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 | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 78 | 0 | 0 | 0 | 61 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.67 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.345 | 10.030 | 0.000 | 0.000 | 0.000 | 3.254 | 0.000 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 117 | 78 | 0 | 0 | 0 | 66 | 0 | 35 | 0 |
N.S. |
1 | 0.96 | 0.64 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.392 | 10.030 | 0.000 | 0.000 | 0.000 | 3.800 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 122 | 90 | 0 | 0 | 0 | 80 | 0 | 35 | 0 |
N.S. |
1 | 0.99 | 0.73 | 0.00 | 0.00 | 0.00 | 0.65 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.468 | 10.066 | 0.000 | 0.000 | 0.000 | 4.294 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 73 | 0 | 0 | 0 | 78 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 0.78 | 0.00 | 0.00 | 0.00 | 0.84 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.397 | 0.023 | 0.000 | 0.000 | 0.000 | 2.817 | 0.000 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 95 | 78 | 0 | 0 | 0 | 82 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.86 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.401 | 10.031 | 0.000 | 0.000 | 0.000 | 2.187 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 124 | 78 | 0 | 0 | 0 | 90 | 0 | 35 | 0 |
N.S. |
1 | 0.99 | 0.62 | 0.00 | 0.00 | 0.00 | 0.72 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.463 | 10.033 | 0.000 | 0.000 | 0.000 | 2.409 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 105 | 77 | 68 | 118 | 88 | 172 | 114 | 73 | 88 |
N.S. |
1 | 1.04 | 0.76 | 0.67 | 1.17 | 0.87 | 1.70 | 1.13 | 0.72 | 0.87 |
time (sec) |
N/A | 0.417 | 0.066 | 0.139 | 0.030 | 0.085 | 1.199 | 0.129 | 0.229 | 3.702 |
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 | 70 | 75 | 56 | 49 | 83 | 63 | 121 | 77 | 73 | 60 |
N.S. |
1 | 1.07 | 0.80 | 0.70 | 1.19 | 0.90 | 1.73 | 1.10 | 1.04 | 0.86 |
time (sec) |
N/A | 0.366 | 0.053 | 0.122 | 0.028 | 0.082 | 0.695 | 0.127 | 0.307 | 3.601 |
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 | 44 | 48 | 33 | 30 | 48 | 41 | 70 | 38 | 73 | 32 |
N.S. |
1 | 1.09 | 0.75 | 0.68 | 1.09 | 0.93 | 1.59 | 0.86 | 1.66 | 0.73 |
time (sec) |
N/A | 0.321 | 0.036 | 0.110 | 0.035 | 0.077 | 0.470 | 0.124 | 0.245 | 3.580 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 93 | 80 | 88 | 94 | 256 | 66 | 214 | 70 | 70 |
N.S. |
1 | 1.12 | 0.96 | 1.06 | 1.13 | 3.08 | 0.80 | 2.58 | 0.84 | 0.84 |
time (sec) |
N/A | 0.361 | 0.129 | 0.135 | 0.114 | 0.105 | 33.579 | 0.129 | 0.254 | 3.927 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | C | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 118 | 105 | 112 | 192 | 797 | 82 | 285 | 69 | 145 |
N.S. |
1 | 0.99 | 0.88 | 0.94 | 1.61 | 6.70 | 0.69 | 2.39 | 0.58 | 1.22 |
time (sec) |
N/A | 0.395 | 0.292 | 0.217 | 0.114 | 0.101 | 58.568 | 0.131 | 0.271 | 4.276 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 118 | 102 | 196 | 224 | 805 | 80 | 0 | 73 | 0 |
N.S. |
1 | 0.94 | 0.82 | 1.57 | 1.79 | 6.44 | 0.64 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.403 | 1.057 | 0.255 | 0.114 | 0.124 | 11.843 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 90 | 82 | 94 | 106 | 276 | 71 | 0 | 69 | 0 |
N.S. |
1 | 1.05 | 0.95 | 1.09 | 1.23 | 3.21 | 0.83 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.340 | 0.045 | 0.158 | 0.113 | 0.102 | 6.062 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 40 | 36 | 52 | 46 | 102 | 0 | 68 | 39 |
N.S. |
1 | 1.00 | 0.78 | 0.71 | 1.02 | 0.90 | 2.00 | 0.00 | 1.33 | 0.76 |
time (sec) |
N/A | 0.296 | 0.348 | 0.161 | 0.029 | 0.109 | 16.421 | 0.000 | 0.281 | 3.466 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 81 | 62 | 55 | 93 | 69 | 396 | 0 | 71 | 96 |
N.S. |
1 | 0.98 | 0.75 | 0.66 | 1.12 | 0.83 | 4.77 | 0.00 | 0.86 | 1.16 |
time (sec) |
N/A | 0.333 | 0.582 | 0.211 | 0.031 | 0.085 | 30.625 | 0.000 | 0.221 | 3.803 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 111 | 86 | 74 | 130 | 94 | 920 | 0 | 71 | 103 |
N.S. |
1 | 0.97 | 0.75 | 0.65 | 1.14 | 0.82 | 8.07 | 0.00 | 0.62 | 0.90 |
time (sec) |
N/A | 0.386 | 0.878 | 0.285 | 0.038 | 0.094 | 48.904 | 0.000 | 0.225 | 3.996 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 122 | 80 | 0 | 0 | 0 | 80 | 0 | 73 | 0 |
N.S. |
1 | 0.99 | 0.65 | 0.00 | 0.00 | 0.00 | 0.65 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.449 | 10.064 | 0.000 | 0.000 | 0.000 | 15.747 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 72 | 0 | 0 | 0 | 80 | 0 | 73 | 0 |
N.S. |
1 | 1.00 | 0.77 | 0.00 | 0.00 | 0.00 | 0.86 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.404 | 10.059 | 0.000 | 0.000 | 0.000 | 7.215 | 0.000 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 71 | 0 | 0 | 0 | 82 | 0 | 72 | 0 |
N.S. |
1 | 1.00 | 0.81 | 0.00 | 0.00 | 0.00 | 0.93 | 0.00 | 0.82 | 0.00 |
time (sec) |
N/A | 0.416 | 10.026 | 0.000 | 0.000 | 0.000 | 12.752 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 118 | 72 | 0 | 0 | 0 | 88 | 0 | 71 | 0 |
N.S. |
1 | 0.96 | 0.59 | 0.00 | 0.00 | 0.00 | 0.72 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.461 | 10.029 | 0.000 | 0.000 | 0.000 | 22.188 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 117 | 79 | 0 | 0 | 0 | 60 | 0 | 73 | 0 |
N.S. |
1 | 0.96 | 0.65 | 0.00 | 0.00 | 0.00 | 0.49 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.392 | 10.057 | 0.000 | 0.000 | 0.000 | 15.274 | 0.000 | 0.292 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 76 | 0 | 0 | 0 | 60 | 0 | 71 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.00 | 0.71 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.343 | 10.051 | 0.000 | 0.000 | 0.000 | 10.874 | 0.000 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 86 | 0 | 0 | 0 | 61 | 0 | 70 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.349 | 10.034 | 0.000 | 0.000 | 0.000 | 17.812 | 0.000 | 0.253 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 117 | 72 | 0 | 0 | 0 | 66 | 0 | 71 | 0 |
N.S. |
1 | 0.96 | 0.59 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.380 | 10.031 | 0.000 | 0.000 | 0.000 | 27.521 | 0.000 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 105 | 74 | 68 | 118 | 88 | 172 | 114 | 73 | 91 |
N.S. |
1 | 1.04 | 0.73 | 0.67 | 1.17 | 0.87 | 1.70 | 1.13 | 0.72 | 0.90 |
time (sec) |
N/A | 0.413 | 0.071 | 0.133 | 0.030 | 0.081 | 1.816 | 0.122 | 0.236 | 3.578 |
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 | 70 | 75 | 56 | 49 | 83 | 64 | 119 | 77 | 73 | 60 |
N.S. |
1 | 1.07 | 0.80 | 0.70 | 1.19 | 0.91 | 1.70 | 1.10 | 1.04 | 0.86 |
time (sec) |
N/A | 0.364 | 0.049 | 0.115 | 0.039 | 0.084 | 1.274 | 0.126 | 0.229 | 3.570 |
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 | 43 | 48 | 34 | 31 | 48 | 42 | 70 | 37 | 73 | 32 |
N.S. |
1 | 1.12 | 0.79 | 0.72 | 1.12 | 0.98 | 1.63 | 0.86 | 1.70 | 0.74 |
time (sec) |
N/A | 0.328 | 0.037 | 0.103 | 0.028 | 0.081 | 0.673 | 0.115 | 0.254 | 3.491 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 100 | 81 | 88 | 96 | 249 | 68 | 215 | 70 | 71 |
N.S. |
1 | 1.16 | 0.94 | 1.02 | 1.12 | 2.90 | 0.79 | 2.50 | 0.81 | 0.83 |
time (sec) |
N/A | 0.368 | 0.136 | 0.139 | 0.116 | 0.095 | 23.743 | 0.132 | 0.257 | 3.716 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | C | C | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 125 | 108 | 136 | 196 | 689 | 82 | 262 | 69 | 147 |
N.S. |
1 | 1.03 | 0.89 | 1.12 | 1.62 | 5.69 | 0.68 | 2.17 | 0.57 | 1.21 |
time (sec) |
N/A | 0.401 | 0.262 | 0.279 | 0.122 | 0.110 | 42.272 | 0.124 | 0.206 | 4.333 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 139 | 107 | 134 | 230 | 697 | 80 | 0 | 73 | 0 |
N.S. |
1 | 1.10 | 0.85 | 1.06 | 1.83 | 5.53 | 0.63 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.444 | 1.055 | 0.315 | 0.115 | 0.099 | 14.539 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 95 | 86 | 97 | 113 | 273 | 73 | 0 | 73 | 0 |
N.S. |
1 | 1.04 | 0.95 | 1.07 | 1.24 | 3.00 | 0.80 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.369 | 0.746 | 0.183 | 0.113 | 0.095 | 8.044 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 39 | 36 | 57 | 45 | 105 | 0 | 72 | 47 |
N.S. |
1 | 1.00 | 0.76 | 0.71 | 1.12 | 0.88 | 2.06 | 0.00 | 1.41 | 0.92 |
time (sec) |
N/A | 0.303 | 0.469 | 0.164 | 0.029 | 0.084 | 11.749 | 0.000 | 0.276 | 4.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 81 | 62 | 57 | 98 | 70 | 398 | 0 | 71 | 58 |
N.S. |
1 | 0.98 | 0.75 | 0.69 | 1.18 | 0.84 | 4.80 | 0.00 | 0.86 | 0.70 |
time (sec) |
N/A | 0.352 | 0.549 | 0.200 | 0.045 | 0.083 | 27.981 | 0.000 | 0.256 | 4.244 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 111 | 81 | 76 | 135 | 94 | 920 | 0 | 71 | 82 |
N.S. |
1 | 0.97 | 0.71 | 0.67 | 1.18 | 0.82 | 8.07 | 0.00 | 0.62 | 0.72 |
time (sec) |
N/A | 0.401 | 0.958 | 0.270 | 0.036 | 0.079 | 68.282 | 0.000 | 0.207 | 3.929 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 164 | 104 | 0 | 0 | 0 | 60 | 0 | 73 | 0 |
N.S. |
1 | 1.08 | 0.68 | 0.00 | 0.00 | 0.00 | 0.39 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.458 | 10.076 | 0.000 | 0.000 | 0.000 | 17.590 | 0.000 | 0.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 133 | 78 | 0 | 0 | 0 | 60 | 0 | 73 | 0 |
N.S. |
1 | 1.11 | 0.65 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.408 | 10.059 | 0.000 | 0.000 | 0.000 | 9.566 | 0.000 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 75 | 0 | 0 | 0 | 60 | 0 | 71 | 0 |
N.S. |
1 | 1.00 | 0.74 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.366 | 10.070 | 0.000 | 0.000 | 0.000 | 8.284 | 0.000 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 121 | 86 | 0 | 0 | 0 | 61 | 0 | 70 | 0 |
N.S. |
1 | 0.99 | 0.70 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.377 | 10.040 | 0.000 | 0.000 | 0.000 | 13.345 | 0.000 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 146 | 73 | 0 | 0 | 0 | 66 | 0 | 71 | 0 |
N.S. |
1 | 0.96 | 0.48 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.423 | 10.044 | 0.000 | 0.000 | 0.000 | 27.642 | 0.000 | 0.266 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 163 | 101 | 0 | 0 | 0 | 80 | 0 | 73 | 0 |
N.S. |
1 | 1.08 | 0.67 | 0.00 | 0.00 | 0.00 | 0.53 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.568 | 10.075 | 0.000 | 0.000 | 0.000 | 20.758 | 0.000 | 0.243 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 135 | 78 | 0 | 0 | 0 | 80 | 0 | 73 | 0 |
N.S. |
1 | 1.12 | 0.65 | 0.00 | 0.00 | 0.00 | 0.67 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.476 | 10.059 | 0.000 | 0.000 | 0.000 | 12.747 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 72 | 0 | 0 | 0 | 78 | 0 | 69 | 0 |
N.S. |
1 | 1.00 | 0.71 | 0.00 | 0.00 | 0.00 | 0.76 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.422 | 0.031 | 0.000 | 0.000 | 0.000 | 10.798 | 0.000 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 120 | 85 | 0 | 0 | 0 | 82 | 0 | 68 | 0 |
N.S. |
1 | 0.98 | 0.69 | 0.00 | 0.00 | 0.00 | 0.67 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.457 | 10.029 | 0.000 | 0.000 | 0.000 | 29.402 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 151 | 72 | 0 | 0 | 0 | 90 | 0 | 71 | 0 |
N.S. |
1 | 0.97 | 0.46 | 0.00 | 0.00 | 0.00 | 0.58 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.512 | 10.031 | 0.000 | 0.000 | 0.000 | 43.412 | 0.000 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 105 | 80 | 68 | 118 | 99 | 338 | 105 | 113 | 90 |
N.S. |
1 | 1.05 | 0.80 | 0.68 | 1.18 | 0.99 | 3.38 | 1.05 | 1.13 | 0.90 |
time (sec) |
N/A | 0.422 | 0.069 | 0.155 | 0.029 | 0.085 | 1.480 | 0.130 | 0.297 | 3.637 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 75 | 56 | 49 | 84 | 75 | 240 | 63 | 113 | 60 |
N.S. |
1 | 1.06 | 0.79 | 0.69 | 1.18 | 1.06 | 3.38 | 0.89 | 1.59 | 0.85 |
time (sec) |
N/A | 0.376 | 0.053 | 0.135 | 0.035 | 0.094 | 1.008 | 0.115 | 0.307 | 3.703 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 48 | 34 | 30 | 49 | 52 | 143 | 32 | 113 | 32 |
N.S. |
1 | 1.09 | 0.77 | 0.68 | 1.11 | 1.18 | 3.25 | 0.73 | 2.57 | 0.73 |
time (sec) |
N/A | 0.328 | 0.038 | 0.100 | 0.029 | 0.079 | 1.309 | 0.125 | 0.254 | 3.701 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 116 | 94 | 104 | 105 | 335 | 88 | 229 | 110 | 85 |
N.S. |
1 | 1.14 | 0.92 | 1.02 | 1.03 | 3.28 | 0.86 | 2.25 | 1.08 | 0.83 |
time (sec) |
N/A | 0.400 | 0.162 | 0.161 | 0.113 | 0.129 | 43.028 | 0.129 | 0.280 | 3.743 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | C | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 141 | 129 | 132 | 218 | 879 | 82 | 287 | 109 | 177 |
N.S. |
1 | 0.97 | 0.88 | 0.90 | 1.49 | 6.02 | 0.56 | 1.97 | 0.75 | 1.21 |
time (sec) |
N/A | 0.434 | 0.329 | 0.309 | 0.120 | 0.127 | 132.243 | 0.130 | 0.283 | 4.239 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 162 | 126 | 131 | 259 | 884 | 80 | 0 | 113 | 0 |
N.S. |
1 | 1.07 | 0.83 | 0.87 | 1.72 | 5.85 | 0.53 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 0.493 | 2.037 | 0.351 | 0.122 | 0.152 | 38.697 | 0.000 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 117 | 99 | 117 | 126 | 358 | 102 | 0 | 113 | 0 |
N.S. |
1 | 1.07 | 0.91 | 1.07 | 1.16 | 3.28 | 0.94 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.413 | 1.345 | 0.217 | 0.110 | 0.109 | 27.469 | 0.000 | 0.249 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 47 | 37 | 34 | 51 | 54 | 190 | 0 | 109 | 33 |
N.S. |
1 | 0.77 | 0.61 | 0.56 | 0.84 | 0.89 | 3.11 | 0.00 | 1.79 | 0.54 |
time (sec) |
N/A | 0.274 | 0.007 | 0.133 | 0.042 | 0.107 | 18.883 | 0.000 | 0.264 | 3.314 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 78 | 62 | 57 | 88 | 81 | 360 | 0 | 108 | 70 |
N.S. |
1 | 0.99 | 0.78 | 0.72 | 1.11 | 1.03 | 4.56 | 0.00 | 1.37 | 0.89 |
time (sec) |
N/A | 0.331 | 0.551 | 0.224 | 0.030 | 0.093 | 39.944 | 0.000 | 0.213 | 3.523 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 108 | 86 | 76 | 131 | 105 | 726 | 0 | 111 | 147 |
N.S. |
1 | 0.96 | 0.76 | 0.67 | 1.16 | 0.93 | 6.42 | 0.00 | 0.98 | 1.30 |
time (sec) |
N/A | 0.372 | 0.796 | 0.285 | 0.040 | 0.088 | 79.394 | 0.000 | 0.216 | 4.259 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 165 | 109 | 0 | 0 | 0 | 80 | 0 | 113 | 0 |
N.S. |
1 | 1.09 | 0.72 | 0.00 | 0.00 | 0.00 | 0.53 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.529 | 10.088 | 0.000 | 0.000 | 0.000 | 63.217 | 0.000 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 135 | 93 | 0 | 0 | 0 | 80 | 0 | 113 | 0 |
N.S. |
1 | 1.11 | 0.76 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.495 | 10.067 | 0.000 | 0.000 | 0.000 | 34.112 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 81 | 0 | 0 | 0 | 80 | 0 | 113 | 0 |
N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.78 | 0.00 | 1.10 | 0.00 |
time (sec) |
N/A | 0.439 | 10.052 | 0.000 | 0.000 | 0.000 | 19.409 | 0.000 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 118 | 80 | 0 | 0 | 0 | 82 | 0 | 112 | 0 |
N.S. |
1 | 0.98 | 0.66 | 0.00 | 0.00 | 0.00 | 0.68 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.464 | 10.028 | 0.000 | 0.000 | 0.000 | 29.570 | 0.000 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 145 | 81 | 0 | 0 | 0 | 88 | 0 | 111 | 0 |
N.S. |
1 | 0.95 | 0.53 | 0.00 | 0.00 | 0.00 | 0.58 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.526 | 10.050 | 0.000 | 0.000 | 0.000 | 77.343 | 0.000 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 159 | 107 | 0 | 0 | 0 | 60 | 0 | 113 | 0 |
N.S. |
1 | 1.05 | 0.71 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 0.449 | 10.094 | 0.000 | 0.000 | 0.000 | 41.381 | 0.000 | 0.266 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 129 | 101 | 0 | 0 | 0 | 60 | 0 | 113 | 0 |
N.S. |
1 | 1.10 | 0.86 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 | 0.97 | 0.00 |
time (sec) |
N/A | 0.393 | 10.080 | 0.000 | 0.000 | 0.000 | 28.204 | 0.000 | 0.274 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 104 | 0 | 0 | 0 | 60 | 0 | 111 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.358 | 10.078 | 0.000 | 0.000 | 0.000 | 20.830 | 0.000 | 0.301 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 121 | 118 | 0 | 0 | 0 | 61 | 0 | 110 | 0 |
N.S. |
1 | 0.99 | 0.97 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.375 | 10.049 | 0.000 | 0.000 | 0.000 | 38.532 | 0.000 | 0.273 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 146 | 81 | 0 | 0 | 0 | 66 | 0 | 111 | 0 |
N.S. |
1 | 0.96 | 0.53 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.420 | 10.037 | 0.000 | 0.000 | 0.000 | 78.090 | 0.000 | 0.319 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 191 | 147 | 150 | 296 | 963 | 0 | 0 | 153 | 0 |
N.S. |
1 | 1.05 | 0.81 | 0.82 | 1.63 | 5.29 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.549 | 6.113 | 0.445 | 0.149 | 0.119 | 0.000 | 0.000 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 143 | 112 | 123 | 145 | 426 | 133 | 0 | 153 | 0 |
N.S. |
1 | 1.09 | 0.85 | 0.94 | 1.11 | 3.25 | 1.02 | 0.00 | 1.17 | 0.00 |
time (sec) |
N/A | 0.450 | 3.191 | 0.273 | 0.113 | 0.129 | 126.474 | 0.000 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 40 | 37 | 53 | 68 | 284 | 0 | 153 | 56 |
N.S. |
1 | 1.00 | 0.61 | 0.56 | 0.80 | 1.03 | 4.30 | 0.00 | 2.32 | 0.85 |
time (sec) |
N/A | 0.312 | 2.130 | 0.175 | 0.042 | 0.106 | 131.628 | 0.000 | 0.222 | 3.610 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 88 | 60 | 52 | 86 | 87 | 709 | 0 | 149 | 87 |
N.S. |
1 | 0.97 | 0.66 | 0.57 | 0.95 | 0.96 | 7.79 | 0.00 | 1.64 | 0.96 |
time (sec) |
N/A | 0.333 | 0.010 | 0.158 | 0.032 | 0.097 | 86.381 | 0.000 | 0.264 | 3.629 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 103 | 81 | 76 | 125 | 116 | 898 | 0 | 148 | 82 |
N.S. |
1 | 0.96 | 0.76 | 0.71 | 1.17 | 1.08 | 8.39 | 0.00 | 1.38 | 0.77 |
time (sec) |
N/A | 0.372 | 0.791 | 0.324 | 0.041 | 0.125 | 165.828 | 0.000 | 0.218 | 3.848 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 133 | 105 | 95 | 168 | 140 | 0 | 0 | 151 | 173 |
N.S. |
1 | 0.93 | 0.73 | 0.66 | 1.17 | 0.98 | 0.00 | 0.00 | 1.06 | 1.21 |
time (sec) |
N/A | 0.420 | 1.137 | 0.404 | 0.038 | 0.097 | 0.000 | 0.000 | 0.237 | 4.241 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 194 | 133 | 0 | 0 | 0 | 0 | 0 | 153 | 0 |
N.S. |
1 | 1.07 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.581 | 10.137 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 164 | 117 | 0 | 0 | 0 | 80 | 0 | 153 | 0 |
N.S. |
1 | 1.08 | 0.77 | 0.00 | 0.00 | 0.00 | 0.53 | 0.00 | 1.01 | 0.00 |
time (sec) |
N/A | 0.541 | 10.106 | 0.000 | 0.000 | 0.000 | 148.982 | 0.000 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 135 | 98 | 0 | 0 | 0 | 80 | 0 | 153 | 0 |
N.S. |
1 | 1.02 | 0.74 | 0.00 | 0.00 | 0.00 | 0.61 | 0.00 | 1.16 | 0.00 |
time (sec) |
N/A | 0.476 | 10.080 | 0.000 | 0.000 | 0.000 | 132.766 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 134 | 122 | 0 | 0 | 0 | 80 | 0 | 153 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.00 | 0.00 | 0.00 | 0.60 | 0.00 | 1.14 | 0.00 |
time (sec) |
N/A | 0.487 | 10.061 | 0.000 | 0.000 | 0.000 | 88.586 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 147 | 84 | 0 | 0 | 0 | 82 | 0 | 152 | 0 |
N.S. |
1 | 0.97 | 0.56 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 | 1.01 | 0.00 |
time (sec) |
N/A | 0.523 | 10.034 | 0.000 | 0.000 | 0.000 | 110.497 | 0.000 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 176 | 83 | 0 | 0 | 0 | 0 | 0 | 151 | 0 |
N.S. |
1 | 0.96 | 0.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.584 | 10.035 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 220 | 169 | 169 | 331 | 1042 | 0 | 0 | 193 | 0 |
N.S. |
1 | 1.03 | 0.79 | 0.79 | 1.55 | 4.89 | 0.00 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 0.602 | 6.534 | 0.599 | 0.147 | 0.145 | 0.000 | 0.000 | 0.298 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 169 | 124 | 136 | 162 | 494 | 0 | 0 | 193 | 0 |
N.S. |
1 | 1.10 | 0.81 | 0.89 | 1.06 | 3.23 | 0.00 | 0.00 | 1.26 | 0.00 |
time (sec) |
N/A | 0.528 | 6.198 | 0.378 | 0.124 | 0.135 | 0.000 | 0.000 | 0.253 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 40 | 37 | 53 | 79 | 0 | 0 | 193 | 156 |
N.S. |
1 | 1.00 | 0.61 | 0.56 | 0.80 | 1.20 | 0.00 | 0.00 | 2.92 | 2.36 |
time (sec) |
N/A | 0.315 | 5.099 | 0.226 | 0.043 | 0.111 | 0.000 | 0.000 | 0.224 | 3.568 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 96 | 62 | 55 | 86 | 102 | 0 | 0 | 193 | 116 |
N.S. |
1 | 0.97 | 0.63 | 0.56 | 0.87 | 1.03 | 0.00 | 0.00 | 1.95 | 1.17 |
time (sec) |
N/A | 0.373 | 2.961 | 0.182 | 0.038 | 0.105 | 0.000 | 0.000 | 0.224 | 3.417 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 115 | 80 | 71 | 120 | 121 | 0 | 0 | 189 | 105 |
N.S. |
1 | 0.95 | 0.66 | 0.59 | 0.99 | 1.00 | 0.00 | 0.00 | 1.56 | 0.87 |
time (sec) |
N/A | 0.378 | 0.016 | 0.177 | 0.039 | 0.114 | 0.000 | 0.000 | 0.246 | 3.402 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 132 | 102 | 95 | 159 | 151 | 0 | 0 | 188 | 120 |
N.S. |
1 | 0.98 | 0.76 | 0.70 | 1.18 | 1.12 | 0.00 | 0.00 | 1.39 | 0.89 |
time (sec) |
N/A | 0.417 | 1.282 | 0.449 | 0.056 | 0.110 | 0.000 | 0.000 | 0.231 | 3.602 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 162 | 126 | 114 | 202 | 175 | 0 | 0 | 191 | 241 |
N.S. |
1 | 0.94 | 0.73 | 0.66 | 1.17 | 1.01 | 0.00 | 0.00 | 1.10 | 1.39 |
time (sec) |
N/A | 0.468 | 1.698 | 0.861 | 0.044 | 0.120 | 0.000 | 0.000 | 0.257 | 4.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 223 | 154 | 0 | 0 | 0 | 0 | 0 | 193 | 0 |
N.S. |
1 | 1.05 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 0.653 | 10.132 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 193 | 139 | 0 | 0 | 0 | 0 | 0 | 193 | 0 |
N.S. |
1 | 1.06 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 0.610 | 10.123 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 164 | 120 | 0 | 0 | 0 | 0 | 0 | 193 | 0 |
N.S. |
1 | 1.01 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.18 | 0.00 |
time (sec) |
N/A | 0.528 | 10.122 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 164 | 134 | 0 | 0 | 0 | 0 | 0 | 193 | 0 |
N.S. |
1 | 0.99 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.16 | 0.00 |
time (sec) |
N/A | 0.532 | 10.074 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 164 | 123 | 0 | 0 | 0 | 0 | 0 | 193 | 0 |
N.S. |
1 | 0.97 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.14 | 0.00 |
time (sec) |
N/A | 0.555 | 10.066 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.268 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 176 | 84 | 0 | 0 | 0 | 0 | 0 | 192 | 0 |
N.S. |
1 | 0.97 | 0.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 0.557 | 10.039 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.248 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 205 | 83 | 0 | 0 | 0 | 0 | 0 | 191 | 0 |
N.S. |
1 | 0.96 | 0.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.647 | 10.044 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.255 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 121 | 108 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.441 | 0.098 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 97 | 81 | 0 | 0 | 0 | 0 | 0 | 119 | 0 |
N.S. |
1 | 1.09 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.34 | 0.00 |
time (sec) |
N/A | 0.408 | 0.114 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 106 | 19 | 32 | 24 | 0 | 37 | 24 | 18 |
N.S. |
1 | 1.00 | 4.82 | 0.86 | 1.45 | 1.09 | 0.00 | 1.68 | 1.09 | 0.82 |
time (sec) |
N/A | 0.267 | 0.118 | 5.714 | 0.071 | 0.085 | 0.000 | 0.133 | 0.209 | 3.983 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 87 | 82 | 78 | 84 | 100 | 0 | 88 | 180 | 88 |
N.S. |
1 | 0.97 | 0.91 | 0.87 | 0.93 | 1.11 | 0.00 | 0.98 | 2.00 | 0.98 |
time (sec) |
N/A | 0.441 | 0.041 | 0.219 | 0.042 | 2.349 | 0.000 | 0.132 | 0.252 | 4.877 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 66 | 66 | 65 | 68 | 72 | 0 | 70 | 150 | 68 |
N.S. |
1 | 0.94 | 0.94 | 0.93 | 0.97 | 1.03 | 0.00 | 1.00 | 2.14 | 0.97 |
time (sec) |
N/A | 0.375 | 0.025 | 0.138 | 0.025 | 0.813 | 0.000 | 0.123 | 0.263 | 4.936 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 52 | 43 | 43 | 49 | 42 | 144 | 51 | 115 | 51 |
N.S. |
1 | 0.98 | 0.81 | 0.81 | 0.92 | 0.79 | 2.72 | 0.96 | 2.17 | 0.96 |
time (sec) |
N/A | 0.348 | 0.020 | 0.124 | 0.025 | 0.275 | 40.790 | 0.124 | 0.255 | 4.394 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 44 | 31 | 32 | 41 | 31 | 138 | 51 | 99 | 1012 |
N.S. |
1 | 0.98 | 0.69 | 0.71 | 0.91 | 0.69 | 3.07 | 1.13 | 2.20 | 22.49 |
time (sec) |
N/A | 0.296 | 0.020 | 0.098 | 0.025 | 0.087 | 0.962 | 0.126 | 0.224 | 4.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 63 | 54 | 55 | 61 | 54 | 0 | 73 | 127 | 58 |
N.S. |
1 | 1.02 | 0.87 | 0.89 | 0.98 | 0.87 | 0.00 | 1.18 | 2.05 | 0.94 |
time (sec) |
N/A | 0.384 | 0.025 | 0.144 | 0.041 | 0.981 | 0.000 | 0.121 | 0.261 | 4.242 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 86 | 88 | 82 | 87 | 99 | 0 | 112 | 185 | 87 |
N.S. |
1 | 0.99 | 1.01 | 0.94 | 1.00 | 1.14 | 0.00 | 1.29 | 2.13 | 1.00 |
time (sec) |
N/A | 0.438 | 0.033 | 0.175 | 0.026 | 4.481 | 0.000 | 0.131 | 0.313 | 5.435 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 132 | 104 | 98 | 100 | 576 | 0 | 112 | 222 | 532 |
N.S. |
1 | 1.18 | 0.93 | 0.88 | 0.89 | 5.14 | 0.00 | 1.00 | 1.98 | 4.75 |
time (sec) |
N/A | 0.576 | 0.110 | 0.197 | 0.113 | 1.294 | 0.000 | 0.129 | 0.232 | 4.939 |