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 | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 36 | 61 | 66 | 209 | 37 | 45 | 50 |
N.S. |
1 | 1.00 | 1.00 | 2.40 | 4.07 | 4.40 | 13.93 | 2.47 | 3.00 | 3.33 |
time (sec) |
N/A | 0.182 | 0.115 | 0.137 | 0.112 | 0.085 | 1.319 | 0.120 | 0.153 | 0.150 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 24 | 46 | 69 | 113 | 908 | 48 | 140 | 63 |
N.S. |
1 | 1.00 | 0.96 | 1.84 | 2.76 | 4.52 | 36.32 | 1.92 | 5.60 | 2.52 |
time (sec) |
N/A | 0.188 | 0.247 | 0.267 | 0.114 | 0.092 | 3.116 | 0.129 | 0.152 | 1.606 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 83 | 127 | 71 | 0 | 247 | 0 | 143 | 273 | 285 |
N.S. |
1 | 1.11 | 1.69 | 0.95 | 0.00 | 3.29 | 0.00 | 1.91 | 3.64 | 3.80 |
time (sec) |
N/A | 0.361 | 5.168 | 0.855 | 0.000 | 0.094 | 0.000 | 0.138 | 0.167 | 3.350 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | C | F | B | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 69 | 64 | 81 | 0 | 618 | 0 | 48 | 767 | 273 |
N.S. |
1 | 0.43 | 0.40 | 0.51 | 0.00 | 3.89 | 0.00 | 0.30 | 4.82 | 1.72 |
time (sec) |
N/A | 0.434 | 2.149 | 4.246 | 0.000 | 0.115 | 0.000 | 0.276 | 0.183 | 3.164 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 21 | 19 | 30 | 38 | 39 | 33 | 25 | 40 |
N.S. |
1 | 1.00 | 0.68 | 0.61 | 0.97 | 1.23 | 1.26 | 1.06 | 0.81 | 1.29 |
time (sec) |
N/A | 0.184 | 0.029 | 0.040 | 0.121 | 0.084 | 0.273 | 0.125 | 0.157 | 0.121 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | C | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 133 | 156 | 60 | 0 | 158 | 5697 | 106 | 155 | 225 |
N.S. |
1 | 1.00 | 1.17 | 0.45 | 0.00 | 1.19 | 42.83 | 0.80 | 1.17 | 1.69 |
time (sec) |
N/A | 0.433 | 5.252 | 0.220 | 0.000 | 0.106 | 41.815 | 0.135 | 0.158 | 3.219 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 233 | 437 | 90 | 0 | 591 | 0 | 4948 | 12 | 0 |
N.S. |
1 | 1.00 | 1.88 | 0.39 | 0.00 | 2.54 | 0.00 | 21.24 | 0.05 | 0.00 |
time (sec) |
N/A | 0.783 | 5.037 | 0.217 | 0.000 | 0.176 | 0.000 | 2.230 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 2 | 2 | 2 | 8 | 10 | 20 | 14 | 10 | 16 | 10 |
N.S. |
1 | 1.00 | 1.00 | 4.00 | 5.00 | 10.00 | 7.00 | 5.00 | 8.00 | 5.00 |
time (sec) |
N/A | 0.219 | 0.001 | 0.059 | 0.035 | 0.076 | 0.332 | 0.120 | 0.150 | 2.917 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 196 | 45 | 36 | 0 | 443 | 0 | 303 | 10 | 205 |
N.S. |
1 | 1.45 | 0.33 | 0.27 | 0.00 | 3.28 | 0.00 | 2.24 | 0.07 | 1.52 |
time (sec) |
N/A | 0.499 | 5.025 | 0.389 | 0.000 | 0.113 | 0.000 | 0.170 | 0.168 | 1.977 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 71 | 87 | 47 | 0 | 564 | 0 | 10 | 451 | 325 |
N.S. |
1 | 0.47 | 0.58 | 0.31 | 0.00 | 3.74 | 0.00 | 0.07 | 2.99 | 2.15 |
time (sec) |
N/A | 0.510 | 5.113 | 2.235 | 0.000 | 0.134 | 0.000 | 0.123 | 0.166 | 5.465 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 411 | 129 | 127 | 64 | 0 | 729 | 0 | 1 | 10 | 0 |
N.S. |
1 | 0.31 | 0.31 | 0.16 | 0.00 | 1.77 | 0.00 | 0.00 | 0.02 | 0.00 |
time (sec) |
N/A | 0.457 | 5.021 | 3.534 | 0.000 | 0.134 | 0.000 | 0.125 | 0.158 | 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 | 30 | 30 | 21 | 19 | 30 | 36 | 39 | 29 | 25 | 40 |
N.S. |
1 | 1.00 | 0.70 | 0.63 | 1.00 | 1.20 | 1.30 | 0.97 | 0.83 | 1.33 |
time (sec) |
N/A | 0.177 | 0.030 | 0.054 | 0.113 | 0.077 | 0.268 | 0.125 | 0.152 | 0.123 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 147 | 156 | 60 | 0 | 160 | 5697 | 102 | 155 | 203 |
N.S. |
1 | 1.06 | 1.12 | 0.43 | 0.00 | 1.15 | 40.99 | 0.73 | 1.12 | 1.46 |
time (sec) |
N/A | 0.431 | 5.301 | 0.355 | 0.000 | 0.098 | 35.323 | 0.128 | 0.159 | 1.731 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 245 | 439 | 90 | 0 | 589 | 0 | 4946 | 10 | 0 |
N.S. |
1 | 1.00 | 1.79 | 0.37 | 0.00 | 2.40 | 0.00 | 20.19 | 0.04 | 0.00 |
time (sec) |
N/A | 0.693 | 5.039 | 0.343 | 0.000 | 0.156 | 0.000 | 2.216 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 138 | 0 | 312 | 15319 | 39 | 98 | 181 |
N.S. |
1 | 1.00 | 1.00 | 4.18 | 0.00 | 9.45 | 464.21 | 1.18 | 2.97 | 5.48 |
time (sec) |
N/A | 0.247 | 0.480 | 0.245 | 0.000 | 0.088 | 15.432 | 0.114 | 0.157 | 0.889 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 352 | 541 | 148 | 94 | 0 | 779 | 0 | 1781 | 12 | 1559 |
N.S. |
1 | 1.54 | 0.42 | 0.27 | 0.00 | 2.21 | 0.00 | 5.06 | 0.03 | 4.43 |
time (sec) |
N/A | 1.466 | 2.743 | 0.481 | 0.000 | 0.122 | 0.000 | 2.048 | 0.153 | 9.649 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 175 | 134 | 128 | 0 | 16401 | 0 | 0 | 12 | 857 |
N.S. |
1 | 1.00 | 0.77 | 0.73 | 0.00 | 93.72 | 0.00 | 0.00 | 0.07 | 4.90 |
time (sec) |
N/A | 0.560 | 5.044 | 1.173 | 0.000 | 1.228 | 0.000 | 0.000 | 0.156 | 67.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 257 | 160 | 162 | 0 | 661332 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.05 | 0.65 | 0.66 | 0.00 | 2699.31 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.744 | 5.075 | 2.774 | 0.000 | 3.262 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 42 | 45 | 35 | 54 | 111 | 110 | 56 | 42 | 49 |
N.S. |
1 | 1.14 | 1.22 | 0.95 | 1.46 | 3.00 | 2.97 | 1.51 | 1.14 | 1.32 |
time (sec) |
N/A | 0.211 | 0.025 | 0.090 | 0.117 | 0.087 | 2.549 | 0.125 | 0.150 | 0.161 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 250 | 107 | 79 | 0 | 16934 | 0 | 0 | 12 | 633 |
N.S. |
1 | 1.00 | 0.43 | 0.32 | 0.00 | 67.74 | 0.00 | 0.00 | 0.05 | 2.53 |
time (sec) |
N/A | 0.692 | 5.035 | 0.444 | 0.000 | 0.968 | 0.000 | 0.000 | 0.153 | 5.407 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 435 | 435 | 141 | 113 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.00 | 0.32 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 1.209 | 5.046 | 1.365 | 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 | C | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 21 | 11 | 19 | 49 | 84 | 104 | 18 | 36 | 18 |
N.S. |
1 | 1.91 | 1.00 | 1.73 | 4.45 | 7.64 | 9.45 | 1.64 | 3.27 | 1.64 |
time (sec) |
N/A | 0.225 | 0.004 | 0.174 | 0.041 | 0.072 | 0.778 | 0.118 | 0.152 | 0.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 31 | 19 | 25 | 111 | 185 | 260 | 24 | 57 | 24 |
N.S. |
1 | 1.63 | 1.00 | 1.32 | 5.84 | 9.74 | 13.68 | 1.26 | 3.00 | 1.26 |
time (sec) |
N/A | 0.238 | 0.004 | 0.325 | 0.039 | 0.071 | 1.769 | 0.122 | 0.151 | 0.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 35 | 60 | 87 | 216 | 2052 | 62 | 224 | 77 |
N.S. |
1 | 1.00 | 0.95 | 1.62 | 2.35 | 5.84 | 55.46 | 1.68 | 6.05 | 2.08 |
time (sec) |
N/A | 0.255 | 0.139 | 0.191 | 0.119 | 0.085 | 4.769 | 0.119 | 0.152 | 0.187 |
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 | 55 | 60 | 51 | 72 | 111 | 575 | 5666 | 74 | 396 | 112 |
N.S. |
1 | 1.09 | 0.93 | 1.31 | 2.02 | 10.45 | 103.02 | 1.35 | 7.20 | 2.04 |
time (sec) |
N/A | 0.359 | 0.309 | 0.477 | 0.115 | 0.087 | 11.672 | 0.125 | 0.154 | 1.738 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 14 | 11 | 2 | 0 | 11 | 9 | 2 |
N.S. |
1 | 1.00 | 1.00 | 1.27 | 1.00 | 0.18 | 0.00 | 1.00 | 0.82 | 0.18 |
time (sec) |
N/A | 0.258 | 0.017 | 0.146 | 0.118 | 0.085 | 0.000 | 0.121 | 0.153 | 1.698 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | C | F | C | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 15 | 25 | 14 | 0 | 11 | 11 | 5 |
N.S. |
1 | 1.00 | 1.00 | 1.15 | 1.92 | 1.08 | 0.00 | 0.85 | 0.85 | 0.38 |
time (sec) |
N/A | 0.279 | 0.016 | 0.099 | 0.115 | 0.096 | 0.000 | 0.119 | 0.152 | 0.176 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 51 | 0 | 0 | 0 | 0 | 11 | 0 |
N.S. |
1 | 1.00 | 1.00 | 4.64 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.175 | 0.020 | 0.994 | 0.000 | 0.000 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 61 | 0 | 0 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.250 | 0.024 | 0.747 | 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 | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 20 | 21 | 23 | 17 | 0 | 25 | 24 | 0 |
N.S. |
1 | 1.00 | 0.69 | 0.72 | 0.79 | 0.59 | 0.00 | 0.86 | 0.83 | 0.00 |
time (sec) |
N/A | 0.322 | 0.007 | 0.084 | 0.114 | 0.100 | 0.000 | 0.117 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | C | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 22 | 21 | 53 | 26 | 0 | 25 | 27 | 0 |
N.S. |
1 | 1.00 | 0.67 | 0.64 | 1.61 | 0.79 | 0.00 | 0.76 | 0.82 | 0.00 |
time (sec) |
N/A | 0.320 | 0.006 | 0.091 | 0.123 | 0.106 | 0.000 | 0.123 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 48 | 45 | 103 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.07 | 1.00 | 2.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.387 | 0.051 | 0.635 | 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 | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 90 | 78 | 106 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.03 | 0.90 | 1.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.569 | 0.088 | 0.768 | 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 | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 15 | 15 | 5 | 8 | 0 | 5 | 18 | 0 |
N.S. |
1 | 1.00 | 1.07 | 1.07 | 0.36 | 0.57 | 0.00 | 0.36 | 1.29 | 0.00 |
time (sec) |
N/A | 0.269 | 0.006 | 0.084 | 0.151 | 0.075 | 0.000 | 0.124 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 41 | 0 | 42 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 1.00 | 3.73 | 0.00 | 3.82 | 0.00 | 0.00 | 2.00 | 0.00 |
time (sec) |
N/A | 0.172 | 0.027 | 0.133 | 0.000 | 0.105 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 61 | 0 | 42 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.85 | 0.00 | 1.27 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.253 | 0.029 | 0.116 | 0.000 | 0.099 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | C | C | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 17 | 34 | 5 | 13 | 0 | 5 | 21 | 0 |
N.S. |
1 | 1.00 | 1.06 | 2.12 | 0.31 | 0.81 | 0.00 | 0.31 | 1.31 | 0.00 |
time (sec) |
N/A | 0.277 | 0.005 | 0.095 | 0.169 | 0.081 | 0.000 | 0.127 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 172 | 173 | 490 | 0 | 0 | 0 | 0 | 56 | 0 |
N.S. |
1 | 1.02 | 1.03 | 2.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 1.027 | 0.388 | 7.285 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 124 | 132 | 333 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 0.99 | 1.06 | 2.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.748 | 0.276 | 2.742 | 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 | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 42 | 54 | 109 | 0 | 0 | 0 | 0 | 11 | 0 |
N.S. |
1 | 0.98 | 1.26 | 2.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.280 | 0.037 | 1.440 | 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 | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 42 | 53 | 63 | 0 | 136 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.98 | 1.23 | 1.47 | 0.00 | 3.16 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.303 | 0.040 | 0.165 | 0.000 | 0.097 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 82 | 81 | 197 | 0 | 1183 | 0 | 0 | 34 | 0 |
N.S. |
1 | 0.99 | 0.98 | 2.37 | 0.00 | 14.25 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.437 | 0.076 | 0.826 | 0.000 | 0.108 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 192 | 159 | 311 | 0 | 4717 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.03 | 0.85 | 1.66 | 0.00 | 25.22 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 1.252 | 0.506 | 1.259 | 0.000 | 0.231 | 0.000 | 0.000 | 0.150 | 0.000 |