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 | 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 | 14 | 16 | 18 | 12 | 16 | 38 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 1.29 | 0.86 | 1.14 | 2.71 | 1.14 |
time (sec) |
N/A | 0.168 | 0.042 | 0.338 | 0.198 | 0.076 | 27.141 | 0.483 | 0.146 | 40.035 |
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 | 20 | 20 | 22 | 20 | 22 | 24 | 15 | 22 | 82 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.20 | 0.75 | 1.10 | 4.10 | 1.10 |
time (sec) |
N/A | 0.182 | 0.055 | 0.019 | 0.460 | 0.078 | 166.501 | 0.515 | 0.151 | 0.002 |
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 | 22 | 22 | 24 | 22 | 24 | 35 | 0 | 24 | 134 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.59 | 0.00 | 1.09 | 6.09 | 1.09 |
time (sec) |
N/A | 0.194 | 0.061 | 0.017 | 2.766 | 0.109 | 0.000 | 0.562 | 0.151 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | F(-1) | 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 | 22 | 22 | 0 | 22 | 1281 | 63 | 0 | 24 | 8294 | 24 |
N.S. |
1 | 1.00 | 0.00 | 1.00 | 58.23 | 2.86 | 0.00 | 1.09 | 377.00 | 1.09 |
time (sec) |
N/A | 0.193 | 0.000 | 0.708 | 25.512 | 0.091 | 0.000 | 4.201 | 0.389 | 40.152 |
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 | 20 | 20 | 22 | 20 | 1103 | 52 | 0 | 22 | 3980 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 55.15 | 2.60 | 0.00 | 1.10 | 199.00 | 1.10 |
time (sec) |
N/A | 0.180 | 18.935 | 0.803 | 1.909 | 0.090 | 0.000 | 3.188 | 0.270 | 40.175 |
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 | 14 | 14 | 16 | 14 | 974 | 47 | 0 | 16 | 1167 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 69.57 | 3.36 | 0.00 | 1.14 | 83.36 | 1.14 |
time (sec) |
N/A | 0.162 | 3.340 | 0.424 | 0.408 | 0.087 | 0.000 | 2.299 | 0.222 | 40.289 |
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 | 20 | 20 | 22 | 20 | 1103 | 52 | 0 | 22 | 3980 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 55.15 | 2.60 | 0.00 | 1.10 | 199.00 | 1.10 |
time (sec) |
N/A | 0.182 | 2.209 | 0.018 | 1.929 | 0.093 | 0.000 | 3.155 | 0.267 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | F(-1) | 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 | 22 | 22 | 0 | 22 | 1281 | 63 | 0 | 24 | 8294 | 24 |
N.S. |
1 | 1.00 | 0.00 | 1.00 | 58.23 | 2.86 | 0.00 | 1.09 | 377.00 | 1.09 |
time (sec) |
N/A | 0.195 | 0.000 | 0.019 | 24.272 | 0.094 | 0.000 | 4.273 | 0.364 | 0.002 |
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 | 22 | 22 | 24 | 22 | 24 | 26 | 0 | 24 | 836 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.18 | 0.00 | 1.09 | 38.00 | 1.09 |
time (sec) |
N/A | 0.190 | 3.155 | 0.494 | 0.568 | 0.084 | 0.000 | 0.193 | 0.242 | 40.418 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 96 | 94 | 0 | 0 | 80 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.83 | 0.82 | 0.00 | 0.00 | 0.70 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.504 | 0.220 | 0.000 | 0.000 | 0.087 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 83 | 47 | 151 | 146 | 74 | 129 | 0 | 54 | 109 |
N.S. |
1 | 0.86 | 0.49 | 1.57 | 1.52 | 0.77 | 1.34 | 0.00 | 0.56 | 1.14 |
time (sec) |
N/A | 0.631 | 0.611 | 1.211 | 0.165 | 0.080 | 1.664 | 0.000 | 0.153 | 40.905 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 63 | 40 | 133 | 99 | 64 | 107 | 0 | 40 | 88 |
N.S. |
1 | 0.85 | 0.54 | 1.80 | 1.34 | 0.86 | 1.45 | 0.00 | 0.54 | 1.19 |
time (sec) |
N/A | 0.503 | 0.502 | 1.227 | 0.192 | 0.080 | 1.018 | 0.000 | 0.140 | 40.194 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 44 | 30 | 117 | 60 | 55 | 70 | 0 | 24 | 63 |
N.S. |
1 | 0.98 | 0.67 | 2.60 | 1.33 | 1.22 | 1.56 | 0.00 | 0.53 | 1.40 |
time (sec) |
N/A | 0.384 | 0.303 | 1.268 | 0.136 | 0.079 | 0.605 | 0.000 | 0.140 | 40.261 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 105 | 31 | 43 | 49 | 0 | 14 | 49 |
N.S. |
1 | 1.00 | 1.00 | 4.20 | 1.24 | 1.72 | 1.96 | 0.00 | 0.56 | 1.96 |
time (sec) |
N/A | 0.244 | 0.113 | 1.786 | 0.115 | 0.078 | 0.394 | 0.000 | 0.146 | 41.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 36 | 36 | 106 | 42 | 57 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.65 | 0.65 | 1.93 | 0.76 | 1.04 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.475 | 0.227 | 1.251 | 0.178 | 0.074 | 0.000 | 0.000 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 51 | 51 | 102 | 229 | 70 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.66 | 0.66 | 1.32 | 2.97 | 0.91 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.562 | 0.487 | 1.289 | 0.166 | 0.092 | 0.000 | 0.000 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 70 | 69 | 123 | 256 | 90 | 0 | 0 | 43 | 0 |
N.S. |
1 | 0.60 | 0.59 | 1.06 | 2.21 | 0.78 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.706 | 0.410 | 1.261 | 0.170 | 0.091 | 0.000 | 0.000 | 0.143 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 130 | 138 | 0 | 0 | 98 | 0 | 0 | 18 | 0 |
N.S. |
1 | 0.85 | 0.90 | 0.00 | 0.00 | 0.64 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.511 | 0.639 | 0.000 | 0.000 | 0.079 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 57 | 38 | 135 | 32 | 67 | 85 | 0 | 31 | 71 |
N.S. |
1 | 0.98 | 0.66 | 2.33 | 0.55 | 1.16 | 1.47 | 0.00 | 0.53 | 1.22 |
time (sec) |
N/A | 0.485 | 0.111 | 0.997 | 0.137 | 0.083 | 1.665 | 0.000 | 0.234 | 41.582 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 119 | 105 | 240 | 73 | 134 | 0 | 0 | 18 | 0 |
N.S. |
1 | 0.77 | 0.68 | 1.55 | 0.47 | 0.86 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.506 | 0.567 | 1.002 | 0.147 | 0.098 | 0.000 | 0.000 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 31 | 119 | 16 | 51 | 63 | 0 | 16 | 53 |
N.S. |
1 | 1.00 | 1.00 | 3.84 | 0.52 | 1.65 | 2.03 | 0.00 | 0.52 | 1.71 |
time (sec) |
N/A | 0.346 | 0.171 | 1.509 | 0.131 | 0.075 | 0.625 | 0.000 | 0.240 | 39.459 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 94 | 80 | 157 | 51 | 120 | 0 | 0 | 14 | 0 |
N.S. |
1 | 0.80 | 0.68 | 1.34 | 0.44 | 1.03 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.340 | 0.173 | 0.953 | 0.138 | 0.082 | 0.000 | 0.000 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 50 | 47 | 128 | 47 | 67 | 0 | 0 | 18 | 0 |
N.S. |
1 | 0.68 | 0.64 | 1.75 | 0.64 | 0.92 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.378 | 0.190 | 0.970 | 0.212 | 0.080 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 112 | 105 | 232 | 76 | 134 | 0 | 0 | 18 | 0 |
N.S. |
1 | 0.83 | 0.78 | 1.72 | 0.56 | 0.99 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.484 | 0.477 | 0.990 | 0.218 | 0.087 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 64 | 67 | 119 | 52 | 86 | 0 | 0 | 18 | 0 |
N.S. |
1 | 0.65 | 0.68 | 1.21 | 0.53 | 0.88 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.646 | 0.352 | 0.991 | 0.208 | 0.079 | 0.000 | 0.000 | 0.150 | 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 | 157 | 134 | 142 | 0 | 0 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 0.85 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.581 | 0.796 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.153 | 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 | 143 | 120 | 129 | 0 | 0 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 0.84 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.504 | 0.438 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.178 | 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 | 143 | 120 | 129 | 0 | 0 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 0.84 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.487 | 0.425 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.150 | 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 | 143 | 120 | 129 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.84 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.441 | 0.362 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 112 | 119 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 0.83 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.321 | 0.176 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 50 | 47 | 131 | 144 | 70 | 0 | 0 | 18 | 0 |
N.S. |
1 | 0.68 | 0.64 | 1.79 | 1.97 | 0.96 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.420 | 0.252 | 2.189 | 0.282 | 0.090 | 0.000 | 0.000 | 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 | 139 | 116 | 110 | 0 | 0 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 0.83 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.438 | 0.343 | 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 | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 120 | 114 | 0 | 0 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 0.84 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.451 | 0.466 | 0.000 | 0.000 | 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 | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 126 | 142 | 0 | 0 | 112 | 0 | 0 | 18 | 0 |
N.S. |
1 | 0.75 | 0.84 | 0.00 | 0.00 | 0.66 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.539 | 0.787 | 0.000 | 0.000 | 0.093 | 0.000 | 0.000 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 121 | 79 | 208 | 286 | 111 | 0 | 0 | 87 | 0 |
N.S. |
1 | 0.73 | 0.48 | 1.26 | 1.73 | 0.67 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.527 | 0.502 | 1.489 | 0.164 | 0.087 | 0.000 | 0.000 | 0.242 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 101 | 69 | 190 | 219 | 95 | 0 | 0 | 70 | 0 |
N.S. |
1 | 0.73 | 0.50 | 1.37 | 1.58 | 0.68 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.464 | 0.441 | 1.497 | 0.153 | 0.082 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 66 | 55 | 174 | 162 | 82 | 0 | 0 | 41 | 0 |
N.S. |
1 | 0.84 | 0.70 | 2.20 | 2.05 | 1.04 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.350 | 0.292 | 1.430 | 0.137 | 0.084 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 48 | 47 | 158 | 116 | 60 | 0 | 0 | 26 | 0 |
N.S. |
1 | 0.87 | 0.85 | 2.87 | 2.11 | 1.09 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.249 | 0.144 | 1.951 | 0.123 | 0.082 | 0.000 | 0.000 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 56 | 50 | 119 | 52 | 63 | 0 | 0 | 18 | 0 |
N.S. |
1 | 0.57 | 0.51 | 1.20 | 0.53 | 0.64 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.422 | 0.197 | 1.467 | 0.165 | 0.096 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 60 | 65 | 112 | 265 | 80 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.70 | 0.76 | 1.30 | 3.08 | 0.93 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.584 | 0.252 | 1.608 | 0.193 | 0.086 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 101 | 85 | 137 | 296 | 104 | 0 | 0 | 527 | 0 |
N.S. |
1 | 0.85 | 0.71 | 1.15 | 2.49 | 0.87 | 0.00 | 0.00 | 4.43 | 0.00 |
time (sec) |
N/A | 0.570 | 0.402 | 1.497 | 0.237 | 0.095 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 209 | 158 | 189 | 0 | 0 | 130 | 0 | 0 | 65 | 0 |
N.S. |
1 | 0.76 | 0.90 | 0.00 | 0.00 | 0.62 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.530 | 1.298 | 0.000 | 0.000 | 0.088 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 81 | 67 | 200 | 47 | 96 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.89 | 0.74 | 2.20 | 0.52 | 1.05 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.435 | 0.489 | 1.308 | 0.134 | 0.088 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 118 | 113 | 309 | 99 | 149 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.61 | 0.58 | 1.58 | 0.51 | 0.76 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.423 | 0.441 | 1.319 | 0.137 | 0.094 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 61 | 55 | 182 | 28 | 72 | 0 | 0 | 32 | 0 |
N.S. |
1 | 0.94 | 0.85 | 2.80 | 0.43 | 1.11 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.387 | 0.200 | 1.793 | 0.202 | 0.086 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 97 | 93 | 224 | 76 | 119 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.66 | 0.63 | 1.51 | 0.51 | 0.80 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.295 | 0.123 | 1.268 | 0.140 | 0.091 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 64 | 60 | 145 | 55 | 73 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.56 | 0.52 | 1.26 | 0.48 | 0.63 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.378 | 0.188 | 1.318 | 0.214 | 0.082 | 0.000 | 0.000 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 111 | 107 | 301 | 90 | 133 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.84 | 0.81 | 2.28 | 0.68 | 1.01 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.576 | 0.316 | 1.286 | 0.209 | 0.092 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 84 | 79 | 134 | 64 | 100 | 0 | 0 | 39 | 0 |
N.S. |
1 | 0.52 | 0.49 | 0.83 | 0.40 | 0.62 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.447 | 0.280 | 1.286 | 0.299 | 0.098 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 166 | 194 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.76 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.591 | 1.245 | 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(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 137 | 161 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.73 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.523 | 0.802 | 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 | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 137 | 168 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.73 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.505 | 0.780 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.153 | 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 | 188 | 137 | 160 | 0 | 0 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 0.73 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.474 | 0.770 | 0.000 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 127 | 149 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.71 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.340 | 0.288 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.249 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 70 | 63 | 147 | 153 | 78 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.58 | 0.52 | 1.21 | 1.26 | 0.64 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.390 | 0.286 | 2.283 | 0.278 | 0.085 | 0.000 | 0.000 | 0.236 | 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 | 180 | 129 | 125 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.72 | 0.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.494 | 0.634 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 133 | 129 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.72 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.499 | 0.596 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 0.000 |