Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | F | A | F(-2) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 103 | 139 | 34 | 0 | 33 | 0 | 35 | 207 | 34 |
N.S. |
1 | 4.68 | 6.32 | 1.55 | 0.00 | 1.50 | 0.00 | 1.59 | 9.41 | 1.55 |
time (sec) |
N/A | 0.685 | 0.087 | 0.227 | 0.000 | 0.086 | 0.000 | 0.176 | 0.147 | 22.649 |
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 | 98 | 102 | 70 | 71 | 71 | 75 | 83 | 73 | 74 | 71 |
N.S. |
1 | 1.04 | 0.71 | 0.72 | 0.72 | 0.77 | 0.85 | 0.74 | 0.76 | 0.72 |
time (sec) |
N/A | 0.419 | 0.097 | 0.336 | 0.040 | 0.079 | 0.576 | 0.132 | 0.157 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 65 | 49 | 49 | 48 | 52 | 63 | 50 | 48 | 49 |
N.S. |
1 | 1.08 | 0.82 | 0.82 | 0.80 | 0.87 | 1.05 | 0.83 | 0.80 | 0.82 |
time (sec) |
N/A | 0.359 | 0.059 | 0.182 | 0.032 | 0.075 | 0.110 | 0.117 | 0.153 | 0.028 |
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 | 38 | 41 | 32 | 27 | 26 | 30 | 36 | 26 | 26 | 26 |
N.S. |
1 | 1.08 | 0.84 | 0.71 | 0.68 | 0.79 | 0.95 | 0.68 | 0.68 | 0.68 |
time (sec) |
N/A | 0.301 | 0.030 | 0.103 | 0.027 | 0.108 | 0.525 | 0.130 | 0.143 | 0.045 |
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 | 166 | 190 | 171 | 176 | 165 | 169 | 248 | 186 | 194 | 150 |
N.S. |
1 | 1.14 | 1.03 | 1.06 | 0.99 | 1.02 | 1.49 | 1.12 | 1.17 | 0.90 |
time (sec) |
N/A | 0.643 | 0.299 | 1.158 | 0.034 | 0.086 | 0.210 | 0.122 | 0.159 | 22.058 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 120 | 97 | 91 | 88 | 92 | 131 | 99 | 98 | 88 |
N.S. |
1 | 1.14 | 0.92 | 0.87 | 0.84 | 0.88 | 1.25 | 0.94 | 0.93 | 0.84 |
time (sec) |
N/A | 0.488 | 0.128 | 0.438 | 0.033 | 0.078 | 0.140 | 0.114 | 0.145 | 21.672 |
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 | 50 | 56 | 45 | 39 | 38 | 42 | 53 | 40 | 38 | 39 |
N.S. |
1 | 1.12 | 0.90 | 0.78 | 0.76 | 0.84 | 1.06 | 0.80 | 0.76 | 0.78 |
time (sec) |
N/A | 0.323 | 0.043 | 0.181 | 0.032 | 0.082 | 0.114 | 0.113 | 0.395 | 0.026 |
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 | 116 | 118 | 103 | 103 | 102 | 106 | 117 | 111 | 109 | 101 |
N.S. |
1 | 1.02 | 0.89 | 0.89 | 0.88 | 0.91 | 1.01 | 0.96 | 0.94 | 0.87 |
time (sec) |
N/A | 0.485 | 0.146 | 0.892 | 0.040 | 0.086 | 0.624 | 0.133 | 0.228 | 0.053 |
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 | 77 | 82 | 73 | 70 | 69 | 73 | 99 | 75 | 71 | 69 |
N.S. |
1 | 1.06 | 0.95 | 0.91 | 0.90 | 0.95 | 1.29 | 0.97 | 0.92 | 0.90 |
time (sec) |
N/A | 0.414 | 0.079 | 0.581 | 0.029 | 0.093 | 0.115 | 0.139 | 0.229 | 0.039 |
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 | 46 | 51 | 47 | 37 | 36 | 40 | 42 | 40 | 37 | 38 |
N.S. |
1 | 1.11 | 1.02 | 0.80 | 0.78 | 0.87 | 0.91 | 0.87 | 0.80 | 0.83 |
time (sec) |
N/A | 0.343 | 0.051 | 0.241 | 0.034 | 0.110 | 0.524 | 0.114 | 0.228 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 242 | 0 | 271 | 271 | 237 | 241 | 386 | 282 | 293 | 233 |
N.S. |
1 | 0.00 | 1.12 | 1.12 | 0.98 | 1.00 | 1.60 | 1.17 | 1.21 | 0.96 |
time (sec) |
N/A | 0.000 | 0.441 | 8.342 | 0.042 | 0.120 | 0.211 | 0.140 | 0.236 | 21.874 |
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 | 140 | 0 | 158 | 127 | 126 | 130 | 206 | 149 | 148 | 126 |
N.S. |
1 | 0.00 | 1.13 | 0.91 | 0.90 | 0.93 | 1.47 | 1.06 | 1.06 | 0.90 |
time (sec) |
N/A | 0.000 | 0.227 | 2.352 | 0.032 | 0.112 | 0.159 | 0.128 | 0.231 | 0.053 |
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 | 63 | 0 | 68 | 52 | 51 | 55 | 85 | 61 | 56 | 55 |
N.S. |
1 | 0.00 | 1.08 | 0.83 | 0.81 | 0.87 | 1.35 | 0.97 | 0.89 | 0.87 |
time (sec) |
N/A | 0.000 | 0.086 | 0.486 | 0.038 | 0.093 | 0.103 | 0.125 | 0.228 | 21.713 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 217 | 222 | 225 | 225 | 243 | 245 | 247 | 208 |
N.S. |
1 | 1.00 | 2.36 | 2.41 | 2.45 | 2.45 | 2.64 | 2.66 | 2.68 | 2.26 |
time (sec) |
N/A | 0.482 | 0.039 | 0.135 | 0.028 | 0.084 | 0.048 | 0.112 | 0.231 | 21.777 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 217 | 222 | 225 | 225 | 243 | 245 | 247 | 208 |
N.S. |
1 | 1.00 | 2.36 | 2.41 | 2.45 | 2.45 | 2.64 | 2.66 | 2.68 | 2.26 |
time (sec) |
N/A | 0.433 | 0.009 | 0.137 | 0.035 | 0.100 | 0.046 | 0.127 | 0.224 | 0.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 217 | 222 | 225 | 225 | 243 | 245 | 247 | 208 |
N.S. |
1 | 1.00 | 2.36 | 2.41 | 2.45 | 2.45 | 2.64 | 2.66 | 2.68 | 2.26 |
time (sec) |
N/A | 0.417 | 0.009 | 0.134 | 0.031 | 0.113 | 0.037 | 0.135 | 0.215 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 217 | 222 | 225 | 225 | 243 | 245 | 247 | 208 |
N.S. |
1 | 1.00 | 2.36 | 2.41 | 2.45 | 2.45 | 2.64 | 2.66 | 2.68 | 2.26 |
time (sec) |
N/A | 0.471 | 0.008 | 0.088 | 0.036 | 0.075 | 0.038 | 0.136 | 0.167 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 145 | 148 | 139 | 0 | 74 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.96 | 0.00 | 0.51 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.653 | 20.282 | 1.672 | 0.000 | 0.167 | 0.000 | 0.000 | 0.142 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 160 | 148 | 143 | 0 | 79 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.89 | 0.00 | 0.49 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.701 | 10.182 | 1.645 | 0.000 | 0.171 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 163 | 146 | 143 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.90 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.696 | 20.306 | 1.645 | 0.000 | 0.000 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 156 | 150 | 139 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.678 | 10.136 | 1.581 | 0.000 | 0.000 | 0.000 | 0.000 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 280 | 280 | 164 | 0 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 0.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.987 | 10.314 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 288 | 288 | 166 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 0.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.987 | 10.289 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 297 | 297 | 167 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 0.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 1.005 | 10.272 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 293 | 293 | 167 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 0.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 1.004 | 10.285 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 249 | 169 | 495 | 0 | 349 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.00 | 0.68 | 1.99 | 0.00 | 1.40 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.848 | 10.318 | 0.506 | 0.000 | 0.224 | 0.000 | 0.000 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 146 | 136 | 132 | 0 | 57 | 0 | 0 | 102 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.90 | 0.00 | 0.39 | 0.00 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.670 | 20.319 | 1.076 | 0.000 | 0.160 | 0.000 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 164 | 136 | 143 | 0 | 66 | 0 | 0 | 115 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.87 | 0.00 | 0.40 | 0.00 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.698 | 10.168 | 1.004 | 0.000 | 0.166 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 167 | 134 | 132 | 0 | 211 | 0 | 0 | 110 | 0 |
N.S. |
1 | 1.00 | 0.80 | 0.79 | 0.00 | 1.26 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.677 | 20.362 | 1.034 | 0.000 | 0.171 | 0.000 | 0.000 | 0.274 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 157 | 138 | 139 | 0 | 213 | 0 | 0 | 107 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.89 | 0.00 | 1.36 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.663 | 10.116 | 0.951 | 0.000 | 0.159 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | B |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 329 | 321 | 128 | 123 | 0 | 0 | 0 | 0 | 15 | 164 |
N.S. |
1 | 0.98 | 0.39 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.50 |
time (sec) |
N/A | 1.511 | 20.126 | 0.396 | 0.000 | 0.000 | 0.000 | 0.000 | 200.024 | 0.247 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | B |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 380 | 371 | 128 | 133 | 0 | 0 | 0 | 0 | 28 | 180 |
N.S. |
1 | 0.98 | 0.34 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.47 |
time (sec) |
N/A | 1.550 | 20.127 | 0.441 | 0.000 | 0.000 | 0.000 | 0.000 | 0.147 | 0.201 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | B |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 374 | 374 | 126 | 124 | 0 | 0 | 0 | 0 | 24 | 164 |
N.S. |
1 | 1.00 | 0.34 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.44 |
time (sec) |
N/A | 1.554 | 20.125 | 0.360 | 0.000 | 0.000 | 0.000 | 0.000 | 22.785 | 21.744 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | B |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 340 | 321 | 130 | 133 | 0 | 0 | 0 | 0 | 17 | 179 |
N.S. |
1 | 0.94 | 0.38 | 0.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.53 |
time (sec) |
N/A | 1.540 | 20.121 | 0.383 | 0.000 | 0.000 | 0.000 | 0.000 | 200.023 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 137 | 215 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 1.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.441 | 1.847 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 139 | 311 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.00 | 2.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.421 | 2.906 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.279 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 168 | 249 | 0 | 0 | 0 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.00 | 1.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.485 | 0.147 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 148 | 1142 | 0 | 298 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 1.53 | 11.77 | 0.00 | 3.07 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.348 | 1.304 | 6.293 | 0.000 | 2.127 | 0.000 | 0.000 | 0.219 | 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 | 186 | 180 | 0 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.705 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.233 | 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 | 187 | 187 | 0 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.474 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 147 | 0 | 3063 | 0 | 712 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.00 | 20.84 | 0.00 | 4.84 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.395 | 0.000 | 33.916 | 0.000 | 3.424 | 0.000 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 0 | 3248 | 0 | 720 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 0.00 | 20.43 | 0.00 | 4.53 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.420 | 0.000 | 32.595 | 0.000 | 3.100 | 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(-1) | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 304 | 373 | 163 | 0 | 0 | 0 | 212 | 0 | 232 | 0 |
N.S. |
1 | 1.23 | 0.54 | 0.00 | 0.00 | 0.00 | 0.70 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.912 | 9.131 | 0.000 | 0.000 | 0.000 | 3.372 | 0.000 | 0.312 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 242 | 234 | 142 | 0 | 0 | 0 | 160 | 0 | 168 | 0 |
N.S. |
1 | 0.97 | 0.59 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.966 | 8.589 | 0.000 | 0.000 | 0.000 | 2.104 | 0.000 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 186 | 111 | 0 | 0 | 0 | 114 | 0 | 109 | 0 |
N.S. |
1 | 1.02 | 0.61 | 0.00 | 0.00 | 0.00 | 0.62 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.684 | 8.370 | 0.000 | 0.000 | 0.000 | 1.662 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 152 | 75 | 0 | 0 | 0 | 82 | 0 | 61 | 0 |
N.S. |
1 | 0.98 | 0.48 | 0.00 | 0.00 | 0.00 | 0.53 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.501 | 7.669 | 0.000 | 0.000 | 0.000 | 1.515 | 0.000 | 0.157 | 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 | 435 | 435 | 0 | 0 | 0 | 0 | 0 | 0 | 92 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 1.197 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 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 | 818 | 818 | 0 | 0 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.803 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 238 | 310 | 392 | 0 | 0 | 0 | 206 | 0 | 98 | 0 |
N.S. |
1 | 1.30 | 1.65 | 0.00 | 0.00 | 0.00 | 0.87 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.665 | 10.530 | 0.000 | 0.000 | 0.000 | 2.725 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 255 | 287 | 0 | 0 | 0 | 155 | 0 | 75 | 0 |
N.S. |
1 | 1.29 | 1.45 | 0.00 | 0.00 | 0.00 | 0.78 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.573 | 10.396 | 0.000 | 0.000 | 0.000 | 2.266 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 147 | 201 | 0 | 0 | 0 | 110 | 0 | 52 | 0 |
N.S. |
1 | 1.00 | 1.37 | 0.00 | 0.00 | 0.00 | 0.75 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.526 | 10.220 | 0.000 | 0.000 | 0.000 | 1.541 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 124 | 163 | 0 | 0 | 0 | 78 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 1.31 | 0.00 | 0.00 | 0.00 | 0.63 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.389 | 10.172 | 0.000 | 0.000 | 0.000 | 1.128 | 0.000 | 0.164 | 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 | 333 | 333 | 0 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.909 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.152 | 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 | 761 | 761 | 0 | 0 | 0 | 0 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.715 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 306 | 166 | 0 | 0 | 0 | 204 | 0 | 100 | 0 |
N.S. |
1 | 1.32 | 0.72 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.669 | 10.162 | 0.000 | 0.000 | 0.000 | 2.761 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 184 | 145 | 0 | 0 | 0 | 153 | 0 | 76 | 0 |
N.S. |
1 | 0.98 | 0.78 | 0.00 | 0.00 | 0.00 | 0.82 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.734 | 10.125 | 0.000 | 0.000 | 0.000 | 2.067 | 0.000 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 141 | 95 | 0 | 0 | 0 | 109 | 0 | 52 | 0 |
N.S. |
1 | 1.00 | 0.67 | 0.00 | 0.00 | 0.00 | 0.77 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.521 | 10.057 | 0.000 | 0.000 | 0.000 | 1.592 | 0.000 | 0.139 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 78 | 0 | 0 | 0 | 78 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 0.64 | 0.00 | 0.00 | 0.00 | 0.64 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.391 | 10.044 | 0.000 | 0.000 | 0.000 | 1.139 | 0.000 | 0.149 | 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 | 332 | 332 | 0 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.895 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.148 | 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 | 760 | 760 | 0 | 0 | 0 | 0 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.770 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.136 | 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 | 62 | 90 | 85 | 74 | 73 | 73 | 85 | 73 | 75 | 73 |
N.S. |
1 | 1.45 | 1.37 | 1.19 | 1.18 | 1.18 | 1.37 | 1.18 | 1.21 | 1.18 |
time (sec) |
N/A | 0.437 | 0.005 | 0.142 | 0.028 | 0.082 | 0.024 | 0.111 | 0.143 | 0.041 |
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 | 48 | 57 | 57 | 50 | 49 | 49 | 54 | 49 | 51 | 49 |
N.S. |
1 | 1.19 | 1.19 | 1.04 | 1.02 | 1.02 | 1.12 | 1.02 | 1.06 | 1.02 |
time (sec) |
N/A | 0.354 | 0.004 | 0.132 | 0.037 | 0.062 | 0.026 | 0.140 | 0.156 | 0.027 |
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 | 34 | 32 | 32 | 27 | 26 | 26 | 29 | 26 | 27 | 26 |
N.S. |
1 | 0.94 | 0.94 | 0.79 | 0.76 | 0.76 | 0.85 | 0.76 | 0.79 | 0.76 |
time (sec) |
N/A | 0.307 | 0.003 | 0.032 | 0.031 | 0.058 | 0.023 | 0.113 | 0.138 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 11 | 10 | 10 | 8 | 10 | 12 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 0.83 | 0.67 | 0.83 | 1.00 | 0.83 |
time (sec) |
N/A | 0.225 | 0.000 | 0.020 | 0.025 | 0.079 | 0.019 | 0.113 | 0.141 | 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 | 69 | 69 | 61 | 61 | 64 | 64 | 63 | 65 | 69 | 63 |
N.S. |
1 | 1.00 | 0.88 | 0.88 | 0.93 | 0.93 | 0.91 | 0.94 | 1.00 | 0.91 |
time (sec) |
N/A | 0.381 | 0.030 | 0.171 | 0.028 | 0.072 | 0.105 | 0.124 | 0.150 | 0.042 |
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 | 70 | 70 | 66 | 67 | 71 | 87 | 70 | 95 | 90 | 74 |
N.S. |
1 | 1.00 | 0.94 | 0.96 | 1.01 | 1.24 | 1.00 | 1.36 | 1.29 | 1.06 |
time (sec) |
N/A | 0.389 | 0.047 | 0.151 | 0.028 | 0.080 | 0.156 | 0.113 | 0.149 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 129 | 148 | 131 | 130 | 130 | 153 | 130 | 133 | 130 |
N.S. |
1 | 1.08 | 1.24 | 1.10 | 1.09 | 1.09 | 1.29 | 1.09 | 1.12 | 1.09 |
time (sec) |
N/A | 0.582 | 0.008 | 0.187 | 0.031 | 0.066 | 0.027 | 0.109 | 0.142 | 21.501 |
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 | 91 | 104 | 104 | 91 | 90 | 90 | 105 | 90 | 92 | 90 |
N.S. |
1 | 1.14 | 1.14 | 1.00 | 0.99 | 0.99 | 1.15 | 0.99 | 1.01 | 0.99 |
time (sec) |
N/A | 0.478 | 0.005 | 0.149 | 0.026 | 0.064 | 0.030 | 0.128 | 0.152 | 0.054 |
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 | 60 | 60 | 60 | 51 | 50 | 50 | 58 | 50 | 51 | 50 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.83 | 0.83 | 0.97 | 0.83 | 0.85 | 0.83 |
time (sec) |
N/A | 0.379 | 0.003 | 0.220 | 0.033 | 0.080 | 0.025 | 0.109 | 0.139 | 0.025 |
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 | 25 | 25 | 22 | 21 | 21 | 22 | 21 | 24 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.84 | 0.84 | 0.88 | 0.84 | 0.96 | 0.84 |
time (sec) |
N/A | 0.262 | 0.001 | 0.124 | 0.028 | 0.068 | 0.027 | 0.109 | 0.138 | 0.029 |
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 | 178 | 178 | 146 | 166 | 185 | 185 | 177 | 188 | 198 | 193 |
N.S. |
1 | 1.00 | 0.82 | 0.93 | 1.04 | 1.04 | 0.99 | 1.06 | 1.11 | 1.08 |
time (sec) |
N/A | 0.613 | 0.073 | 0.233 | 0.027 | 0.080 | 0.217 | 0.127 | 0.159 | 0.059 |
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 | 178 | 178 | 178 | 172 | 195 | 231 | 199 | 252 | 242 | 262 |
N.S. |
1 | 1.00 | 1.00 | 0.97 | 1.10 | 1.30 | 1.12 | 1.42 | 1.36 | 1.47 |
time (sec) |
N/A | 0.663 | 0.092 | 0.171 | 0.028 | 0.083 | 0.364 | 0.133 | 0.143 | 21.462 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 320 | 322 | 54 | 310 | 141845 | 384 | 314 | 433 | 894 |
N.S. |
1 | 1.29 | 1.30 | 0.22 | 1.25 | 571.96 | 1.55 | 1.27 | 1.75 | 3.60 |
time (sec) |
N/A | 0.774 | 0.247 | 0.173 | 0.113 | 15.659 | 3.867 | 0.124 | 0.143 | 0.653 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 220 | 291 | 243 | 43 | 275 | 86139 | 277 | 287 | 371 | 556 |
N.S. |
1 | 1.32 | 1.10 | 0.20 | 1.25 | 391.54 | 1.26 | 1.30 | 1.69 | 2.53 |
time (sec) |
N/A | 0.687 | 0.108 | 0.263 | 0.112 | 3.037 | 2.444 | 0.116 | 0.156 | 21.724 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 219 | 184 | 32 | 207 | 41851 | 124 | 213 | 213 | 160 |
N.S. |
1 | 1.31 | 1.10 | 0.19 | 1.24 | 250.60 | 0.74 | 1.28 | 1.28 | 0.96 |
time (sec) |
N/A | 0.572 | 0.061 | 0.161 | 0.111 | 1.792 | 0.529 | 0.117 | 0.137 | 21.461 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 200 | 134 | 27 | 169 | 112 | 20 | 179 | 112 | 33 |
N.S. |
1 | 1.49 | 1.00 | 0.20 | 1.26 | 0.84 | 0.15 | 1.34 | 0.84 | 0.25 |
time (sec) |
N/A | 0.594 | 0.023 | 0.180 | 0.112 | 0.094 | 0.099 | 0.113 | 0.142 | 0.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 331 | 416 | 404 | 211 | 345 | 352864 | 0 | 377 | 454 | 874 |
N.S. |
1 | 1.26 | 1.22 | 0.64 | 1.04 | 1066.05 | 0.00 | 1.14 | 1.37 | 2.64 |
time (sec) |
N/A | 1.077 | 0.165 | 0.305 | 0.115 | 93.920 | 0.000 | 0.147 | 0.155 | 22.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 443 | 552 | 524 | 354 | 561 | 0 | 0 | 668 | 19 | 2436 |
N.S. |
1 | 1.25 | 1.18 | 0.80 | 1.27 | 0.00 | 0.00 | 1.51 | 0.04 | 5.50 |
time (sec) |
N/A | 1.581 | 0.638 | 0.237 | 0.133 | 0.000 | 0.000 | 0.297 | 200.017 | 22.419 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 284 | 354 | 347 | 100 | 332 | 91191 | 350 | 345 | 836 | 670 |
N.S. |
1 | 1.25 | 1.22 | 0.35 | 1.17 | 321.10 | 1.23 | 1.21 | 2.94 | 2.36 |
time (sec) |
N/A | 0.889 | 0.387 | 0.204 | 0.129 | 15.245 | 9.112 | 0.119 | 0.153 | 22.355 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 328 | 321 | 90 | 318 | 90963 | 318 | 325 | 805 | 391 |
N.S. |
1 | 1.31 | 1.28 | 0.36 | 1.27 | 363.85 | 1.27 | 1.30 | 3.22 | 1.56 |
time (sec) |
N/A | 0.812 | 0.360 | 0.174 | 0.113 | 3.845 | 2.528 | 0.119 | 0.153 | 21.746 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 246 | 224 | 66 | 238 | 43065 | 155 | 238 | 468 | 282 |
N.S. |
1 | 1.30 | 1.19 | 0.35 | 1.26 | 227.86 | 0.82 | 1.26 | 2.48 | 1.49 |
time (sec) |
N/A | 0.643 | 0.217 | 0.249 | 0.113 | 2.155 | 0.905 | 0.119 | 0.159 | 0.281 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 225 | 183 | 46 | 189 | 183 | 39 | 194 | 305 | 58 |
N.S. |
1 | 1.49 | 1.21 | 0.30 | 1.25 | 1.21 | 0.26 | 1.28 | 2.02 | 0.38 |
time (sec) |
N/A | 0.630 | 0.114 | 0.158 | 0.110 | 0.096 | 0.189 | 0.116 | 0.147 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 703 | 855 | 558 | 430 | 601 | 0 | 0 | 795 | 1946 | 1591 |
N.S. |
1 | 1.22 | 0.79 | 0.61 | 0.85 | 0.00 | 0.00 | 1.13 | 2.77 | 2.26 |
time (sec) |
N/A | 1.918 | 0.403 | 0.240 | 0.137 | 0.000 | 0.000 | 0.166 | 0.171 | 22.278 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 937 | 1141 | 807 | 534 | 961 | 0 | 0 | 1145 | 5777 | 2246 |
N.S. |
1 | 1.22 | 0.86 | 0.57 | 1.03 | 0.00 | 0.00 | 1.22 | 6.17 | 2.40 |
time (sec) |
N/A | 3.107 | 0.775 | 0.287 | 0.135 | 0.000 | 0.000 | 4.339 | 0.620 | 23.376 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 328 | 408 | 388 | 141 | 392 | 95566 | 413 | 392 | 1303 | 721 |
N.S. |
1 | 1.24 | 1.18 | 0.43 | 1.20 | 291.36 | 1.26 | 1.20 | 3.97 | 2.20 |
time (sec) |
N/A | 1.031 | 0.389 | 0.178 | 0.115 | 15.068 | 6.251 | 0.321 | 0.161 | 0.495 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 288 | 374 | 358 | 126 | 364 | 91420 | 374 | 358 | 1265 | 676 |
N.S. |
1 | 1.30 | 1.24 | 0.44 | 1.26 | 317.43 | 1.30 | 1.24 | 4.39 | 2.35 |
time (sec) |
N/A | 0.986 | 0.344 | 0.268 | 0.119 | 8.111 | 3.725 | 0.125 | 0.159 | 21.859 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 280 | 249 | 86 | 269 | 43180 | 192 | 256 | 740 | 315 |
N.S. |
1 | 1.31 | 1.16 | 0.40 | 1.26 | 201.78 | 0.90 | 1.20 | 3.46 | 1.47 |
time (sec) |
N/A | 0.759 | 0.213 | 0.250 | 0.116 | 2.674 | 0.979 | 0.118 | 0.162 | 0.305 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 250 | 200 | 57 | 212 | 255 | 63 | 204 | 474 | 80 |
N.S. |
1 | 1.49 | 1.19 | 0.34 | 1.26 | 1.52 | 0.38 | 1.21 | 2.82 | 0.48 |
time (sec) |
N/A | 0.701 | 0.093 | 0.162 | 0.112 | 0.088 | 0.304 | 0.128 | 0.159 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1133 | 1352 | 835 | 677 | 1015 | 0 | 0 | 1311 | 4499 | 2720 |
N.S. |
1 | 1.19 | 0.74 | 0.60 | 0.90 | 0.00 | 0.00 | 1.16 | 3.97 | 2.40 |
time (sec) |
N/A | 2.951 | 0.716 | 0.301 | 0.140 | 0.000 | 0.000 | 0.180 | 0.378 | 23.610 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1533 | 1830 | 1115 | 829 | 1564 | 0 | 0 | 1809 | 11727 | 3572 |
N.S. |
1 | 1.19 | 0.73 | 0.54 | 1.02 | 0.00 | 0.00 | 1.18 | 7.65 | 2.33 |
time (sec) |
N/A | 4.898 | 1.326 | 0.336 | 0.181 | 0.000 | 0.000 | 28.688 | 2.498 | 25.243 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 355 | 355 | 186 | 261 | 0 | 189 | 175 | 0 | 197 | 0 |
N.S. |
1 | 1.00 | 0.52 | 0.74 | 0.00 | 0.53 | 0.49 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.785 | 10.182 | 1.257 | 0.000 | 0.154 | 2.373 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 326 | 326 | 146 | 234 | 0 | 165 | 138 | 0 | 158 | 0 |
N.S. |
1 | 1.00 | 0.45 | 0.72 | 0.00 | 0.51 | 0.42 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.721 | 10.157 | 1.063 | 0.000 | 0.161 | 2.414 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 158 | 109 | 119 | 0 | 94 | 88 | 0 | 104 | 0 |
N.S. |
1 | 1.00 | 0.69 | 0.75 | 0.00 | 0.59 | 0.56 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.459 | 8.471 | 0.631 | 0.000 | 0.147 | 2.004 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 89 | 85 | 0 | 41 | 37 | 0 | 35 | 37 |
N.S. |
1 | 1.00 | 0.85 | 0.81 | 0.00 | 0.39 | 0.35 | 0.00 | 0.33 | 0.35 |
time (sec) |
N/A | 0.296 | 5.191 | 0.365 | 0.000 | 0.084 | 0.553 | 0.000 | 0.161 | 21.431 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 605 | 660 | 421 | 404 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.09 | 0.70 | 0.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 2.018 | 11.414 | 1.527 | 0.000 | 0.000 | 0.000 | 0.000 | 200.030 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 648 | 975 | 394 | 402 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.50 | 0.61 | 0.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 4.374 | 12.735 | 0.510 | 0.000 | 0.000 | 0.000 | 0.000 | 200.031 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 811 | 0 | 989 | 509 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 0.00 | 1.22 | 0.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.02 | 0.00 |
time (sec) |
N/A | 0.000 | 12.005 | 0.647 | 0.000 | 0.000 | 0.000 | 0.000 | 200.064 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 414 | 414 | 185 | 315 | 0 | 250 | 434 | 0 | 289 | 0 |
N.S. |
1 | 1.00 | 0.45 | 0.76 | 0.00 | 0.60 | 1.05 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.893 | 10.603 | 1.279 | 0.000 | 0.177 | 5.779 | 0.000 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 382 | 382 | 158 | 265 | 0 | 209 | 316 | 0 | 225 | 0 |
N.S. |
1 | 1.00 | 0.41 | 0.69 | 0.00 | 0.55 | 0.83 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.831 | 10.209 | 1.135 | 0.000 | 0.174 | 5.126 | 0.000 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 198 | 121 | 139 | 0 | 117 | 214 | 0 | 146 | 0 |
N.S. |
1 | 1.00 | 0.61 | 0.70 | 0.00 | 0.59 | 1.08 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.519 | 10.183 | 0.653 | 0.000 | 0.212 | 4.237 | 0.000 | 0.177 | 0.000 |