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 | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 52 | 67 | 45 | 61 | 51 | 49 | 245 | 44 | 41 |
N.S. |
1 | 1.02 | 1.31 | 0.88 | 1.20 | 1.00 | 0.96 | 4.80 | 0.86 | 0.80 |
time (sec) |
N/A | 0.236 | 0.008 | 0.152 | 0.029 | 0.073 | 0.355 | 0.118 | 0.164 | 3.651 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 52 | 50 | 47 | 46 | 55 | 54 | 255 | 52 | 43 |
N.S. |
1 | 1.04 | 1.00 | 0.94 | 0.92 | 1.10 | 1.08 | 5.10 | 1.04 | 0.86 |
time (sec) |
N/A | 0.233 | 0.008 | 0.108 | 0.025 | 0.081 | 0.320 | 0.122 | 0.179 | 3.664 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 42 | 57 | 37 | 52 | 43 | 41 | 195 | 36 | 33 |
N.S. |
1 | 1.02 | 1.39 | 0.90 | 1.27 | 1.05 | 1.00 | 4.76 | 0.88 | 0.80 |
time (sec) |
N/A | 0.221 | 0.008 | 0.095 | 0.028 | 0.085 | 0.285 | 0.123 | 0.174 | 3.553 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 42 | 40 | 38 | 35 | 44 | 46 | 206 | 44 | 35 |
N.S. |
1 | 1.05 | 1.00 | 0.95 | 0.88 | 1.10 | 1.15 | 5.15 | 1.10 | 0.88 |
time (sec) |
N/A | 0.218 | 0.007 | 0.074 | 0.024 | 0.097 | 0.239 | 0.117 | 0.172 | 3.572 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 32 | 47 | 27 | 41 | 34 | 32 | 144 | 27 | 26 |
N.S. |
1 | 1.03 | 1.52 | 0.87 | 1.32 | 1.10 | 1.03 | 4.65 | 0.87 | 0.84 |
time (sec) |
N/A | 0.192 | 0.007 | 0.088 | 0.023 | 0.081 | 0.206 | 0.119 | 0.173 | 3.560 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 23 | 25 | 33 | 27 | 153 | 28 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 1.00 | 1.32 | 1.08 | 6.12 | 1.12 | 0.88 |
time (sec) |
N/A | 0.177 | 0.002 | 0.059 | 0.031 | 0.069 | 0.141 | 0.121 | 0.164 | 3.550 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 26 | 28 | 86 | 0 | 0 | 0 | 10 | 0 |
N.S. |
1 | 1.00 | 0.93 | 1.00 | 3.07 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.183 | 0.008 | 0.089 | 0.031 | 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 | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 33 | 30 | 35 | 30 | 39 | 26 | 143 | 38 | 27 |
N.S. |
1 | 1.10 | 1.00 | 1.17 | 1.00 | 1.30 | 0.87 | 4.77 | 1.27 | 0.90 |
time (sec) |
N/A | 0.198 | 0.008 | 0.076 | 0.024 | 0.099 | 0.141 | 0.115 | 0.160 | 3.591 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 29 | 47 | 26 | 36 | 35 | 24 | 140 | 26 | 40 |
N.S. |
1 | 0.94 | 1.52 | 0.84 | 1.16 | 1.13 | 0.77 | 4.52 | 0.84 | 1.29 |
time (sec) |
N/A | 0.193 | 0.007 | 0.090 | 0.031 | 0.090 | 0.271 | 0.113 | 0.164 | 3.602 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 47 | 48 | 40 | 50 | 46 | 209 | 55 | 39 |
N.S. |
1 | 1.00 | 1.00 | 1.02 | 0.85 | 1.06 | 0.98 | 4.45 | 1.17 | 0.83 |
time (sec) |
N/A | 0.229 | 0.008 | 0.091 | 0.029 | 0.090 | 0.251 | 0.117 | 0.173 | 3.567 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 57 | 36 | 51 | 43 | 32 | 205 | 35 | 60 |
N.S. |
1 | 1.00 | 1.39 | 0.88 | 1.24 | 1.05 | 0.78 | 5.00 | 0.85 | 1.46 |
time (sec) |
N/A | 0.205 | 0.008 | 0.110 | 0.028 | 0.080 | 0.275 | 0.118 | 0.171 | 3.974 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 177 | 80 | 92 | 135 | 98 | 114 | 534 | 94 | 85 |
N.S. |
1 | 1.69 | 0.76 | 0.88 | 1.29 | 0.93 | 1.09 | 5.09 | 0.90 | 0.81 |
time (sec) |
N/A | 1.306 | 0.017 | 0.286 | 0.032 | 0.092 | 0.426 | 0.126 | 0.164 | 3.760 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 172 | 87 | 164 | 155 | 0 | 0 | 0 | 82 | 0 |
N.S. |
1 | 1.35 | 0.69 | 1.29 | 1.22 | 0.00 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 1.130 | 0.303 | 0.316 | 0.034 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 115 | 62 | 72 | 118 | 81 | 90 | 335 | 73 | 65 |
N.S. |
1 | 1.42 | 0.77 | 0.89 | 1.46 | 1.00 | 1.11 | 4.14 | 0.90 | 0.80 |
time (sec) |
N/A | 0.834 | 0.014 | 0.201 | 0.031 | 0.086 | 0.319 | 0.128 | 0.162 | 3.818 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 120 | 66 | 144 | 134 | 0 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.17 | 0.64 | 1.40 | 1.30 | 0.00 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.732 | 0.172 | 0.284 | 0.032 | 0.000 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 61 | 43 | 49 | 97 | 62 | 60 | 154 | 53 | 44 |
N.S. |
1 | 1.13 | 0.80 | 0.91 | 1.80 | 1.15 | 1.11 | 2.85 | 0.98 | 0.81 |
time (sec) |
N/A | 0.456 | 0.011 | 0.172 | 0.031 | 0.115 | 0.241 | 0.117 | 0.164 | 3.769 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 71 | 46 | 116 | 135 | 0 | 0 | 0 | 8 | 0 |
N.S. |
1 | 1.22 | 0.79 | 2.00 | 2.33 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.429 | 0.061 | 0.240 | 0.034 | 0.000 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 128 | 114 | 459 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.32 | 1.18 | 4.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.717 | 0.041 | 3.542 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 60 | 49 | 145 | 146 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.09 | 0.89 | 2.64 | 2.65 | 0.00 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.416 | 0.071 | 0.141 | 0.035 | 0.000 | 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 | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 60 | 57 | 72 | 96 | 79 | 56 | 137 | 75 | 145 |
N.S. |
1 | 0.98 | 0.93 | 1.18 | 1.57 | 1.30 | 0.92 | 2.25 | 1.23 | 2.38 |
time (sec) |
N/A | 0.471 | 0.013 | 0.146 | 0.032 | 0.085 | 0.280 | 0.119 | 0.174 | 3.781 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 97 | 87 | 184 | 176 | 0 | 0 | 0 | 69 | 0 |
N.S. |
1 | 0.94 | 0.84 | 1.79 | 1.71 | 0.00 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.708 | 0.153 | 0.157 | 0.036 | 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 | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 114 | 82 | 101 | 154 | 97 | 90 | 319 | 96 | 196 |
N.S. |
1 | 1.27 | 0.91 | 1.12 | 1.71 | 1.08 | 1.00 | 3.54 | 1.07 | 2.18 |
time (sec) |
N/A | 0.863 | 0.016 | 0.158 | 0.034 | 0.084 | 0.292 | 0.125 | 0.161 | 4.232 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | C | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 421 | 117 | 2133 | 289 | 0 | 0 | 0 | 132 | 0 |
N.S. |
1 | 2.26 | 0.63 | 11.47 | 1.55 | 0.00 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 2.957 | 0.366 | 5.857 | 0.036 | 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 | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 304 | 175 | 1223 | 0 | 0 | 0 | 0 | 123 | 0 |
N.S. |
1 | 1.55 | 0.89 | 6.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 2.627 | 0.411 | 5.506 | 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 | C | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 239 | 88 | 871 | 262 | 0 | 0 | 0 | 96 | 0 |
N.S. |
1 | 1.72 | 0.63 | 6.27 | 1.88 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 1.793 | 0.212 | 4.686 | 0.036 | 0.000 | 0.000 | 0.000 | 0.158 | 0.000 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 177 | 140 | 776 | 0 | 0 | 0 | 0 | 89 | 0 |
N.S. |
1 | 1.19 | 0.94 | 5.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 1.528 | 0.260 | 4.335 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 109 | 68 | 2910 | 215 | 0 | 0 | 0 | 85 | 0 |
N.S. |
1 | 1.15 | 0.72 | 30.63 | 2.26 | 0.00 | 0.00 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.841 | 0.099 | 3.546 | 0.035 | 0.000 | 0.000 | 0.000 | 0.158 | 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 | 85 | 101 | 79 | 168 | 0 | 0 | 0 | 0 | 8 | 0 |
N.S. |
1 | 1.19 | 0.93 | 1.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.653 | 0.076 | 0.308 | 0.000 | 0.000 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 182 | 156 | 536 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.21 | 1.04 | 3.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.046 | 0.054 | 3.959 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 93 | 72 | 718 | 0 | 0 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.18 | 0.91 | 9.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.676 | 0.091 | 5.003 | 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 | C | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 90 | 79 | 3498 | 252 | 0 | 0 | 0 | 86 | 0 |
N.S. |
1 | 0.95 | 0.83 | 36.82 | 2.65 | 0.00 | 0.00 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 0.802 | 0.110 | 3.792 | 0.043 | 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 | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 158 | 142 | 836 | 0 | 0 | 0 | 0 | 120 | 0 |
N.S. |
1 | 1.03 | 0.92 | 5.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 1.580 | 0.153 | 6.372 | 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 | A | C | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 191 | 118 | 657 | 342 | 0 | 0 | 0 | 108 | 0 |
N.S. |
1 | 1.35 | 0.84 | 4.66 | 2.43 | 0.00 | 0.00 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 1.502 | 0.164 | 4.562 | 0.039 | 0.000 | 0.000 | 0.000 | 0.160 | 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 | 10 | 10 | 12 | 10 | 124 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 12.40 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.184 | 0.720 | 0.285 | 1.102 | 0.089 | 2.331 | 0.139 | 0.166 | 3.525 |
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 | 10 | 10 | 12 | 10 | 93 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 9.30 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.186 | 0.731 | 0.193 | 0.728 | 0.098 | 1.220 | 0.140 | 0.161 | 3.662 |
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 | 57 | 57 | 52 | 0 | 0 | 0 | 0 | 0 | 99 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.74 | 0.00 |
time (sec) |
N/A | 0.213 | 0.028 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 32 | 26 | 95 | 104 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.14 | 0.93 | 3.39 | 3.71 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.236 | 0.011 | 0.170 | 0.035 | 0.000 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 17 | 16 | 15 | 23 | 15 | 104 | 17 | 26 |
N.S. |
1 | 1.00 | 0.89 | 0.84 | 0.79 | 1.21 | 0.79 | 5.47 | 0.89 | 1.37 |
time (sec) |
N/A | 0.183 | 0.001 | 0.145 | 0.023 | 0.109 | 0.098 | 0.116 | 0.161 | 0.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 52 | 59 | 42 | 41 | 38 | 0 | 164 | 30 | 31 |
N.S. |
1 | 1.02 | 1.16 | 0.82 | 0.80 | 0.75 | 0.00 | 3.22 | 0.59 | 0.61 |
time (sec) |
N/A | 0.204 | 0.014 | 0.043 | 0.025 | 0.095 | 0.000 | 0.121 | 0.164 | 3.668 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 43 | 52 | 37 | 36 | 31 | 0 | 114 | 23 | 26 |
N.S. |
1 | 1.02 | 1.24 | 0.88 | 0.86 | 0.74 | 0.00 | 2.71 | 0.55 | 0.62 |
time (sec) |
N/A | 0.194 | 0.010 | 0.031 | 0.031 | 0.095 | 0.000 | 0.123 | 0.168 | 3.686 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 29 | 22 | 27 | 26 | 24 | 0 | 65 | 15 | 16 |
N.S. |
1 | 1.32 | 1.00 | 1.23 | 1.18 | 1.09 | 0.00 | 2.95 | 0.68 | 0.73 |
time (sec) |
N/A | 0.189 | 0.016 | 0.029 | 0.030 | 0.089 | 0.000 | 0.118 | 0.179 | 3.683 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 27 | 19 | 33 | 66 | 0 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.42 | 1.00 | 1.74 | 3.47 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.230 | 0.009 | 0.142 | 0.034 | 0.000 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 32 | 45 | 32 | 31 | 30 | 92 | 65 | 17 | 18 |
N.S. |
1 | 1.28 | 1.80 | 1.28 | 1.24 | 1.20 | 3.68 | 2.60 | 0.68 | 0.72 |
time (sec) |
N/A | 0.202 | 0.015 | 0.042 | 0.028 | 0.098 | 0.457 | 0.123 | 0.169 | 3.728 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 43 | 58 | 37 | 36 | 38 | 160 | 114 | 26 | 45 |
N.S. |
1 | 1.02 | 1.38 | 0.88 | 0.86 | 0.90 | 3.81 | 2.71 | 0.62 | 1.07 |
time (sec) |
N/A | 0.200 | 0.015 | 0.042 | 0.025 | 0.133 | 0.918 | 0.121 | 0.178 | 4.153 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 35 | 31 | 35 | 24 | 35 | 121 | 168 | 31 | 24 |
N.S. |
1 | 0.92 | 0.82 | 0.92 | 0.63 | 0.92 | 3.18 | 4.42 | 0.82 | 0.63 |
time (sec) |
N/A | 0.208 | 0.012 | 0.036 | 0.028 | 0.100 | 0.833 | 0.124 | 0.171 | 3.859 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 28 | 25 | 30 | 19 | 30 | 0 | 119 | 24 | 0 |
N.S. |
1 | 0.90 | 0.81 | 0.97 | 0.61 | 0.97 | 0.00 | 3.84 | 0.77 | 0.00 |
time (sec) |
N/A | 0.200 | 0.009 | 0.033 | 0.027 | 0.082 | 0.000 | 0.115 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 15 | 16 | 24 | 87 | 70 | 20 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 0.80 | 1.20 | 4.35 | 3.50 | 1.00 | 0.70 |
time (sec) |
N/A | 0.176 | 0.006 | 0.033 | 0.023 | 0.096 | 0.206 | 0.117 | 0.167 | 3.753 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 29 | 18 | 36 | 126 | 70 | 34 | 22 |
N.S. |
1 | 1.00 | 1.00 | 1.21 | 0.75 | 1.50 | 5.25 | 2.92 | 1.42 | 0.92 |
time (sec) |
N/A | 0.182 | 0.014 | 0.034 | 0.025 | 0.099 | 0.356 | 0.121 | 0.178 | 3.774 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 36 | 52 | 45 | 147 | 128 | 0 | 0 | 12 | 0 |
N.S. |
1 | 0.95 | 1.37 | 1.18 | 3.87 | 3.37 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.233 | 0.037 | 0.272 | 0.101 | 0.102 | 0.000 | 0.000 | 0.179 | 0.000 |