1 | 0.00 | 0.00 | 1.09 | 1.36 | 1.05 | 1.00 | 3.32 | 4.32 | 0.95 |
time (sec) |
N/A | 0.000 | 0.000 | 82.604 | 0.164 | 0.069 | 0.805 | 2.300 | 200.021 | 0.991 |
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 | 5 | 3 | 3 | 4 | 3 | 3 | 3 | 4 | 3 | 3 |
N.S. |
1 | 0.60 | 0.60 | 0.80 | 0.60 | 0.60 | 0.60 | 0.80 | 0.60 | 0.60 |
time (sec) |
N/A | 0.194 | 0.001 | 0.072 | 0.031 | 0.067 | 0.044 | 0.109 | 0.196 | 0.479 |
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 | 50 | 26 | 18 | 23 | 28 | 15 | 30 | 37 | 19 |
N.S. |
1 | 1.61 | 0.84 | 0.58 | 0.74 | 0.90 | 0.48 | 0.97 | 1.19 | 0.61 |
time (sec) |
N/A | 0.524 | 0.355 | 0.413 | 0.153 | 0.068 | 0.073 | 0.113 | 0.226 | 0.095 |
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 | 16 | 16 | 26 | 24 | 25 | 27 | 14 | 18 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.62 | 1.50 | 1.56 | 1.69 | 0.88 | 1.12 | 0.94 |
time (sec) |
N/A | 0.361 | 0.020 | 0.472 | 0.034 | 0.068 | 0.092 | 0.115 | 0.219 | 0.558 |
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 | 22 | 22 | 22 | 20 | 0 | 19 | 17 | 19 | 20 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.00 | 0.86 | 0.77 | 0.86 | 0.91 | 0.86 |
time (sec) |
N/A | 0.633 | 0.128 | 0.398 | 0.000 | 0.072 | 0.072 | 0.105 | 0.203 | 0.039 |
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 | 26 | 26 | 35 | 29 | 27 | 35 | 34 | 143 |
N.S. |
1 | 0.00 | 0.84 | 0.84 | 1.13 | 0.94 | 0.87 | 1.13 | 1.10 | 4.61 |
time (sec) |
N/A | 0.000 | 0.106 | 6.208 | 0.157 | 0.071 | 0.176 | 0.258 | 0.233 | 0.752 |
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 | 35 | 35 | 31 | 57 | 27 | 35 | 37 | 69 |
N.S. |
1 | 0.00 | 1.09 | 1.09 | 0.97 | 1.78 | 0.84 | 1.09 | 1.16 | 2.16 |
time (sec) |
N/A | 0.000 | 0.789 | 2.759 | 0.121 | 0.072 | 0.108 | 0.127 | 3.303 | 0.611 |
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 | 11 | 13 | 7 | 11 | 14 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 1.00 | 0.54 | 0.85 | 1.08 | 0.85 |
time (sec) |
N/A | 0.258 | 0.003 | 0.091 | 0.040 | 0.057 | 0.039 | 0.108 | 0.219 | 0.020 |
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 | 33 | 33 | 18 | 18 | 30 | 15 | 18 | 31 | 17 |
N.S. |
1 | 1.38 | 1.38 | 0.75 | 0.75 | 1.25 | 0.62 | 0.75 | 1.29 | 0.71 |
time (sec) |
N/A | 0.500 | 0.015 | 0.268 | 0.039 | 0.066 | 0.126 | 0.108 | 0.210 | 0.532 |
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 | 41 | 39 | 29 | 33 | 33 | 27 | 33 | 32 | 33 |
N.S. |
1 | 1.41 | 1.34 | 1.00 | 1.14 | 1.14 | 0.93 | 1.14 | 1.10 | 1.14 |
time (sec) |
N/A | 0.182 | 0.005 | 0.108 | 0.038 | 0.065 | 0.026 | 0.109 | 0.204 | 0.517 |
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 | 26 | 0 | 24 | 30 | 36 | 28 | 22 | 43 | 33 | 1156 |
N.S. |
1 | 0.00 | 0.92 | 1.15 | 1.38 | 1.08 | 0.85 | 1.65 | 1.27 | 44.46 |
time (sec) |
N/A | 0.000 | 0.892 | 133.167 | 0.243 | 0.069 | 0.805 | 0.244 | 0.225 | 1.473 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 27 | 27 | 82 | 57 | 49 | 19 | 1737 | 136 | 27 |
N.S. |
1 | 0.93 | 0.93 | 2.83 | 1.97 | 1.69 | 0.66 | 59.90 | 4.69 | 0.93 |
time (sec) |
N/A | 6.002 | 0.125 | 2.979 | 0.257 | 0.078 | 0.182 | 2.001 | 0.235 | 0.992 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | F(-2) | A | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 0 | 31 | 30 | 34 | 0 | 34 | 53 | 51 |
N.S. |
1 | 0.00 | 0.00 | 1.35 | 1.30 | 1.48 | 0.00 | 1.48 | 2.30 | 2.22 |
time (sec) |
N/A | 0.000 | 0.000 | 0.706 | 0.187 | 0.077 | 0.000 | 0.132 | 0.214 | 1.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 108 | 26 | 44 | 96 | 43 | 46 | 51 | 52 | 43 |
N.S. |
1 | 4.70 | 1.13 | 1.91 | 4.17 | 1.87 | 2.00 | 2.22 | 2.26 | 1.87 |
time (sec) |
N/A | 1.414 | 1.231 | 0.541 | 0.087 | 0.075 | 0.112 | 0.111 | 0.222 | 0.547 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 55 | 55 | 60 | 61 | 57 | 65 | 65 | 68 | 56 |
N.S. |
1 | 1.83 | 1.83 | 2.00 | 2.03 | 1.90 | 2.17 | 2.17 | 2.27 | 1.87 |
time (sec) |
N/A | 0.315 | 0.017 | 0.105 | 0.033 | 0.062 | 0.245 | 0.112 | 0.222 | 0.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | C | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 80 | 37 | 38 | 100 | 38 | 60 | 74 | 85 | 58 |
N.S. |
1 | 2.76 | 1.28 | 1.31 | 3.45 | 1.31 | 2.07 | 2.55 | 2.93 | 2.00 |
time (sec) |
N/A | 0.370 | 0.685 | 0.589 | 0.105 | 0.070 | 0.080 | 0.116 | 0.224 | 0.519 |
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 | 11 | 11 | 11 | 12 | 23 | 11 | 12 | 11 | 23 | 11 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 2.09 | 1.00 | 1.09 | 1.00 | 2.09 | 1.00 |
time (sec) |
N/A | 0.446 | 0.204 | 0.189 | 0.160 | 0.075 | 0.062 | 0.117 | 0.199 | 0.574 |
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 | 26 | 0 | 22 | 26 | 31 | 26 | 17 | 26 | 25 | 25 |
N.S. |
1 | 0.00 | 0.85 | 1.00 | 1.19 | 1.00 | 0.65 | 1.00 | 0.96 | 0.96 |
time (sec) |
N/A | 0.000 | 0.257 | 2.155 | 0.164 | 0.063 | 0.078 | 0.137 | 0.207 | 0.691 |
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 | 51 | 32 | 26 | 27 | 31 | 27 | 31 | 31 | 24 |
N.S. |
1 | 2.43 | 1.52 | 1.24 | 1.29 | 1.48 | 1.29 | 1.48 | 1.48 | 1.14 |
time (sec) |
N/A | 1.187 | 0.169 | 0.585 | 0.084 | 0.075 | 0.134 | 0.115 | 0.250 | 0.602 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 43 | 43 | 41 | 49 | 35 | 37 | 38 | 43 | 43 |
N.S. |
1 | 2.53 | 2.53 | 2.41 | 2.88 | 2.06 | 2.18 | 2.24 | 2.53 | 2.53 |
time (sec) |
N/A | 0.357 | 0.015 | 0.646 | 0.035 | 0.072 | 0.084 | 0.115 | 0.211 | 0.529 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 54 | 54 | 53 | 54 | 52 | 51 | 56 | 54 | 52 |
N.S. |
1 | 2.45 | 2.45 | 2.41 | 2.45 | 2.36 | 2.32 | 2.55 | 2.45 | 2.36 |
time (sec) |
N/A | 1.704 | 0.042 | 0.091 | 0.032 | 0.091 | 0.089 | 0.122 | 0.228 | 0.586 |
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 | 20 | 20 | 18 | 17 | 19 | 19 | 20 | 18 | 17 |
N.S. |
1 | 0.71 | 0.71 | 0.64 | 0.61 | 0.68 | 0.68 | 0.71 | 0.64 | 0.61 |
time (sec) |
N/A | 0.398 | 0.010 | 0.157 | 0.038 | 0.067 | 0.291 | 0.114 | 0.204 | 0.611 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 31 | 36 | 38 | 42 | 46 | 0 | 43 | 41 |
N.S. |
1 | 0.00 | 1.00 | 1.16 | 1.23 | 1.35 | 1.48 | 0.00 | 1.39 | 1.32 |
time (sec) |
N/A | 0.000 | 1.658 | 1.546 | 0.194 | 0.070 | 0.180 | 0.000 | 0.217 | 0.789 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | B | B | F(-1) | F(-1) | B | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 61 | 828 | 1058 | 114 | 0 | 0 | 96 | 76 |
N.S. |
1 | 0.00 | 1.74 | 23.66 | 30.23 | 3.26 | 0.00 | 0.00 | 2.74 | 2.17 |
time (sec) |
N/A | 0.000 | 0.291 | 0.091 | 4.263 | 0.083 | 0.000 | 0.000 | 1.203 | 1.656 |
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 | 30 | 20 | 18 | 19 | 32 | 17 | 19 | 36 | 19 |
N.S. |
1 | 1.30 | 0.87 | 0.78 | 0.83 | 1.39 | 0.74 | 0.83 | 1.57 | 0.83 |
time (sec) |
N/A | 1.027 | 0.024 | 0.587 | 0.081 | 0.068 | 0.095 | 0.118 | 0.208 | 0.549 |
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 | 30 | 37 | 40 | 35 | 32 | 43 | 29 | 32 | 49 | 31 |
N.S. |
1 | 1.23 | 1.33 | 1.17 | 1.07 | 1.43 | 0.97 | 1.07 | 1.63 | 1.03 |
time (sec) |
N/A | 0.599 | 0.044 | 0.284 | 0.055 | 0.074 | 0.186 | 0.117 | 0.227 | 0.527 |
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 | 21 | 0 | 21 | 17 | 17 | 46 | 14 | 17 | 38 | 17 |
N.S. |
1 | 0.00 | 1.00 | 0.81 | 0.81 | 2.19 | 0.67 | 0.81 | 1.81 | 0.81 |
time (sec) |
N/A | 0.000 | 0.078 | 0.073 | 0.197 | 0.071 | 0.085 | 0.123 | 0.227 | 0.079 |
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 | 25 | 41 | 27 | 38 | 32 | 31 | 86 | 27 | 0 |
N.S. |
1 | 1.00 | 1.64 | 1.08 | 1.52 | 1.28 | 1.24 | 3.44 | 1.08 | 0.00 |
time (sec) |
N/A | 0.611 | 6.532 | 0.983 | 0.158 | 0.078 | 0.179 | 0.119 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 36 | 33 | 0 | 58 | 27 | 58 | 0 | 32 |
N.S. |
1 | 0.00 | 1.03 | 0.94 | 0.00 | 1.66 | 0.77 | 1.66 | 0.00 | 0.91 |
time (sec) |
N/A | 0.000 | 0.300 | 112.002 | 0.000 | 0.082 | 1.573 | 0.286 | 0.442 | 0.859 |
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 | 22 | 32 | 20 | 29 | 22 | 0 | 46 | 54 |
N.S. |
1 | 0.00 | 0.85 | 1.23 | 0.77 | 1.12 | 0.85 | 0.00 | 1.77 | 2.08 |
time (sec) |
N/A | 0.000 | 0.322 | 0.522 | 0.155 | 0.072 | 0.198 | 0.000 | 0.201 | 0.753 |
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 | 30 | 0 | 24 | 21 | 76 | 25 | 22 | 27 | 30 | 27 |
N.S. |
1 | 0.00 | 0.80 | 0.70 | 2.53 | 0.83 | 0.73 | 0.90 | 1.00 | 0.90 |
time (sec) |
N/A | 0.000 | 1.075 | 5.705 | 0.343 | 0.067 | 0.314 | 0.130 | 0.222 | 0.846 |
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 | 22 | 0 | 22 | 28 | 0 | 27 | 20 | 100 | 58 | 26 |
N.S. |
1 | 0.00 | 1.00 | 1.27 | 0.00 | 1.23 | 0.91 | 4.55 | 2.64 | 1.18 |
time (sec) |
N/A | 0.000 | 0.109 | 0.881 | 0.000 | 0.070 | 0.095 | 0.124 | 0.242 | 0.082 |
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 | 36 | 37 | 26 | 35 | 35 | 37 | 37 | 24 | 48 |
N.S. |
1 | 1.64 | 1.68 | 1.18 | 1.59 | 1.59 | 1.68 | 1.68 | 1.09 | 2.18 |
time (sec) |
N/A | 0.250 | 0.016 | 0.347 | 0.029 | 0.060 | 0.104 | 0.109 | 0.227 | 0.517 |
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 | 26 | 69 | 46 | 44 | 77 | 47 | 42 | 55 | 59 | 93 |
N.S. |
1 | 2.65 | 1.77 | 1.69 | 2.96 | 1.81 | 1.62 | 2.12 | 2.27 | 3.58 |
time (sec) |
N/A | 0.420 | 0.120 | 0.325 | 0.173 | 0.080 | 0.126 | 0.199 | 0.219 | 0.587 |
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 | 35 | 0 | 63 | 103 | 467 | 81 | 75 | 104 | 114 | 76 |
N.S. |
1 | 0.00 | 1.80 | 2.94 | 13.34 | 2.31 | 2.14 | 2.97 | 3.26 | 2.17 |
time (sec) |
N/A | 0.000 | 0.121 | 26.318 | 0.194 | 0.076 | 0.302 | 9.395 | 4.818 | 0.661 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 0 | 17 | 18 | 83 | 83 | 95 | 146 | 119 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.06 | 4.88 | 4.88 | 5.59 | 8.59 | 7.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.108 | 1.236 | 0.523 | 0.069 | 0.216 | 2.339 | 0.239 | 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 | 21 | 27 | 23 | 20 | 19 | 19 | 20 | 19 | 18 | 16 |
N.S. |
1 | 1.29 | 1.10 | 0.95 | 0.90 | 0.90 | 0.95 | 0.90 | 0.86 | 0.76 |
time (sec) |
N/A | 0.171 | 0.001 | 0.081 | 0.032 | 0.064 | 0.047 | 0.107 | 0.200 | 0.500 |
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 | 30 | 0 | 28 | 29 | 24 | 28 | 29 | 0 | 28 | 29 |
N.S. |
1 | 0.00 | 0.93 | 0.97 | 0.80 | 0.93 | 0.97 | 0.00 | 0.93 | 0.97 |
time (sec) |
N/A | 0.000 | 0.479 | 0.288 | 0.159 | 0.071 | 0.113 | 0.000 | 0.218 | 0.129 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 188 | 120 | 31 | 92 | 30 | 32 | 69 | 31 | 17 |
N.S. |
1 | 10.44 | 6.67 | 1.72 | 5.11 | 1.67 | 1.78 | 3.83 | 1.72 | 0.94 |
time (sec) |
N/A | 0.554 | 2.356 | 0.317 | 0.039 | 0.071 | 0.072 | 0.110 | 0.199 | 0.509 |
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 | 21 | 23 | 29 | 29 | 26 | 30 | 24 | 20 |
N.S. |
1 | 0.00 | 0.88 | 0.96 | 1.21 | 1.21 | 1.08 | 1.25 | 1.00 | 0.83 |
time (sec) |
N/A | 0.000 | 1.169 | 0.241 | 0.197 | 0.067 | 0.121 | 0.115 | 0.223 | 0.123 |
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 | 20 | 20 | 20 | 16 | 15 | 15 | 19 | 15 | 94 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.75 | 0.75 | 0.95 | 0.75 | 4.70 | 0.90 |
time (sec) |
N/A | 0.380 | 0.350 | 0.152 | 0.034 | 0.072 | 0.151 | 0.133 | 0.248 | 0.519 |
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 | 19 | 11 | 13 | 16 | 21 | 17 | 17 | 19 | 13 |
N.S. |
1 | 1.58 | 0.92 | 1.08 | 1.33 | 1.75 | 1.42 | 1.42 | 1.58 | 1.08 |
time (sec) |
N/A | 0.197 | 0.002 | 0.060 | 0.033 | 0.058 | 0.060 | 0.110 | 0.213 | 0.026 |
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 | 27 | 70 | 43 | 41 | 41 | 37 | 44 | 38 | 46 | 40 |
N.S. |
1 | 2.59 | 1.59 | 1.52 | 1.52 | 1.37 | 1.63 | 1.41 | 1.70 | 1.48 |
time (sec) |
N/A | 0.267 | 0.077 | 7.104 | 0.033 | 0.073 | 0.199 | 0.107 | 0.255 | 0.567 |
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 | 36 | 0 | 52 | 61 | 54 | 58 | 27 | 61 | 151 | 68 |
N.S. |
1 | 0.00 | 1.44 | 1.69 | 1.50 | 1.61 | 0.75 | 1.69 | 4.19 | 1.89 |
time (sec) |
N/A | 0.000 | 0.137 | 8.497 | 0.126 | 0.076 | 0.144 | 0.204 | 200.022 | 0.577 |
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 | 21 | 6 | 6 | 6 | 5 | 5 | 5 | 5 | 6 | 5 |
N.S. |
1 | 0.29 | 0.29 | 0.29 | 0.24 | 0.24 | 0.24 | 0.24 | 0.29 | 0.24 |
time (sec) |
N/A | 0.136 | 0.000 | 0.038 | 0.028 | 0.050 | 0.019 | 0.113 | 0.234 | 0.001 |
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 | 21 | 23 | 21 | 20 | 25 | 20 | 20 | 33 | 20 |
N.S. |
1 | 0.91 | 1.00 | 0.91 | 0.87 | 1.09 | 0.87 | 0.87 | 1.43 | 0.87 |
time (sec) |
N/A | 0.441 | 0.148 | 1.275 | 0.078 | 0.067 | 0.138 | 0.111 | 0.243 | 0.541 |
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 | 23 | 20 | 20 | 30 | 29 | 29 | 29 | 29 | 517 | 29 |
N.S. |
1 | 0.87 | 0.87 | 1.30 | 1.26 | 1.26 | 1.26 | 1.26 | 22.48 | 1.26 |
time (sec) |
N/A | 3.957 | 0.445 | 0.732 | 0.098 | 0.074 | 0.218 | 0.251 | 0.224 | 0.771 |
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 | 23 | 18 | 18 | 17 | 22 | 18 | 23 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.78 | 0.74 | 0.96 | 0.78 | 1.00 | 0.83 |
time (sec) |
N/A | 0.507 | 0.054 | 0.081 | 0.118 | 0.068 | 0.095 | 0.113 | 0.272 | 0.049 |
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 | 21 | 21 | 21 | 22 | 22 | 22 | 23 | 29 | 21 |
N.S. |
1 | 0.91 | 0.91 | 0.91 | 0.96 | 0.96 | 0.96 | 1.00 | 1.26 | 0.91 |
time (sec) |
N/A | 0.940 | 0.244 | 0.452 | 0.179 | 0.067 | 0.528 | 0.158 | 0.248 | 0.706 |
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 | 16 | 14 | 14 | 28 | 66 | 49 | 15 | 12 | 15 | 12 |
N.S. |
1 | 0.88 | 0.88 | 1.75 | 4.12 | 3.06 | 0.94 | 0.75 | 0.94 | 0.75 |
time (sec) |
N/A | 0.331 | 0.046 | 5.173 | 0.047 | 0.073 | 0.058 | 0.107 | 0.249 | 0.620 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 156 | 47 | 35 | 0 | 49 | 31 | 52 | 31 | 30 |
N.S. |
1 | 6.24 | 1.88 | 1.40 | 0.00 | 1.96 | 1.24 | 2.08 | 1.24 | 1.20 |
time (sec) |
N/A | 0.915 | 0.152 | 1.001 | 0.000 | 0.073 | 0.126 | 0.115 | 0.279 | 0.129 |
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 | 9 | 9 | 9 | 8 | 8 | 8 | 8 | 9 | 8 |
N.S. |
1 | 0.50 | 0.50 | 0.50 | 0.44 | 0.44 | 0.44 | 0.44 | 0.50 | 0.44 |
time (sec) |
N/A | 0.146 | 0.001 | 0.080 | 0.034 | 0.060 | 0.028 | 0.107 | 0.236 | 0.019 |
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 | 20 | 0 | 18 | 28 | 20 | 27 | 22 | 56 | 23 | 60 |
N.S. |
1 | 0.00 | 0.90 | 1.40 | 1.00 | 1.35 | 1.10 | 2.80 | 1.15 | 3.00 |
time (sec) |
N/A | 0.000 | 1.030 | 0.252 | 0.175 | 0.062 | 0.093 | 0.107 | 0.275 | 0.722 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | F | A | B | A | F(-1) | A | B | B |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 94 | 0 | 50 | 71 | 46 | 0 | 42 | 45 | 47 |
N.S. |
1 | 2.94 | 0.00 | 1.56 | 2.22 | 1.44 | 0.00 | 1.31 | 1.41 | 1.47 |
time (sec) |
N/A | 0.774 | 0.000 | 16.600 | 0.239 | 0.067 | 0.000 | 0.395 | 0.258 | 0.999 |
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 | 25 | 19 | 17 | 16 | 16 | 15 | 16 | 19 | 16 |
N.S. |
1 | 1.19 | 0.90 | 0.81 | 0.76 | 0.76 | 0.71 | 0.76 | 0.90 | 0.76 |
time (sec) |
N/A | 0.159 | 0.012 | 0.142 | 0.024 | 0.062 | 0.047 | 0.106 | 0.218 | 0.036 |
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 | 26 | 0 | 26 | 21 | 20 | 24 | 26 | 24 | 26 | 22 |
N.S. |
1 | 0.00 | 1.00 | 0.81 | 0.77 | 0.92 | 1.00 | 0.92 | 1.00 | 0.85 |
time (sec) |
N/A | 0.000 | 0.458 | 0.078 | 0.066 | 0.073 | 0.129 | 0.130 | 0.227 | 0.595 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | C | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 20 | 24 | 31 | 27 | 15 | 23 | 18 | 18 |
N.S. |
1 | 0.00 | 1.00 | 1.20 | 1.55 | 1.35 | 0.75 | 1.15 | 0.90 | 0.90 |
time (sec) |
N/A | 0.000 | 0.065 | 0.533 | 0.110 | 0.078 | 0.081 | 0.111 | 0.211 | 0.599 |
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 | 29 | 21 | 18 | 26 | 19 | 18 | 24 | 22 |
N.S. |
1 | 1.14 | 1.32 | 0.95 | 0.82 | 1.18 | 0.86 | 0.82 | 1.09 | 1.00 |
time (sec) |
N/A | 0.211 | 0.011 | 0.348 | 0.036 | 0.056 | 0.070 | 0.119 | 0.208 | 0.537 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 38 | 46 | 44 | 44 | 42 | 48 | 56 | 101 |
N.S. |
1 | 0.00 | 1.46 | 1.77 | 1.69 | 1.69 | 1.62 | 1.85 | 2.15 | 3.88 |
time (sec) |
N/A | 0.000 | 0.071 | 8.703 | 0.196 | 0.072 | 0.163 | 0.366 | 0.234 | 0.855 |
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 | 24 | 24 | 24 | 30 | 33 | 22 | 33 | 33 | 23 |
N.S. |
1 | 0.96 | 0.96 | 0.96 | 1.20 | 1.32 | 0.88 | 1.32 | 1.32 | 0.92 |
time (sec) |
N/A | 2.478 | 0.092 | 5.681 | 0.083 | 0.076 | 0.246 | 0.122 | 0.235 | 0.624 |
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 | 9 | 9 | 7 | 6 | 6 | 7 | 6 | 7 | 6 |
N.S. |
1 | 0.82 | 0.82 | 0.64 | 0.55 | 0.55 | 0.64 | 0.55 | 0.64 | 0.55 |
time (sec) |
N/A | 0.152 | 0.007 | 0.074 | 0.036 | 0.063 | 0.040 | 0.111 | 0.223 | 0.013 |
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 | 23 | 0 | 25 | 19 | 0 | 18 | 19 | 34 | 21 | 18 |
N.S. |
1 | 0.00 | 1.09 | 0.83 | 0.00 | 0.78 | 0.83 | 1.48 | 0.91 | 0.78 |
time (sec) |
N/A | 0.000 | 0.082 | 0.628 | 0.000 | 0.070 | 0.095 | 0.141 | 0.221 | 0.568 |
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 | 13 | 13 | 16 | 15 | 13 | 17 | 15 | 13 | 13 |
N.S. |
1 | 0.52 | 0.52 | 0.64 | 0.60 | 0.52 | 0.68 | 0.60 | 0.52 | 0.52 |
time (sec) |
N/A | 0.466 | 0.053 | 0.381 | 0.033 | 0.075 | 0.238 | 0.123 | 0.237 | 0.712 |
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 | 13 | 15 | 20 | 11 | 21 | 10 | 10 | 10 | 11 | 10 |
N.S. |
1 | 1.15 | 1.54 | 0.85 | 1.62 | 0.77 | 0.77 | 0.77 | 0.85 | 0.77 |
time (sec) |
N/A | 0.164 | 0.012 | 0.173 | 0.115 | 0.070 | 0.049 | 0.114 | 0.224 | 0.808 |
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 | 25 | 0 | 25 | 38 | 34 | 36 | 32 | 86 | 30 | 53 |
N.S. |
1 | 0.00 | 1.00 | 1.52 | 1.36 | 1.44 | 1.28 | 3.44 | 1.20 | 2.12 |
time (sec) |
N/A | 0.000 | 2.266 | 5.280 | 0.238 | 0.072 | 0.258 | 0.149 | 0.266 | 0.778 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | A | B | A | F(-1) | A | B | B |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 36 | 0 | 20 | 114 | 54 | 0 | 54 | 30 | 68 |
N.S. |
1 | 1.38 | 0.00 | 0.77 | 4.38 | 2.08 | 0.00 | 2.08 | 1.15 | 2.62 |
time (sec) |
N/A | 3.423 | 0.000 | 1.283 | 0.653 | 0.081 | 0.000 | 0.119 | 0.238 | 0.895 |
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 | 25 | 25 | 21 | 21 | 19 | 19 | 21 | 21 | 18 |
N.S. |
1 | 0.93 | 0.93 | 0.78 | 0.78 | 0.70 | 0.70 | 0.78 | 0.78 | 0.67 |
time (sec) |
N/A | 0.195 | 0.002 | 0.131 | 0.033 | 0.066 | 0.056 | 0.113 | 0.234 | 0.566 |
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 | 15 | 15 | 14 | 13 | 15 | 12 | 14 | 16 | 13 |
N.S. |
1 | 0.94 | 0.94 | 0.88 | 0.81 | 0.94 | 0.75 | 0.88 | 1.00 | 0.81 |
time (sec) |
N/A | 0.163 | 0.002 | 0.051 | 0.031 | 0.060 | 0.036 | 0.111 | 0.224 | 0.018 |
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 | 22 | 22 | 21 | 20 | 22 | 15 | 20 | 23 | 20 |
N.S. |
1 | 0.96 | 0.96 | 0.91 | 0.87 | 0.96 | 0.65 | 0.87 | 1.00 | 0.87 |
time (sec) |
N/A | 0.220 | 0.021 | 0.252 | 0.031 | 0.073 | 0.090 | 0.115 | 0.253 | 0.644 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 33 | 40 | 48 | 40 | 0 | 48 | 39 | 32 |
N.S. |
1 | 0.00 | 1.03 | 1.25 | 1.50 | 1.25 | 0.00 | 1.50 | 1.22 | 1.00 |
time (sec) |
N/A | 0.000 | 0.135 | 127.517 | 0.217 | 0.078 | 0.000 | 0.181 | 0.275 | 1.442 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | B | B | B | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 0 | 36 | 41 | 36 | 49 | 609 | 39 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.38 | 1.58 | 1.38 | 1.88 | 23.42 | 1.50 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.069 | 0.302 | 0.080 | 0.174 | 0.432 | 0.248 | 0.000 |
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 | 26 | 380 | 162 | 38 | 641 | 37 | 31 | 546 | 179 | 27 |
N.S. |
1 | 14.62 | 6.23 | 1.46 | 24.65 | 1.42 | 1.19 | 21.00 | 6.88 | 1.04 |
time (sec) |
N/A | 2.154 | 0.089 | 4.931 | 0.121 | 0.072 | 0.122 | 0.232 | 0.230 | 0.802 |
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 | 19 | 87 | 19 | 27 | 28 | 17 | 19 | 30 | 17 | 17 |
N.S. |
1 | 4.58 | 1.00 | 1.42 | 1.47 | 0.89 | 1.00 | 1.58 | 0.89 | 0.89 |
time (sec) |
N/A | 1.037 | 0.083 | 1.548 | 0.169 | 0.071 | 0.165 | 0.124 | 0.233 | 0.646 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 30 | 24 | 28 | 24 | 42 | 36 | 32 | 24 |
N.S. |
1 | 0.00 | 0.97 | 0.77 | 0.90 | 0.77 | 1.35 | 1.16 | 1.03 | 0.77 |
time (sec) |
N/A | 0.000 | 1.642 | 0.575 | 0.110 | 0.071 | 0.098 | 0.114 | 0.217 | 0.111 |
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 | 36 | 21 | 33 | 32 | 32 | 41 | 32 | 40 | 34 |
N.S. |
1 | 1.71 | 1.00 | 1.57 | 1.52 | 1.52 | 1.95 | 1.52 | 1.90 | 1.62 |
time (sec) |
N/A | 0.210 | 0.033 | 10.939 | 0.128 | 0.067 | 0.198 | 0.113 | 0.264 | 0.587 |
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 | 15 | 16 | 16 | 16 | 43 | 15 | 14 | 15 | 14 | 15 |
N.S. |
1 | 1.07 | 1.07 | 1.07 | 2.87 | 1.00 | 0.93 | 1.00 | 0.93 | 1.00 |
time (sec) |
N/A | 0.353 | 0.018 | 0.269 | 0.048 | 0.071 | 0.065 | 0.112 | 0.269 | 0.142 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 119 | 26 | 59 | 72 | 57 | 51 | 75 | 61 | 20 |
N.S. |
1 | 5.17 | 1.13 | 2.57 | 3.13 | 2.48 | 2.22 | 3.26 | 2.65 | 0.87 |
time (sec) |
N/A | 0.313 | 0.262 | 3.963 | 0.035 | 0.065 | 0.146 | 0.106 | 0.260 | 0.535 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 43 | 31 | 55 | 44 | 44 | 57 | 66 | 34 |
N.S. |
1 | 0.00 | 1.43 | 1.03 | 1.83 | 1.47 | 1.47 | 1.90 | 2.20 | 1.13 |
time (sec) |
N/A | 0.000 | 2.473 | 0.523 | 0.121 | 0.077 | 0.139 | 0.121 | 0.224 | 0.570 |
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 | 26 | 0 | 21 | 21 | 74 | 23 | 17 | 23 | 24 | 23 |
N.S. |
1 | 0.00 | 0.81 | 0.81 | 2.85 | 0.88 | 0.65 | 0.88 | 0.92 | 0.88 |
time (sec) |
N/A | 0.000 | 0.122 | 16.414 | 0.189 | 0.071 | 0.181 | 0.163 | 0.258 | 0.694 |
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 | 22 | 42 | 32 | 23 | 43 | 27 | 24 | 35 | 33 | 33 |
N.S. |
1 | 1.91 | 1.45 | 1.05 | 1.95 | 1.23 | 1.09 | 1.59 | 1.50 | 1.50 |
time (sec) |
N/A | 0.313 | 0.099 | 0.313 | 0.046 | 0.068 | 0.125 | 0.116 | 0.229 | 0.514 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 37 | 47 | 34 | 32 | 34 | 34 | 274 | 30 |
N.S. |
1 | 0.00 | 1.54 | 1.96 | 1.42 | 1.33 | 1.42 | 1.42 | 11.42 | 1.25 |
time (sec) |
N/A | 0.000 | 0.186 | 0.275 | 0.182 | 0.067 | 0.690 | 0.112 | 0.213 | 0.620 |
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 | 27 | 18 | 18 | 18 | 60 | 18 | 14 | 18 | 21 | 18 |
N.S. |
1 | 0.67 | 0.67 | 0.67 | 2.22 | 0.67 | 0.52 | 0.67 | 0.78 | 0.67 |
time (sec) |
N/A | 0.190 | 0.021 | 0.120 | 0.079 | 0.070 | 0.051 | 0.113 | 0.207 | 0.051 |
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 | 17 | 16 | 15 | 21 | 15 | 15 | 21 | 15 |
N.S. |
1 | 0.94 | 0.94 | 0.89 | 0.83 | 1.17 | 0.83 | 0.83 | 1.17 | 0.83 |
time (sec) |
N/A | 0.184 | 0.005 | 0.136 | 0.045 | 0.066 | 0.077 | 0.111 | 0.235 | 0.502 |
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 | 27 | 42 | 23 | 40 | 39 | 30 | 37 | 103 |
N.S. |
1 | 0.00 | 0.87 | 1.35 | 0.74 | 1.29 | 1.26 | 0.97 | 1.19 | 3.32 |
time (sec) |
N/A | 0.000 | 1.063 | 0.395 | 0.403 | 0.068 | 0.141 | 0.227 | 0.213 | 0.638 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | C | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 24 | 56 | 53 | 38 | 19 | 25 | 39 | 25 |
N.S. |
1 | 0.00 | 0.96 | 2.24 | 2.12 | 1.52 | 0.76 | 1.00 | 1.56 | 1.00 |
time (sec) |
N/A | 0.000 | 0.066 | 0.909 | 0.168 | 0.071 | 0.140 | 0.665 | 0.198 | 0.808 |
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 | 10 | 10 | 11 | 10 | 10 | 8 | 11 | 17 | 8 |
N.S. |
1 | 0.62 | 0.62 | 0.69 | 0.62 | 0.62 | 0.50 | 0.69 | 1.06 | 0.50 |
time (sec) |
N/A | 0.142 | 0.002 | 0.132 | 0.033 | 0.059 | 0.031 | 0.110 | 0.204 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 39 | 39 | 40 | 39 | 32 | 39 | 39 | 44 | 39 |
N.S. |
1 | 1.86 | 1.86 | 1.90 | 1.86 | 1.52 | 1.86 | 1.86 | 2.10 | 1.86 |
time (sec) |
N/A | 0.221 | 0.007 | 0.103 | 0.031 | 0.058 | 0.062 | 0.116 | 0.210 | 0.509 |
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 | 26 | 52 | 32 | 28 | 60 | 27 | 27 | 36 | 43 | 26 |
N.S. |
1 | 2.00 | 1.23 | 1.08 | 2.31 | 1.04 | 1.04 | 1.38 | 1.65 | 1.00 |
time (sec) |
N/A | 0.444 | 0.205 | 0.032 | 0.161 | 0.074 | 0.122 | 0.129 | 0.217 | 0.593 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | F(-2) | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 33 | 41 | 50 | 48 | 0 | 40 | 40 | 104 |
N.S. |
1 | 0.00 | 1.27 | 1.58 | 1.92 | 1.85 | 0.00 | 1.54 | 1.54 | 4.00 |
time (sec) |
N/A | 0.000 | 0.274 | 1.717 | 0.223 | 0.074 | 0.000 | 0.258 | 0.209 | 0.358 |
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 | 31 | 125 | 34 | 34 | 117 | 45 | 31 | 52 | 57 | 37 |
N.S. |
1 | 4.03 | 1.10 | 1.10 | 3.77 | 1.45 | 1.00 | 1.68 | 1.84 | 1.19 |
time (sec) |
N/A | 3.370 | 8.242 | 1.509 | 0.110 | 0.075 | 0.102 | 0.121 | 0.220 | 0.622 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | C | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 62 | 55 | 74 | 116 | 83 | 110 | 86 | 73 | 112 |
N.S. |
1 | 1.94 | 1.72 | 2.31 | 3.62 | 2.59 | 3.44 | 2.69 | 2.28 | 3.50 |
time (sec) |
N/A | 0.735 | 0.034 | 0.350 | 0.107 | 0.071 | 0.168 | 0.117 | 0.217 | 0.653 |
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 | 24 | 0 | 24 | 26 | 28 | 28 | 29 | 28 | 26 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.08 | 1.17 | 1.17 | 1.21 | 1.17 | 1.08 | 0.00 |
time (sec) |
N/A | 0.000 | 0.075 | 31.592 | 0.206 | 0.070 | 0.374 | 0.485 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | A | A | F(-1) | F | F | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 27 | 124 | 30 | 39 | 0 | 0 | 272 | 39 |
N.S. |
1 | 0.00 | 0.93 | 4.28 | 1.03 | 1.34 | 0.00 | 0.00 | 9.38 | 1.34 |
time (sec) |
N/A | 0.000 | 0.176 | 0.105 | 0.384 | 0.080 | 0.000 | 0.000 | 200.021 | 1.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 112 | 35 | 108 | 128 | 91 | 87 | 113 | 136 | 107 |
N.S. |
1 | 4.67 | 1.46 | 4.50 | 5.33 | 3.79 | 3.62 | 4.71 | 5.67 | 4.46 |
time (sec) |
N/A | 0.604 | 0.071 | 101.546 | 0.047 | 0.073 | 0.167 | 0.115 | 0.224 | 0.652 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | A | A | F(-2) | F(-2) | B | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 40 | 147 | 32 | 31 | 0 | 0 | 32 | 31 |
N.S. |
1 | 0.00 | 1.18 | 4.32 | 0.94 | 0.91 | 0.00 | 0.00 | 0.94 | 0.91 |
time (sec) |
N/A | 0.000 | 0.071 | 0.388 | 0.222 | 0.073 | 0.000 | 0.000 | 0.310 | 5.387 |