Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 105 | 65 | 95 | 83 | 221 | 89 | 84 | 225 |
N.S. |
1 | 1.00 | 1.03 | 0.64 | 0.93 | 0.81 | 2.17 | 0.87 | 0.82 | 2.21 |
time (sec) |
N/A | 0.294 | 0.327 | 8.127 | 0.038 | 0.117 | 0.245 | 0.130 | 0.176 | 20.193 |
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 | 129 | 129 | 115 | 76 | 143 | 96 | 379 | 106 | 100 | 294 |
N.S. |
1 | 1.00 | 0.89 | 0.59 | 1.11 | 0.74 | 2.94 | 0.82 | 0.78 | 2.28 |
time (sec) |
N/A | 0.348 | 0.408 | 43.770 | 0.039 | 0.095 | 0.371 | 0.127 | 0.172 | 20.136 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 101 | 40 | 180 | 70 | 1221 | 67 | 78 | 78 |
N.S. |
1 | 1.00 | 1.91 | 0.75 | 3.40 | 1.32 | 23.04 | 1.26 | 1.47 | 1.47 |
time (sec) |
N/A | 0.374 | 0.127 | 0.428 | 0.114 | 0.133 | 1.884 | 0.131 | 0.166 | 17.844 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 87 | 36 | 128 | 53 | 665 | 56 | 61 | 59 |
N.S. |
1 | 1.00 | 2.07 | 0.86 | 3.05 | 1.26 | 15.83 | 1.33 | 1.45 | 1.40 |
time (sec) |
N/A | 0.275 | 0.100 | 0.281 | 0.114 | 0.100 | 0.945 | 0.132 | 0.157 | 17.747 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 24 | 48 | 30 | 78 | 35 | 221 | 44 | 41 | 46 |
N.S. |
1 | 0.89 | 1.78 | 1.11 | 2.89 | 1.30 | 8.19 | 1.63 | 1.52 | 1.70 |
time (sec) |
N/A | 0.305 | 0.074 | 0.206 | 0.112 | 0.080 | 0.444 | 0.127 | 0.156 | 17.809 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 42 | 22 | 32 | 28 | 34 | 19 | 26 | 19 |
N.S. |
1 | 1.00 | 2.47 | 1.29 | 1.88 | 1.65 | 2.00 | 1.12 | 1.53 | 1.12 |
time (sec) |
N/A | 0.231 | 0.060 | 0.139 | 0.109 | 0.124 | 0.217 | 0.123 | 0.165 | 17.734 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 29 | 14 | 16 | 22 | 10 | 13 | 17 | 13 |
N.S. |
1 | 1.00 | 2.42 | 1.17 | 1.33 | 1.83 | 0.83 | 1.08 | 1.42 | 1.08 |
time (sec) |
N/A | 0.171 | 0.012 | 0.094 | 0.027 | 0.086 | 0.113 | 0.119 | 0.156 | 0.013 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 40 | 21 | 31 | 53 | 0 | 24 | 34 | 23 |
N.S. |
1 | 1.00 | 2.00 | 1.05 | 1.55 | 2.65 | 0.00 | 1.20 | 1.70 | 1.15 |
time (sec) |
N/A | 0.275 | 0.053 | 0.198 | 0.032 | 0.092 | 0.000 | 0.130 | 0.158 | 17.606 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 27 | 63 | 36 | 68 | 91 | 0 | 53 | 59 | 49 |
N.S. |
1 | 1.04 | 2.42 | 1.38 | 2.62 | 3.50 | 0.00 | 2.04 | 2.27 | 1.88 |
time (sec) |
N/A | 0.377 | 0.244 | 0.266 | 0.029 | 0.085 | 0.000 | 0.130 | 0.159 | 17.807 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 43 | 83 | 54 | 97 | 134 | 0 | 73 | 75 | 69 |
N.S. |
1 | 1.02 | 1.98 | 1.29 | 2.31 | 3.19 | 0.00 | 1.74 | 1.79 | 1.64 |
time (sec) |
N/A | 0.449 | 0.480 | 0.319 | 0.033 | 0.102 | 0.000 | 0.133 | 0.158 | 17.243 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 54 | 113 | 68 | 120 | 168 | 0 | 96 | 91 | 89 |
N.S. |
1 | 0.98 | 2.05 | 1.24 | 2.18 | 3.05 | 0.00 | 1.75 | 1.65 | 1.62 |
time (sec) |
N/A | 0.483 | 0.744 | 0.362 | 0.028 | 0.092 | 0.000 | 0.130 | 0.163 | 17.372 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 72 | 100 | 65 | 198 | 105 | 1423 | 72 | 103 | 77 |
N.S. |
1 | 1.09 | 1.52 | 0.98 | 3.00 | 1.59 | 21.56 | 1.09 | 1.56 | 1.17 |
time (sec) |
N/A | 0.428 | 0.259 | 0.495 | 0.112 | 0.094 | 3.761 | 0.119 | 0.183 | 17.389 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 51 | 84 | 55 | 144 | 95 | 779 | 51 | 89 | 62 |
N.S. |
1 | 1.09 | 1.79 | 1.17 | 3.06 | 2.02 | 16.57 | 1.09 | 1.89 | 1.32 |
time (sec) |
N/A | 0.542 | 0.228 | 0.349 | 0.108 | 0.084 | 2.027 | 0.122 | 0.190 | 17.257 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 39 | 69 | 39 | 90 | 82 | 321 | 35 | 73 | 34 |
N.S. |
1 | 1.11 | 1.97 | 1.11 | 2.57 | 2.34 | 9.17 | 1.00 | 2.09 | 0.97 |
time (sec) |
N/A | 0.347 | 0.139 | 0.251 | 0.111 | 0.079 | 1.049 | 0.124 | 0.205 | 17.375 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 32 | 21 | 22 | 62 | 60 | 87 | 21 | 37 | 21 |
N.S. |
1 | 0.97 | 0.64 | 0.67 | 1.88 | 1.82 | 2.64 | 0.64 | 1.12 | 0.64 |
time (sec) |
N/A | 0.250 | 0.034 | 0.185 | 0.029 | 0.093 | 0.609 | 0.125 | 0.168 | 17.357 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 32 | 31 | 27 | 74 | 58 | 134 | 29 | 37 | 29 |
N.S. |
1 | 0.97 | 0.94 | 0.82 | 2.24 | 1.76 | 4.06 | 0.88 | 1.12 | 0.88 |
time (sec) |
N/A | 0.238 | 0.075 | 0.170 | 0.029 | 0.079 | 0.308 | 0.122 | 0.171 | 17.382 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 28 | 41 | 89 | 117 | 0 | 40 | 89 | 38 |
N.S. |
1 | 1.00 | 0.74 | 1.08 | 2.34 | 3.08 | 0.00 | 1.05 | 2.34 | 1.00 |
time (sec) |
N/A | 0.373 | 0.056 | 0.301 | 0.028 | 0.092 | 0.000 | 0.131 | 0.173 | 17.281 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 53 | 166 | 56 | 126 | 168 | 0 | 69 | 117 | 91 |
N.S. |
1 | 1.18 | 3.69 | 1.24 | 2.80 | 3.73 | 0.00 | 1.53 | 2.60 | 2.02 |
time (sec) |
N/A | 0.531 | 0.996 | 0.342 | 0.037 | 0.132 | 0.000 | 0.125 | 0.158 | 17.321 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 70 | 203 | 74 | 155 | 220 | 0 | 93 | 139 | 111 |
N.S. |
1 | 1.09 | 3.17 | 1.16 | 2.42 | 3.44 | 0.00 | 1.45 | 2.17 | 1.73 |
time (sec) |
N/A | 0.637 | 0.883 | 0.461 | 0.035 | 0.091 | 0.000 | 0.130 | 0.171 | 17.377 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 84 | 238 | 89 | 178 | 266 | 0 | 114 | 153 | 101 |
N.S. |
1 | 1.29 | 3.66 | 1.37 | 2.74 | 4.09 | 0.00 | 1.75 | 2.35 | 1.55 |
time (sec) |
N/A | 0.686 | 3.628 | 0.509 | 0.034 | 0.084 | 0.000 | 0.135 | 0.173 | 17.332 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 114 | 191 | 99 | 306 | 158 | 3288 | 99 | 161 | 110 |
N.S. |
1 | 1.13 | 1.89 | 0.98 | 3.03 | 1.56 | 32.55 | 0.98 | 1.59 | 1.09 |
time (sec) |
N/A | 0.781 | 0.138 | 1.071 | 0.116 | 0.104 | 18.744 | 0.132 | 0.174 | 17.833 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 104 | 170 | 97 | 252 | 145 | 2259 | 88 | 147 | 93 |
N.S. |
1 | 1.16 | 1.89 | 1.08 | 2.80 | 1.61 | 25.10 | 0.98 | 1.63 | 1.03 |
time (sec) |
N/A | 0.598 | 0.145 | 0.836 | 0.114 | 0.090 | 11.677 | 0.133 | 0.193 | 17.617 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 76 | 140 | 66 | 198 | 132 | 1425 | 67 | 133 | 78 |
N.S. |
1 | 1.07 | 1.97 | 0.93 | 2.79 | 1.86 | 20.07 | 0.94 | 1.87 | 1.10 |
time (sec) |
N/A | 0.744 | 0.104 | 0.573 | 0.118 | 0.089 | 6.938 | 0.128 | 0.166 | 17.405 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 69 | 112 | 54 | 144 | 119 | 777 | 51 | 119 | 50 |
N.S. |
1 | 1.17 | 1.90 | 0.92 | 2.44 | 2.02 | 13.17 | 0.86 | 2.02 | 0.85 |
time (sec) |
N/A | 0.581 | 0.191 | 0.371 | 0.113 | 0.098 | 3.994 | 0.124 | 0.214 | 17.249 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 52 | 27 | 30 | 104 | 90 | 206 | 29 | 61 | 29 |
N.S. |
1 | 1.04 | 0.54 | 0.60 | 2.08 | 1.80 | 4.12 | 0.58 | 1.22 | 0.58 |
time (sec) |
N/A | 0.372 | 0.049 | 0.292 | 0.033 | 0.110 | 2.200 | 0.125 | 0.197 | 17.297 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 54 | 25 | 38 | 116 | 88 | 277 | 37 | 56 | 37 |
N.S. |
1 | 1.08 | 0.50 | 0.76 | 2.32 | 1.76 | 5.54 | 0.74 | 1.12 | 0.74 |
time (sec) |
N/A | 0.328 | 0.037 | 0.267 | 0.034 | 0.077 | 1.234 | 0.130 | 0.173 | 17.189 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 54 | 45 | 33 | 128 | 92 | 348 | 45 | 69 | 45 |
N.S. |
1 | 1.08 | 0.90 | 0.66 | 2.56 | 1.84 | 6.96 | 0.90 | 1.38 | 0.90 |
time (sec) |
N/A | 0.309 | 0.078 | 0.221 | 0.036 | 0.091 | 0.608 | 0.127 | 0.180 | 16.897 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 67 | 49 | 61 | 143 | 168 | 0 | 56 | 147 | 54 |
N.S. |
1 | 1.16 | 0.84 | 1.05 | 2.47 | 2.90 | 0.00 | 0.97 | 2.53 | 0.93 |
time (sec) |
N/A | 0.542 | 0.069 | 0.379 | 0.036 | 0.086 | 0.000 | 0.128 | 0.162 | 17.391 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 75 | 206 | 75 | 180 | 225 | 0 | 85 | 173 | 129 |
N.S. |
1 | 1.15 | 3.17 | 1.15 | 2.77 | 3.46 | 0.00 | 1.31 | 2.66 | 1.98 |
time (sec) |
N/A | 0.764 | 1.145 | 0.460 | 0.036 | 0.096 | 0.000 | 0.139 | 0.178 | 17.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 100 | 247 | 91 | 209 | 276 | 0 | 109 | 191 | 97 |
N.S. |
1 | 1.16 | 2.87 | 1.06 | 2.43 | 3.21 | 0.00 | 1.27 | 2.22 | 1.13 |
time (sec) |
N/A | 0.860 | 1.416 | 0.545 | 0.037 | 0.164 | 0.000 | 0.129 | 0.168 | 17.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 116 | 299 | 107 | 232 | 333 | 0 | 128 | 205 | 117 |
N.S. |
1 | 1.13 | 2.90 | 1.04 | 2.25 | 3.23 | 0.00 | 1.24 | 1.99 | 1.14 |
time (sec) |
N/A | 0.923 | 1.752 | 0.639 | 0.039 | 0.106 | 0.000 | 0.125 | 0.193 | 17.381 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 179 | 165 | 83 | 0 | 132 | 0 | 147 | 23 | 0 |
N.S. |
1 | 1.13 | 1.04 | 0.53 | 0.00 | 0.84 | 0.00 | 0.93 | 0.15 | 0.00 |
time (sec) |
N/A | 0.832 | 0.630 | 0.467 | 0.000 | 0.087 | 0.000 | 0.152 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 138 | 141 | 73 | 0 | 111 | 0 | 120 | 23 | 0 |
N.S. |
1 | 1.13 | 1.16 | 0.60 | 0.00 | 0.91 | 0.00 | 0.98 | 0.19 | 0.00 |
time (sec) |
N/A | 0.627 | 0.423 | 0.348 | 0.000 | 0.098 | 0.000 | 0.144 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 97 | 117 | 63 | 0 | 92 | 0 | 93 | 23 | 0 |
N.S. |
1 | 1.13 | 1.36 | 0.73 | 0.00 | 1.07 | 0.00 | 1.08 | 0.27 | 0.00 |
time (sec) |
N/A | 0.442 | 0.483 | 0.341 | 0.000 | 0.085 | 0.000 | 0.143 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 81 | 51 | 0 | 67 | 0 | 65 | 21 | 0 |
N.S. |
1 | 1.00 | 1.45 | 0.91 | 0.00 | 1.20 | 0.00 | 1.16 | 0.38 | 0.00 |
time (sec) |
N/A | 0.288 | 0.163 | 0.273 | 0.000 | 0.093 | 0.000 | 0.137 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 65 | 43 | 0 | 50 | 0 | 36 | 14 | 33 |
N.S. |
1 | 1.00 | 2.50 | 1.65 | 0.00 | 1.92 | 0.00 | 1.38 | 0.54 | 1.27 |
time (sec) |
N/A | 0.188 | 0.025 | 0.225 | 0.000 | 0.075 | 0.000 | 0.134 | 0.168 | 0.126 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 66 | 68 | 0 | 219 | 0 | 67 | 21 | 0 |
N.S. |
1 | 1.00 | 1.78 | 1.84 | 0.00 | 5.92 | 0.00 | 1.81 | 0.57 | 0.00 |
time (sec) |
N/A | 0.238 | 0.096 | 0.339 | 0.000 | 0.093 | 0.000 | 0.148 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 178 | 104 | 0 | 258 | 0 | 122 | 23 | 0 |
N.S. |
1 | 1.00 | 2.78 | 1.62 | 0.00 | 4.03 | 0.00 | 1.91 | 0.36 | 0.00 |
time (sec) |
N/A | 0.352 | 0.781 | 0.370 | 0.000 | 0.109 | 0.000 | 0.149 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 103 | 249 | 132 | 0 | 319 | 0 | 155 | 23 | 0 |
N.S. |
1 | 1.01 | 2.44 | 1.29 | 0.00 | 3.13 | 0.00 | 1.52 | 0.23 | 0.00 |
time (sec) |
N/A | 0.503 | 0.894 | 0.414 | 0.000 | 0.097 | 0.000 | 0.157 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 144 | 285 | 158 | 0 | 361 | 0 | 184 | 23 | 0 |
N.S. |
1 | 1.04 | 2.07 | 1.14 | 0.00 | 2.62 | 0.00 | 1.33 | 0.17 | 0.00 |
time (sec) |
N/A | 0.660 | 1.331 | 0.404 | 0.000 | 0.148 | 0.000 | 0.166 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 68 | 67 | 0 | 223 | 0 | 104 | 23 | 0 |
N.S. |
1 | 1.00 | 1.79 | 1.76 | 0.00 | 5.87 | 0.00 | 2.74 | 0.61 | 0.00 |
time (sec) |
N/A | 0.227 | 0.098 | 0.352 | 0.000 | 0.119 | 0.000 | 0.195 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 67 | 70 | 0 | 223 | 0 | 106 | 21 | 0 |
N.S. |
1 | 1.00 | 1.72 | 1.79 | 0.00 | 5.72 | 0.00 | 2.72 | 0.54 | 0.00 |
time (sec) |
N/A | 0.242 | 0.177 | 0.319 | 0.000 | 0.096 | 0.000 | 0.201 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 67 | 69 | 0 | 221 | 0 | 69 | 22 | 0 |
N.S. |
1 | 1.00 | 1.68 | 1.72 | 0.00 | 5.52 | 0.00 | 1.72 | 0.55 | 0.00 |
time (sec) |
N/A | 0.239 | 0.066 | 0.342 | 0.000 | 0.091 | 0.000 | 0.153 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 182 | 165 | 85 | 0 | 145 | 0 | 152 | 45 | 0 |
N.S. |
1 | 1.12 | 1.02 | 0.52 | 0.00 | 0.90 | 0.00 | 0.94 | 0.28 | 0.00 |
time (sec) |
N/A | 0.844 | 1.391 | 0.406 | 0.000 | 0.079 | 0.000 | 0.157 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 131 | 145 | 75 | 0 | 122 | 0 | 124 | 45 | 0 |
N.S. |
1 | 1.13 | 1.25 | 0.65 | 0.00 | 1.05 | 0.00 | 1.07 | 0.39 | 0.00 |
time (sec) |
N/A | 0.564 | 1.830 | 0.336 | 0.000 | 0.078 | 0.000 | 0.143 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 91 | 157 | 63 | 0 | 99 | 0 | 95 | 43 | 0 |
N.S. |
1 | 1.06 | 1.83 | 0.73 | 0.00 | 1.15 | 0.00 | 1.10 | 0.50 | 0.00 |
time (sec) |
N/A | 0.380 | 1.264 | 0.334 | 0.000 | 0.075 | 0.000 | 0.139 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 89 | 53 | 0 | 76 | 0 | 67 | 34 | 0 |
N.S. |
1 | 1.00 | 1.51 | 0.90 | 0.00 | 1.29 | 0.00 | 1.14 | 0.58 | 0.00 |
time (sec) |
N/A | 0.262 | 0.062 | 0.213 | 0.000 | 0.076 | 0.000 | 0.136 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 118 | 84 | 0 | 239 | 0 | 104 | 47 | 0 |
N.S. |
1 | 1.00 | 1.79 | 1.27 | 0.00 | 3.62 | 0.00 | 1.58 | 0.71 | 0.00 |
time (sec) |
N/A | 0.378 | 1.373 | 0.337 | 0.000 | 0.088 | 0.000 | 0.160 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 95 | 103 | 0 | 268 | 0 | 125 | 51 | 0 |
N.S. |
1 | 1.00 | 1.44 | 1.56 | 0.00 | 4.06 | 0.00 | 1.89 | 0.77 | 0.00 |
time (sec) |
N/A | 0.360 | 0.592 | 0.365 | 0.000 | 0.089 | 0.000 | 0.161 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | B | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 106 | 250 | 126 | 0 | 337 | 0 | 158 | 51 | 0 |
N.S. |
1 | 1.00 | 2.36 | 1.19 | 0.00 | 3.18 | 0.00 | 1.49 | 0.48 | 0.00 |
time (sec) |
N/A | 0.505 | 1.664 | 0.389 | 0.000 | 0.101 | 0.000 | 0.162 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 147 | 286 | 144 | 0 | 380 | 0 | 188 | 51 | 0 |
N.S. |
1 | 1.02 | 1.99 | 1.00 | 0.00 | 2.64 | 0.00 | 1.31 | 0.35 | 0.00 |
time (sec) |
N/A | 0.654 | 3.301 | 0.406 | 0.000 | 0.102 | 0.000 | 0.162 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 227 | 187 | 95 | 0 | 192 | 0 | 192 | 69 | 0 |
N.S. |
1 | 1.12 | 0.92 | 0.47 | 0.00 | 0.95 | 0.00 | 0.95 | 0.34 | 0.00 |
time (sec) |
N/A | 1.060 | 1.536 | 3.745 | 0.000 | 0.093 | 0.000 | 0.157 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 165 | 167 | 85 | 0 | 167 | 0 | 162 | 69 | 0 |
N.S. |
1 | 1.13 | 1.14 | 0.58 | 0.00 | 1.14 | 0.00 | 1.11 | 0.47 | 0.00 |
time (sec) |
N/A | 0.680 | 1.485 | 1.143 | 0.000 | 0.086 | 0.000 | 0.152 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 125 | 271 | 75 | 0 | 140 | 0 | 132 | 67 | 0 |
N.S. |
1 | 1.08 | 2.34 | 0.65 | 0.00 | 1.21 | 0.00 | 1.14 | 0.58 | 0.00 |
time (sec) |
N/A | 0.477 | 3.398 | 0.436 | 0.000 | 0.077 | 0.000 | 0.139 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 93 | 117 | 65 | 0 | 115 | 0 | 102 | 58 | 0 |
N.S. |
1 | 1.04 | 1.31 | 0.73 | 0.00 | 1.29 | 0.00 | 1.15 | 0.65 | 0.00 |
time (sec) |
N/A | 0.350 | 0.169 | 0.271 | 0.000 | 0.073 | 0.000 | 0.142 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 101 | 143 | 103 | 0 | 279 | 0 | 141 | 77 | 0 |
N.S. |
1 | 1.03 | 1.46 | 1.05 | 0.00 | 2.85 | 0.00 | 1.44 | 0.79 | 0.00 |
time (sec) |
N/A | 0.545 | 5.792 | 0.700 | 0.000 | 0.086 | 0.000 | 0.162 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 100 | 182 | 127 | 0 | 308 | 0 | 159 | 83 | 0 |
N.S. |
1 | 1.06 | 1.94 | 1.35 | 0.00 | 3.28 | 0.00 | 1.69 | 0.88 | 0.00 |
time (sec) |
N/A | 0.535 | 6.293 | 2.130 | 0.000 | 0.155 | 0.000 | 0.157 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | B | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 108 | 252 | 126 | 0 | 359 | 0 | 164 | 83 | 0 |
N.S. |
1 | 1.02 | 2.38 | 1.19 | 0.00 | 3.39 | 0.00 | 1.55 | 0.78 | 0.00 |
time (sec) |
N/A | 0.583 | 6.165 | 8.008 | 0.000 | 0.105 | 0.000 | 0.171 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 150 | 288 | 144 | 0 | 408 | 0 | 196 | 83 | 0 |
N.S. |
1 | 1.04 | 2.00 | 1.00 | 0.00 | 2.83 | 0.00 | 1.36 | 0.58 | 0.00 |
time (sec) |
N/A | 0.727 | 6.553 | 25.991 | 0.000 | 0.100 | 0.000 | 0.169 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | B | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 191 | 370 | 162 | 0 | 473 | 0 | 228 | 83 | 0 |
N.S. |
1 | 1.05 | 2.03 | 0.89 | 0.00 | 2.60 | 0.00 | 1.25 | 0.46 | 0.00 |
time (sec) |
N/A | 0.940 | 6.550 | 72.502 | 0.000 | 0.097 | 0.000 | 0.172 | 0.253 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 154 | 150 | 130 | 0 | 234 | 0 | 163 | 36 | 0 |
N.S. |
1 | 1.11 | 1.08 | 0.94 | 0.00 | 1.68 | 0.00 | 1.17 | 0.26 | 0.00 |
time (sec) |
N/A | 0.761 | 0.525 | 0.331 | 0.000 | 0.090 | 0.000 | 0.151 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 112 | 105 | 96 | 0 | 209 | 0 | 121 | 36 | 0 |
N.S. |
1 | 1.07 | 1.00 | 0.91 | 0.00 | 1.99 | 0.00 | 1.15 | 0.34 | 0.00 |
time (sec) |
N/A | 0.452 | 0.551 | 0.282 | 0.000 | 0.091 | 0.000 | 0.152 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 98 | 94 | 0 | 191 | 0 | 118 | 34 | 99 |
N.S. |
1 | 1.00 | 1.36 | 1.31 | 0.00 | 2.65 | 0.00 | 1.64 | 0.47 | 1.38 |
time (sec) |
N/A | 0.300 | 0.375 | 0.463 | 0.000 | 0.087 | 0.000 | 0.149 | 0.188 | 0.468 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 73 | 75 | 0 | 193 | 0 | 61 | 28 | 49 |
N.S. |
1 | 1.00 | 1.55 | 1.60 | 0.00 | 4.11 | 0.00 | 1.30 | 0.60 | 1.04 |
time (sec) |
N/A | 0.205 | 0.023 | 0.266 | 0.000 | 0.154 | 0.000 | 0.138 | 0.179 | 0.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 128 | 96 | 0 | 290 | 0 | 142 | 34 | 0 |
N.S. |
1 | 1.00 | 1.52 | 1.14 | 0.00 | 3.45 | 0.00 | 1.69 | 0.40 | 0.00 |
time (sec) |
N/A | 0.429 | 0.587 | 0.313 | 0.000 | 0.132 | 0.000 | 0.173 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 118 | 168 | 133 | 0 | 412 | 0 | 217 | 36 | 0 |
N.S. |
1 | 1.08 | 1.54 | 1.22 | 0.00 | 3.78 | 0.00 | 1.99 | 0.33 | 0.00 |
time (sec) |
N/A | 0.633 | 1.755 | 0.339 | 0.000 | 0.137 | 0.000 | 0.166 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 160 | 307 | 164 | 0 | 492 | 0 | 222 | 36 | 0 |
N.S. |
1 | 1.10 | 2.10 | 1.12 | 0.00 | 3.37 | 0.00 | 1.52 | 0.25 | 0.00 |
time (sec) |
N/A | 0.919 | 3.507 | 0.345 | 0.000 | 0.115 | 0.000 | 0.178 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 199 | 178 | 193 | 0 | 314 | 0 | 197 | 46 | 0 |
N.S. |
1 | 1.09 | 0.97 | 1.05 | 0.00 | 1.72 | 0.00 | 1.08 | 0.25 | 0.00 |
time (sec) |
N/A | 1.089 | 0.947 | 0.349 | 0.000 | 0.097 | 0.000 | 0.160 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 154 | 156 | 193 | 0 | 295 | 0 | 197 | 46 | 0 |
N.S. |
1 | 1.06 | 1.08 | 1.33 | 0.00 | 2.03 | 0.00 | 1.36 | 0.32 | 0.00 |
time (sec) |
N/A | 0.766 | 0.775 | 0.312 | 0.000 | 0.097 | 0.000 | 0.163 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 109 | 134 | 147 | 0 | 274 | 0 | 172 | 46 | 0 |
N.S. |
1 | 1.04 | 1.28 | 1.40 | 0.00 | 2.61 | 0.00 | 1.64 | 0.44 | 0.00 |
time (sec) |
N/A | 0.466 | 0.657 | 0.317 | 0.000 | 0.104 | 0.000 | 0.154 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 108 | 123 | 0 | 253 | 0 | 137 | 44 | 0 |
N.S. |
1 | 1.00 | 1.40 | 1.60 | 0.00 | 3.29 | 0.00 | 1.78 | 0.57 | 0.00 |
time (sec) |
N/A | 0.311 | 0.295 | 0.278 | 0.000 | 0.090 | 0.000 | 0.143 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 108 | 125 | 0 | 252 | 0 | 133 | 38 | 0 |
N.S. |
1 | 1.00 | 1.40 | 1.62 | 0.00 | 3.27 | 0.00 | 1.73 | 0.49 | 0.00 |
time (sec) |
N/A | 0.285 | 0.100 | 0.217 | 0.000 | 0.094 | 0.000 | 0.143 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 120 | 223 | 172 | 0 | 453 | 0 | 138 | 44 | 0 |
N.S. |
1 | 1.05 | 1.96 | 1.51 | 0.00 | 3.97 | 0.00 | 1.21 | 0.39 | 0.00 |
time (sec) |
N/A | 0.628 | 1.054 | 0.333 | 0.000 | 0.105 | 0.000 | 0.172 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 152 | 449 | 219 | 0 | 539 | 0 | 260 | 46 | 0 |
N.S. |
1 | 1.06 | 3.12 | 1.52 | 0.00 | 3.74 | 0.00 | 1.81 | 0.32 | 0.00 |
time (sec) |
N/A | 0.869 | 2.146 | 0.343 | 0.000 | 0.110 | 0.000 | 0.178 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 200 | 620 | 299 | 0 | 626 | 0 | 205 | 46 | 0 |
N.S. |
1 | 1.08 | 3.33 | 1.61 | 0.00 | 3.37 | 0.00 | 1.10 | 0.25 | 0.00 |
time (sec) |
N/A | 1.191 | 5.083 | 0.365 | 0.000 | 0.116 | 0.000 | 0.184 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 247 | 221 | 323 | 0 | 381 | 0 | 241 | 56 | 0 |
N.S. |
1 | 1.12 | 1.00 | 1.46 | 0.00 | 1.72 | 0.00 | 1.09 | 0.25 | 0.00 |
time (sec) |
N/A | 1.375 | 0.895 | 0.565 | 0.000 | 0.098 | 0.000 | 0.205 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 199 | 197 | 293 | 0 | 360 | 0 | 143 | 56 | 0 |
N.S. |
1 | 1.09 | 1.08 | 1.60 | 0.00 | 1.97 | 0.00 | 0.78 | 0.31 | 0.00 |
time (sec) |
N/A | 1.046 | 0.766 | 0.415 | 0.000 | 0.099 | 0.000 | 0.186 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 155 | 173 | 243 | 0 | 341 | 0 | 191 | 56 | 0 |
N.S. |
1 | 1.07 | 1.19 | 1.68 | 0.00 | 2.35 | 0.00 | 1.32 | 0.39 | 0.00 |
time (sec) |
N/A | 0.775 | 0.600 | 0.371 | 0.000 | 0.102 | 0.000 | 0.180 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 113 | 196 | 193 | 0 | 320 | 0 | 162 | 56 | 0 |
N.S. |
1 | 1.06 | 1.83 | 1.80 | 0.00 | 2.99 | 0.00 | 1.51 | 0.52 | 0.00 |
time (sec) |
N/A | 0.479 | 0.510 | 0.320 | 0.000 | 0.096 | 0.000 | 0.169 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 112 | 196 | 193 | 0 | 318 | 0 | 81 | 54 | 0 |
N.S. |
1 | 1.05 | 1.83 | 1.80 | 0.00 | 2.97 | 0.00 | 0.76 | 0.50 | 0.00 |
time (sec) |
N/A | 0.401 | 0.321 | 0.278 | 0.000 | 0.095 | 0.000 | 0.157 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 112 | 196 | 199 | 0 | 320 | 0 | 153 | 48 | 0 |
N.S. |
1 | 1.05 | 1.83 | 1.86 | 0.00 | 2.99 | 0.00 | 1.43 | 0.45 | 0.00 |
time (sec) |
N/A | 0.376 | 0.101 | 0.228 | 0.000 | 0.098 | 0.000 | 0.152 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 156 | 296 | 262 | 0 | 539 | 0 | 163 | 54 | 0 |
N.S. |
1 | 1.08 | 2.06 | 1.82 | 0.00 | 3.74 | 0.00 | 1.13 | 0.38 | 0.00 |
time (sec) |
N/A | 0.831 | 1.811 | 0.332 | 0.000 | 0.124 | 0.000 | 0.179 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 190 | 509 | 356 | 0 | 631 | 0 | 205 | 56 | 0 |
N.S. |
1 | 1.09 | 2.93 | 2.05 | 0.00 | 3.63 | 0.00 | 1.18 | 0.32 | 0.00 |
time (sec) |
N/A | 1.141 | 3.682 | 0.350 | 0.000 | 0.126 | 0.000 | 0.186 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 224 | 242 | 680 | 404 | 0 | 715 | 0 | 298 | 56 | 0 |
N.S. |
1 | 1.08 | 3.04 | 1.80 | 0.00 | 3.19 | 0.00 | 1.33 | 0.25 | 0.00 |
time (sec) |
N/A | 1.499 | 4.364 | 0.375 | 0.000 | 0.116 | 0.000 | 0.189 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 164 | 268 | 210 | 330 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 4.43 | 7.24 | 5.68 | 8.92 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.234 | 0.666 | 7.931 | 0.138 | 0.151 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 119 | 272 | 0 | 341 | 0 | 95 | 34 | 0 |
N.S. |
1 | 1.00 | 3.13 | 7.16 | 0.00 | 8.97 | 0.00 | 2.50 | 0.89 | 0.00 |
time (sec) |
N/A | 0.255 | 0.828 | 9.284 | 0.000 | 0.195 | 0.000 | 0.172 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 44 | 51 | 0 | 28 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 2.59 | 3.00 | 0.00 | 1.65 | 0.00 | 0.00 | 1.18 | 0.00 |
time (sec) |
N/A | 0.210 | 0.322 | 0.762 | 0.000 | 0.085 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 47 | 48 | 0 | 163 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 1.12 | 1.14 | 0.00 | 3.88 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.246 | 0.157 | 0.772 | 0.000 | 0.143 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 45 | 53 | 0 | 31 | 0 | 146 | 26 | 0 |
N.S. |
1 | 1.00 | 1.45 | 1.71 | 0.00 | 1.00 | 0.00 | 4.71 | 0.84 | 0.00 |
time (sec) |
N/A | 0.224 | 0.323 | 0.837 | 0.000 | 0.076 | 0.000 | 0.440 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 48 | 50 | 0 | 168 | 0 | 149 | 31 | 0 |
N.S. |
1 | 1.00 | 1.14 | 1.19 | 0.00 | 4.00 | 0.00 | 3.55 | 0.74 | 0.00 |
time (sec) |
N/A | 0.248 | 0.205 | 0.776 | 0.000 | 0.132 | 0.000 | 0.471 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 193 | 121 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.05 | 0.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.654 | 0.316 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.216 | 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 | 161 | 180 | 160 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.12 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.903 | 0.840 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 136 | 151 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.08 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.581 | 0.912 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 96 | 138 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 1.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.390 | 0.330 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 124 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.00 | 1.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.270 | 0.145 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 0 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.376 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.390 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.205 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 180 | 258 | 0 | 0 | 0 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.11 | 1.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.951 | 1.804 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 138 | 250 | 0 | 0 | 0 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.09 | 1.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.568 | 4.056 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 234 | 0 | 0 | 0 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.00 | 2.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.384 | 2.268 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.209 | 0.000 |