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 | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 228 | 225 | 0 | 0 | 0 | 0 | 0 | 15 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.298 | 0.072 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 201 | 155 | 0 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.299 | 0.070 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 256 | 256 | 256 | 0 | 0 | 0 | 0 | 0 | 1002 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.91 | 0.00 |
time (sec) |
N/A | 0.321 | 0.314 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.461 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 281 | 285 | 270 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.387 | 0.555 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.518 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 339 | 340 | 319 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.440 | 0.598 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.592 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 42 | 36 | 39 | 38 | 0 | 38 | 39 | 39 |
N.S. |
1 | 1.00 | 1.05 | 0.90 | 0.98 | 0.95 | 0.00 | 0.95 | 0.98 | 0.98 |
time (sec) |
N/A | 0.248 | 0.197 | 0.273 | 0.779 | 0.121 | 0.000 | 0.758 | 0.347 | 0.562 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 275 | 282 | 0 | 1171 | 0 | 0 | 0 | 0 | 150 | 0 |
N.S. |
1 | 1.03 | 0.00 | 4.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.846 | 0.000 | 0.404 | 0.000 | 0.000 | 0.000 | 0.000 | 0.372 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 212 | 0 | 657 | 0 | 0 | 0 | 0 | 108 | 0 |
N.S. |
1 | 1.03 | 0.00 | 3.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.643 | 0.000 | 0.125 | 0.000 | 0.000 | 0.000 | 0.000 | 0.317 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 144 | 0 | 273 | 0 | 0 | 0 | 0 | 64 | 0 |
N.S. |
1 | 1.02 | 0.00 | 1.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.492 | 0.000 | 0.121 | 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 | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 42 | 36 | 39 | 48 | 61 | 38 | 63 | 39 |
N.S. |
1 | 1.00 | 1.05 | 0.90 | 0.98 | 1.20 | 1.52 | 0.95 | 1.58 | 0.98 |
time (sec) |
N/A | 0.245 | 0.286 | 0.112 | 0.242 | 0.077 | 109.169 | 0.260 | 0.259 | 0.308 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 42 | 36 | 225 | 91 | 0 | 38 | 123 | 39 |
N.S. |
1 | 1.00 | 1.05 | 0.90 | 5.62 | 2.28 | 0.00 | 0.95 | 3.08 | 0.98 |
time (sec) |
N/A | 0.273 | 2.497 | 0.111 | 1.665 | 0.080 | 0.000 | 0.370 | 0.330 | 1.153 |
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 | 22 | 22 | 22 | 18 | 17 | 17 | 17 | 17 | 10 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.77 | 0.77 | 0.77 | 0.77 | 0.45 | 0.77 |
time (sec) |
N/A | 0.249 | 0.043 | 0.030 | 0.101 | 0.083 | 0.163 | 0.119 | 0.158 | 0.193 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | A | F | F(-2) | F | F | F | B |
verified |
N/A | No | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 85 | 0 | 170 | 0 | 0 | 0 | 0 | 12 | 70 |
N.S. |
1 | 1.01 | 0.00 | 2.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.83 |
time (sec) |
N/A | 0.446 | 0.000 | 0.142 | 0.000 | 0.000 | 0.000 | 0.000 | 0.155 | 0.650 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 73 | 50 | 0 | 0 | 54 | 100 | 97 | 12 | 0 |
N.S. |
1 | 0.90 | 0.62 | 0.00 | 0.00 | 0.67 | 1.23 | 1.20 | 0.15 | 0.00 |
time (sec) |
N/A | 0.319 | 0.143 | 0.000 | 0.000 | 0.101 | 0.421 | 0.127 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 75 | 50 | 0 | 0 | 45 | 80 | 76 | 12 | 0 |
N.S. |
1 | 0.91 | 0.61 | 0.00 | 0.00 | 0.55 | 0.98 | 0.93 | 0.15 | 0.00 |
time (sec) |
N/A | 0.302 | 0.125 | 0.000 | 0.000 | 0.089 | 0.267 | 0.143 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 42 | 30 | 0 | 0 | 35 | 53 | 53 | 35 | 0 |
N.S. |
1 | 1.02 | 0.73 | 0.00 | 0.00 | 0.85 | 1.29 | 1.29 | 0.85 | 0.00 |
time (sec) |
N/A | 0.315 | 0.071 | 0.000 | 0.000 | 0.089 | 0.180 | 0.123 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 41 | 31 | 0 | 0 | 26 | 32 | 31 | 26 | 0 |
N.S. |
1 | 1.05 | 0.79 | 0.00 | 0.00 | 0.67 | 0.82 | 0.79 | 0.67 | 0.00 |
time (sec) |
N/A | 0.260 | 0.059 | 0.000 | 0.000 | 0.088 | 0.077 | 0.121 | 0.151 | 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 | 43 | 43 | 75 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.00 | 1.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.317 | 0.079 | 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 | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 54 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.00 | 0.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.386 | 0.109 | 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 | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 93 | 67 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 0.92 | 0.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.433 | 0.095 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 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 | 129 | 121 | 84 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 0.94 | 0.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.473 | 0.099 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 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 | 49 | 47 | 36 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 0.96 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.325 | 0.057 | 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 | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 63 | 48 | 0 | 0 | 0 | 0 | 0 | 10 | 0 |
N.S. |
1 | 0.97 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.319 | 0.064 | 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 | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 11 | 13 | 13 | 10 | 13 | 14 | 13 |
N.S. |
1 | 1.00 | 1.17 | 0.92 | 1.08 | 1.08 | 0.83 | 1.08 | 1.17 | 1.08 |
time (sec) |
N/A | 0.294 | 0.186 | 0.004 | 0.231 | 0.076 | 0.281 | 0.164 | 0.156 | 0.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 11 | 13 | 13 | 12 | 13 | 14 | 13 |
N.S. |
1 | 1.00 | 1.17 | 0.92 | 1.08 | 1.08 | 1.00 | 1.08 | 1.17 | 1.08 |
time (sec) |
N/A | 0.328 | 1.299 | 0.005 | 0.219 | 0.077 | 0.311 | 0.170 | 0.157 | 0.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 309 | 278 | 148 | 0 | 0 | 129 | 416 | 334 | 14 | 0 |
N.S. |
1 | 0.90 | 0.48 | 0.00 | 0.00 | 0.42 | 1.35 | 1.08 | 0.05 | 0.00 |
time (sec) |
N/A | 0.904 | 0.333 | 0.000 | 0.000 | 0.096 | 0.516 | 0.141 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 185 | 103 | 0 | 0 | 85 | 243 | 208 | 14 | 0 |
N.S. |
1 | 0.90 | 0.50 | 0.00 | 0.00 | 0.41 | 1.19 | 1.01 | 0.07 | 0.00 |
time (sec) |
N/A | 0.618 | 0.177 | 0.000 | 0.000 | 0.093 | 0.318 | 0.139 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 94 | 59 | 0 | 0 | 63 | 146 | 108 | 82 | 0 |
N.S. |
1 | 0.93 | 0.58 | 0.00 | 0.00 | 0.62 | 1.45 | 1.07 | 0.81 | 0.00 |
time (sec) |
N/A | 0.469 | 0.154 | 0.000 | 0.000 | 0.088 | 0.219 | 0.130 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 49 | 35 | 0 | 0 | 39 | 65 | 43 | 39 | 0 |
N.S. |
1 | 0.96 | 0.69 | 0.00 | 0.00 | 0.76 | 1.27 | 0.84 | 0.76 | 0.00 |
time (sec) |
N/A | 0.217 | 0.047 | 0.000 | 0.000 | 0.098 | 0.098 | 0.128 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 11 | 13 | 13 | 10 | 13 | 14 | 13 |
N.S. |
1 | 1.00 | 1.17 | 0.92 | 1.08 | 1.08 | 0.83 | 1.08 | 1.17 | 1.08 |
time (sec) |
N/A | 0.527 | 0.154 | 0.003 | 0.239 | 0.121 | 0.320 | 0.223 | 0.155 | 0.132 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 11 | 13 | 13 | 12 | 13 | 14 | 13 |
N.S. |
1 | 1.00 | 1.17 | 0.92 | 1.08 | 1.08 | 1.00 | 1.08 | 1.17 | 1.08 |
time (sec) |
N/A | 0.507 | 0.213 | 0.006 | 0.244 | 0.102 | 0.355 | 0.237 | 0.171 | 0.127 |
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 | 381 | 350 | 221 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.92 | 0.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.947 | 0.287 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 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 | 265 | 245 | 161 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.92 | 0.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.719 | 0.169 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 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 | 123 | 116 | 93 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 0.94 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.548 | 0.135 | 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 | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 67 | 52 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 0.97 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.274 | 0.047 | 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 | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 13 | 15 | 15 | 12 | 15 | 16 | 15 |
N.S. |
1 | 1.00 | 1.14 | 0.93 | 1.07 | 1.07 | 0.86 | 1.07 | 1.14 | 1.07 |
time (sec) |
N/A | 0.509 | 0.162 | 0.003 | 0.263 | 0.081 | 0.339 | 0.215 | 0.166 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 13 | 15 | 15 | 14 | 15 | 16 | 15 |
N.S. |
1 | 1.00 | 1.14 | 0.93 | 1.07 | 1.07 | 1.00 | 1.07 | 1.14 | 1.07 |
time (sec) |
N/A | 0.510 | 0.352 | 0.003 | 0.263 | 0.084 | 0.367 | 0.228 | 0.173 | 0.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 167 | 69 | 0 | 0 | 71 | 141 | 0 | 76 | 0 |
N.S. |
1 | 1.03 | 0.43 | 0.00 | 0.00 | 0.44 | 0.87 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 1.081 | 0.324 | 0.000 | 0.000 | 0.091 | 11.332 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 114 | 51 | 0 | 0 | 55 | 95 | 0 | 49 | 0 |
N.S. |
1 | 1.02 | 0.46 | 0.00 | 0.00 | 0.49 | 0.85 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.790 | 0.173 | 0.000 | 0.000 | 0.089 | 1.126 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 61 | 31 | 0 | 0 | 35 | 49 | 0 | 20 | 0 |
N.S. |
1 | 0.98 | 0.50 | 0.00 | 0.00 | 0.56 | 0.79 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.677 | 0.109 | 0.000 | 0.000 | 0.091 | 0.118 | 0.000 | 0.160 | 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 | 10 | 10 | 10 | 10 | 9 | 9 | 8 | 9 | 10 | 9 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.90 | 0.90 | 0.80 | 0.90 | 1.00 | 0.90 |
time (sec) |
N/A | 0.603 | 0.052 | 0.081 | 0.106 | 0.070 | 0.185 | 0.112 | 0.159 | 0.113 |
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 | 45 | 45 | 45 | 0 | 0 | 0 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.741 | 0.082 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 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 | 95 | 84 | 0 | 0 | 0 | 0 | 0 | 60 | 0 |
N.S. |
1 | 0.99 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.761 | 0.151 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | B | F | B | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 48 | 529 | 47 | 0 | 141 | 0 | 95 | 12 | 42 |
N.S. |
1 | 1.02 | 11.26 | 1.00 | 0.00 | 3.00 | 0.00 | 2.02 | 0.26 | 0.89 |
time (sec) |
N/A | 0.290 | 2.590 | 0.219 | 0.000 | 0.102 | 0.000 | 0.136 | 0.164 | 0.581 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | A | A | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 28 | 0 | 1 | 3 | 0 | 0 | 9 | 0 |
N.S. |
1 | 0.00 | 1.04 | 0.00 | 0.04 | 0.11 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.000 | 0.485 | 0.000 | 0.106 | 0.065 | 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(-2) | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 38 | 0 | 0 | 41 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 1.08 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.303 | 0.069 | 0.000 | 0.000 | 0.106 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 26 | 0 | 0 | 28 | 0 | 0 | 24 | 26 |
N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.93 | 0.00 | 0.00 | 0.80 | 0.87 |
time (sec) |
N/A | 0.274 | 0.056 | 0.000 | 0.000 | 0.069 | 0.000 | 0.000 | 0.161 | 0.193 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 17 | 12 | 14 | 12 | 14 | 16 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 0.75 | 0.88 | 0.75 | 0.88 | 1.00 | 0.75 |
time (sec) |
N/A | 0.187 | 0.053 | 0.125 | 0.099 | 0.086 | 0.075 | 0.111 | 0.156 | 0.175 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | F | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 0 | 22 | 17 | 0 | 14 | 0 | 20 | 16 | 12 |
N.S. |
1 | 0.00 | 1.38 | 1.06 | 0.00 | 0.88 | 0.00 | 1.25 | 1.00 | 0.75 |
time (sec) |
N/A | 0.000 | 0.199 | 0.126 | 0.000 | 0.091 | 0.000 | 0.149 | 0.159 | 0.146 |