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 | A | B | F(-1) | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 73 | 87 | 193 | 87 | 347 | 0 | 86 | 30 | 0 |
N.S. |
1 | 0.94 | 1.12 | 2.47 | 1.12 | 4.45 | 0.00 | 1.10 | 0.38 | 0.00 |
time (sec) |
N/A | 0.413 | 0.425 | 4.211 | 0.127 | 0.138 | 0.000 | 0.133 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F(-1) | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 112 | 109 | 312 | 123 | 467 | 0 | 121 | 32 | 0 |
N.S. |
1 | 0.99 | 0.96 | 2.76 | 1.09 | 4.13 | 0.00 | 1.07 | 0.28 | 0.00 |
time (sec) |
N/A | 0.471 | 2.583 | 19.529 | 0.111 | 0.212 | 0.000 | 0.140 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F(-1) | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 153 | 119 | 346 | 155 | 561 | 0 | 150 | 32 | 0 |
N.S. |
1 | 1.07 | 0.83 | 2.42 | 1.08 | 3.92 | 0.00 | 1.05 | 0.22 | 0.00 |
time (sec) |
N/A | 0.315 | 1.739 | 129.931 | 0.112 | 0.134 | 0.000 | 0.141 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 136 | 74 | 112 | 0 | 129 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.05 | 0.57 | 0.86 | 0.00 | 0.99 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.619 | 0.692 | 1012.292 | 0.000 | 0.114 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 101 | 64 | 104 | 0 | 114 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.01 | 0.64 | 1.04 | 0.00 | 1.14 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.483 | 0.481 | 151.632 | 0.000 | 0.130 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 52 | 90 | 0 | 101 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 0.74 | 1.29 | 0.00 | 1.44 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.348 | 0.417 | 14.858 | 0.000 | 0.121 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 51 | 90 | 0 | 101 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.73 | 1.29 | 0.00 | 1.44 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.326 | 0.114 | 2.608 | 0.000 | 0.085 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 96 | 67 | 104 | 0 | 131 | 0 | 0 | 32 | 0 |
N.S. |
1 | 0.98 | 0.68 | 1.06 | 0.00 | 1.34 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.473 | 0.580 | 8.360 | 0.000 | 0.123 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 129 | 79 | 124 | 0 | 193 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.05 | 0.64 | 1.01 | 0.00 | 1.57 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.612 | 0.790 | 53.494 | 0.000 | 0.106 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 80 | 52 | 54 | 63 | 61 | 0 | 108 | 32 | 0 |
N.S. |
1 | 0.92 | 0.60 | 0.62 | 0.72 | 0.70 | 0.00 | 1.24 | 0.37 | 0.00 |
time (sec) |
N/A | 0.248 | 0.636 | 3.459 | 0.032 | 0.092 | 0.000 | 0.149 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 60 | 42 | 44 | 50 | 51 | 0 | 85 | 32 | 0 |
N.S. |
1 | 0.92 | 0.65 | 0.68 | 0.77 | 0.78 | 0.00 | 1.31 | 0.49 | 0.00 |
time (sec) |
N/A | 0.242 | 0.438 | 1.835 | 0.034 | 0.089 | 0.000 | 0.143 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 42 | 32 | 34 | 37 | 41 | 0 | 62 | 32 | 0 |
N.S. |
1 | 0.98 | 0.74 | 0.79 | 0.86 | 0.95 | 0.00 | 1.44 | 0.74 | 0.00 |
time (sec) |
N/A | 0.235 | 0.392 | 1.669 | 0.035 | 0.113 | 0.000 | 0.134 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 17 | 23 | 28 | 0 | 33 | 30 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 1.15 | 1.40 | 0.00 | 1.65 | 1.50 | 1.40 |
time (sec) |
N/A | 0.192 | 0.173 | 0.636 | 0.029 | 0.114 | 0.000 | 0.133 | 0.166 | 25.770 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 51 | 73 | 142 | 73 | 273 | 0 | 56 | 30 | 0 |
N.S. |
1 | 0.86 | 1.24 | 2.41 | 1.24 | 4.63 | 0.00 | 0.95 | 0.51 | 0.00 |
time (sec) |
N/A | 0.230 | 0.303 | 1.654 | 0.111 | 0.117 | 0.000 | 0.132 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 90 | 93 | 281 | 105 | 381 | 0 | 104 | 32 | 0 |
N.S. |
1 | 0.97 | 1.00 | 3.02 | 1.13 | 4.10 | 0.00 | 1.12 | 0.34 | 0.00 |
time (sec) |
N/A | 0.264 | 1.020 | 1.779 | 0.115 | 0.133 | 0.000 | 0.142 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 131 | 107 | 217 | 138 | 469 | 0 | 135 | 32 | 0 |
N.S. |
1 | 1.07 | 0.87 | 1.76 | 1.12 | 3.81 | 0.00 | 1.10 | 0.26 | 0.00 |
time (sec) |
N/A | 0.475 | 1.052 | 1.865 | 0.115 | 0.162 | 0.000 | 0.145 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 133 | 73 | 232 | 0 | 117 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.08 | 0.59 | 1.89 | 0.00 | 0.95 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 1.074 | 0.819 | 10.229 | 0.000 | 0.092 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 100 | 63 | 212 | 0 | 107 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.05 | 0.66 | 2.23 | 0.00 | 1.13 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.770 | 0.658 | 5.095 | 0.000 | 0.087 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 60 | 192 | 0 | 94 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 0.90 | 2.87 | 0.00 | 1.40 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.566 | 0.390 | 3.664 | 0.000 | 0.084 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 38 | 175 | 0 | 66 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 1.00 | 4.61 | 0.00 | 1.74 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.390 | 0.067 | 2.298 | 0.000 | 0.089 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 48 | 152 | 0 | 109 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 0.76 | 2.41 | 0.00 | 1.73 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.560 | 0.466 | 2.094 | 0.000 | 0.109 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 96 | 74 | 170 | 0 | 158 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.01 | 0.78 | 1.79 | 0.00 | 1.66 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.779 | 0.472 | 2.553 | 0.000 | 0.095 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 129 | 86 | 186 | 0 | 199 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.05 | 0.70 | 1.51 | 0.00 | 1.62 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 1.024 | 0.521 | 3.581 | 0.000 | 0.108 | 0.000 | 0.000 | 0.249 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 80 | 52 | 59 | 63 | 61 | 0 | 110 | 32 | 0 |
N.S. |
1 | 0.92 | 0.60 | 0.68 | 0.72 | 0.70 | 0.00 | 1.26 | 0.37 | 0.00 |
time (sec) |
N/A | 0.411 | 0.924 | 2.701 | 0.034 | 0.095 | 0.000 | 0.149 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 60 | 42 | 49 | 50 | 51 | 0 | 87 | 32 | 0 |
N.S. |
1 | 0.92 | 0.65 | 0.75 | 0.77 | 0.78 | 0.00 | 1.34 | 0.49 | 0.00 |
time (sec) |
N/A | 0.408 | 0.551 | 1.947 | 0.031 | 0.099 | 0.000 | 0.150 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 42 | 32 | 39 | 37 | 41 | 0 | 64 | 32 | 0 |
N.S. |
1 | 0.98 | 0.74 | 0.91 | 0.86 | 0.95 | 0.00 | 1.49 | 0.74 | 0.00 |
time (sec) |
N/A | 0.395 | 0.459 | 1.658 | 0.034 | 0.099 | 0.000 | 0.139 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 17 | 23 | 28 | 0 | 35 | 30 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 1.15 | 1.40 | 0.00 | 1.75 | 1.50 | 1.40 |
time (sec) |
N/A | 0.327 | 0.178 | 0.721 | 0.030 | 0.077 | 0.000 | 0.132 | 0.182 | 25.523 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | B | F | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 74 | 36 | 197 | 89 | 314 | 0 | 73 | 30 | 0 |
N.S. |
1 | 0.95 | 0.46 | 2.53 | 1.14 | 4.03 | 0.00 | 0.94 | 0.38 | 0.00 |
time (sec) |
N/A | 0.417 | 0.531 | 1.556 | 0.116 | 0.216 | 0.000 | 0.138 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 96 | 98 | 277 | 106 | 384 | 0 | 93 | 32 | 0 |
N.S. |
1 | 1.03 | 1.05 | 2.98 | 1.14 | 4.13 | 0.00 | 1.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.461 | 0.877 | 1.668 | 0.112 | 0.132 | 0.000 | 0.141 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 137 | 109 | 214 | 137 | 473 | 0 | 128 | 32 | 0 |
N.S. |
1 | 1.11 | 0.89 | 1.74 | 1.11 | 3.85 | 0.00 | 1.04 | 0.26 | 0.00 |
time (sec) |
N/A | 0.492 | 0.961 | 1.685 | 0.110 | 0.157 | 0.000 | 0.139 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 136 | 81 | 114 | 0 | 109 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.08 | 0.64 | 0.90 | 0.00 | 0.87 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 1.158 | 0.503 | 6.392 | 0.000 | 0.104 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 103 | 71 | 104 | 0 | 99 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.05 | 0.72 | 1.06 | 0.00 | 1.01 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.755 | 0.351 | 4.350 | 0.000 | 0.096 | 0.000 | 0.000 | 0.266 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 59 | 92 | 0 | 87 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.82 | 1.28 | 0.00 | 1.21 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.551 | 0.094 | 2.201 | 0.000 | 0.096 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 58 | 92 | 0 | 101 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.35 | 0.00 | 1.49 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.586 | 0.440 | 2.354 | 0.000 | 0.095 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 100 | 62 | 106 | 0 | 148 | 0 | 0 | 32 | 0 |
N.S. |
1 | 0.98 | 0.61 | 1.04 | 0.00 | 1.45 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.798 | 0.552 | 2.205 | 0.000 | 0.108 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 133 | 74 | 116 | 0 | 197 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.01 | 0.56 | 0.88 | 0.00 | 1.49 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 1.023 | 0.863 | 2.894 | 0.000 | 0.110 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 80 | 62 | 59 | 63 | 61 | 0 | 110 | 32 | 0 |
N.S. |
1 | 0.92 | 0.71 | 0.68 | 0.72 | 0.70 | 0.00 | 1.26 | 0.37 | 0.00 |
time (sec) |
N/A | 0.422 | 0.940 | 3.157 | 0.035 | 0.124 | 0.000 | 0.153 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 60 | 52 | 49 | 50 | 51 | 0 | 87 | 32 | 0 |
N.S. |
1 | 0.92 | 0.80 | 0.75 | 0.77 | 0.78 | 0.00 | 1.34 | 0.49 | 0.00 |
time (sec) |
N/A | 0.406 | 0.562 | 1.893 | 0.035 | 0.098 | 0.000 | 0.145 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 42 | 42 | 39 | 37 | 41 | 0 | 64 | 32 | 0 |
N.S. |
1 | 0.98 | 0.98 | 0.91 | 0.86 | 0.95 | 0.00 | 1.49 | 0.74 | 0.00 |
time (sec) |
N/A | 0.396 | 0.518 | 1.655 | 0.036 | 0.091 | 0.000 | 0.139 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 17 | 23 | 28 | 0 | 35 | 30 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 1.15 | 1.40 | 0.00 | 1.75 | 1.50 | 1.40 |
time (sec) |
N/A | 0.331 | 0.215 | 0.444 | 0.028 | 0.078 | 0.000 | 0.132 | 0.204 | 26.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 76 | 90 | 186 | 90 | 319 | 0 | 81 | 30 | 0 |
N.S. |
1 | 0.94 | 1.11 | 2.30 | 1.11 | 3.94 | 0.00 | 1.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.415 | 0.470 | 2.022 | 0.120 | 0.230 | 0.000 | 0.135 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 96 | 98 | 286 | 106 | 389 | 0 | 101 | 32 | 0 |
N.S. |
1 | 1.03 | 1.05 | 3.08 | 1.14 | 4.18 | 0.00 | 1.09 | 0.34 | 0.00 |
time (sec) |
N/A | 0.453 | 1.101 | 2.049 | 0.114 | 0.149 | 0.000 | 0.141 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 137 | 110 | 220 | 136 | 477 | 0 | 131 | 32 | 0 |
N.S. |
1 | 1.11 | 0.89 | 1.79 | 1.11 | 3.88 | 0.00 | 1.07 | 0.26 | 0.00 |
time (sec) |
N/A | 0.491 | 2.090 | 2.046 | 0.114 | 0.136 | 0.000 | 0.148 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 136 | 83 | 235 | 0 | 117 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.08 | 0.66 | 1.87 | 0.00 | 0.93 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 1.123 | 0.927 | 8.742 | 0.000 | 0.104 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 103 | 66 | 215 | 0 | 107 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.05 | 0.67 | 2.19 | 0.00 | 1.09 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.754 | 0.715 | 6.791 | 0.000 | 0.129 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 60 | 191 | 0 | 95 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.83 | 2.65 | 0.00 | 1.32 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.552 | 0.123 | 3.998 | 0.000 | 0.086 | 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 | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 51 | 165 | 0 | 109 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 0.75 | 2.43 | 0.00 | 1.60 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.594 | 0.503 | 2.937 | 0.000 | 0.085 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 101 | 79 | 173 | 0 | 162 | 0 | 0 | 32 | 0 |
N.S. |
1 | 0.99 | 0.77 | 1.70 | 0.00 | 1.59 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.793 | 0.587 | 2.612 | 0.000 | 0.086 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 134 | 87 | 189 | 0 | 203 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.02 | 0.66 | 1.43 | 0.00 | 1.54 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 1.029 | 0.854 | 3.017 | 0.000 | 0.093 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 350 | 388 | 169 | 458 | 0 | 538 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.11 | 0.48 | 1.31 | 0.00 | 1.54 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 1.441 | 3.293 | 51.645 | 0.000 | 0.172 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 315 | 347 | 157 | 438 | 0 | 522 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.10 | 0.50 | 1.39 | 0.00 | 1.66 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.712 | 2.163 | 13.231 | 0.000 | 0.136 | 0.000 | 0.000 | 0.184 | 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 | 275 | 309 | 122 | 362 | 0 | 465 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.12 | 0.44 | 1.32 | 0.00 | 1.69 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.556 | 1.524 | 3.515 | 0.000 | 0.159 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 37 | 35 | 0 | 44 | 0 | 0 | 33 | 36 |
N.S. |
1 | 1.00 | 1.12 | 1.06 | 0.00 | 1.33 | 0.00 | 0.00 | 1.00 | 1.09 |
time (sec) |
N/A | 0.218 | 0.644 | 0.431 | 0.000 | 0.086 | 0.000 | 0.000 | 0.193 | 26.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 52 | 53 | 0 | 73 | 0 | 0 | 33 | 83 |
N.S. |
1 | 1.00 | 0.73 | 0.75 | 0.00 | 1.03 | 0.00 | 0.00 | 0.46 | 1.17 |
time (sec) |
N/A | 0.331 | 0.883 | 0.487 | 0.000 | 0.087 | 0.000 | 0.000 | 0.169 | 27.197 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 114 | 65 | 65 | 0 | 96 | 0 | 0 | 33 | 169 |
N.S. |
1 | 1.08 | 0.61 | 0.61 | 0.00 | 0.91 | 0.00 | 0.00 | 0.31 | 1.59 |
time (sec) |
N/A | 0.471 | 1.163 | 0.547 | 0.000 | 0.120 | 0.000 | 0.000 | 0.177 | 32.714 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 132 | 90 | 990 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.03 | 0.70 | 7.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.680 | 17.784 | 4.835 | 0.000 | 0.000 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 66 | 133 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 0.73 | 1.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.493 | 11.575 | 0.685 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 66 | 112 | 0 | 59 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 1.25 | 2.11 | 0.00 | 1.11 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.359 | 0.926 | 0.372 | 0.000 | 0.093 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 95 | 75 | 126 | 0 | 125 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 0.79 | 1.33 | 0.00 | 1.32 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.499 | 1.101 | 0.503 | 0.000 | 0.102 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 138 | 111 | 146 | 0 | 173 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.06 | 0.85 | 1.12 | 0.00 | 1.33 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 1.098 | 2.071 | 0.609 | 0.000 | 0.100 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 120 | 86 | 234 | 0 | 0 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.04 | 0.75 | 2.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 1.016 | 11.080 | 0.557 | 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 | C | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 74 | 224 | 0 | 0 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.00 | 0.87 | 2.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.769 | 0.645 | 0.370 | 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 | C | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 60 | 214 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 1.18 | 4.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.566 | 1.819 | 0.347 | 0.000 | 0.000 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 63 | 361 | 0 | 171 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.00 | 0.78 | 4.46 | 0.00 | 2.11 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.771 | 0.579 | 0.238 | 0.000 | 0.103 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 116 | 82 | 248 | 0 | 239 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.01 | 0.71 | 2.16 | 0.00 | 2.08 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.976 | 0.847 | 0.319 | 0.000 | 0.126 | 0.000 | 0.000 | 0.177 | 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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 276 | 287 | 145 | 451 | 0 | 417 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.04 | 0.53 | 1.63 | 0.00 | 1.51 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 1.019 | 2.110 | 0.436 | 0.000 | 0.136 | 0.000 | 0.000 | 0.176 | 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 | 238 | 254 | 113 | 347 | 0 | 386 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.07 | 0.47 | 1.46 | 0.00 | 1.62 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.797 | 1.336 | 2.235 | 0.000 | 0.133 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 30 | 0 | 48 | 0 | 0 | 39 | 57 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.00 | 1.60 | 0.00 | 0.00 | 1.30 | 1.90 |
time (sec) |
N/A | 0.328 | 0.413 | 0.240 | 0.000 | 0.098 | 0.000 | 0.000 | 0.202 | 26.152 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 42 | 43 | 0 | 72 | 0 | 0 | 39 | 103 |
N.S. |
1 | 1.00 | 0.69 | 0.70 | 0.00 | 1.18 | 0.00 | 0.00 | 0.64 | 1.69 |
time (sec) |
N/A | 0.489 | 0.491 | 0.248 | 0.000 | 0.108 | 0.000 | 0.000 | 0.175 | 27.942 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 96 | 52 | 53 | 0 | 95 | 0 | 0 | 39 | 163 |
N.S. |
1 | 1.05 | 0.57 | 0.58 | 0.00 | 1.04 | 0.00 | 0.00 | 0.43 | 1.79 |
time (sec) |
N/A | 0.672 | 0.776 | 0.346 | 0.000 | 0.144 | 0.000 | 0.000 | 0.183 | 33.282 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 131 | 62 | 63 | 0 | 116 | 0 | 0 | 39 | 192 |
N.S. |
1 | 1.08 | 0.51 | 0.52 | 0.00 | 0.96 | 0.00 | 0.00 | 0.32 | 1.59 |
time (sec) |
N/A | 0.885 | 1.154 | 0.448 | 0.000 | 0.188 | 0.000 | 0.000 | 0.173 | 32.687 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 391 | 433 | 176 | 449 | 0 | 559 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.11 | 0.45 | 1.15 | 0.00 | 1.43 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 1.786 | 2.913 | 1.222 | 0.000 | 0.196 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 354 | 392 | 165 | 454 | 0 | 546 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.11 | 0.47 | 1.28 | 0.00 | 1.54 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 1.498 | 2.312 | 4.665 | 0.000 | 0.138 | 0.000 | 0.000 | 0.209 | 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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 319 | 351 | 151 | 430 | 0 | 509 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.10 | 0.47 | 1.35 | 0.00 | 1.60 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 1.196 | 1.697 | 3.434 | 0.000 | 0.149 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 309 | 349 | 144 | 457 | 0 | 545 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.13 | 0.47 | 1.48 | 0.00 | 1.76 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 1.223 | 2.046 | 3.209 | 0.000 | 0.146 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 45 | 40 | 0 | 68 | 0 | 0 | 44 | 84 |
N.S. |
1 | 1.00 | 1.29 | 1.14 | 0.00 | 1.94 | 0.00 | 0.00 | 1.26 | 2.40 |
time (sec) |
N/A | 0.360 | 0.882 | 0.653 | 0.000 | 0.096 | 0.000 | 0.000 | 0.180 | 27.255 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 177 | 103 | 157 | 0 | 0 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.03 | 0.60 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 1.444 | 1.636 | 2.643 | 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 | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 136 | 87 | 996 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.01 | 0.64 | 7.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 1.120 | 0.830 | 2.407 | 0.000 | 0.000 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 84 | 126 | 0 | 0 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.00 | 0.89 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.851 | 1.185 | 1.768 | 0.000 | 0.000 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 78 | 129 | 0 | 131 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.00 | 0.78 | 1.29 | 0.00 | 1.31 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.875 | 1.121 | 0.827 | 0.000 | 0.121 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 143 | 119 | 144 | 0 | 178 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.04 | 0.87 | 1.05 | 0.00 | 1.30 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 1.139 | 1.926 | 0.962 | 0.000 | 0.133 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 186 | 131 | 154 | 0 | 230 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.07 | 0.75 | 0.89 | 0.00 | 1.32 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 1.448 | 2.468 | 1.154 | 0.000 | 0.126 | 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(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 96 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.557 | 9.174 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.209 | 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 | 75 | 75 | 96 | 0 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.570 | 8.860 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.247 | 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 | 77 | 77 | 106 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 1.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.554 | 8.589 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.285 | 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 | 77 | 77 | 89 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.531 | 28.755 | 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 | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 116 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 1.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.587 | 11.697 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 285 | 0 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 3.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.541 | 2.021 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 287 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 3.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.522 | 0.561 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 287 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 3.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.570 | 0.582 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 289 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 3.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.533 | 0.676 | 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 | A | A | A | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 75 | 80 | 87 | 85 | 85 | 0 | 0 | 23 | 134 |
N.S. |
1 | 0.94 | 1.00 | 1.09 | 1.06 | 1.06 | 0.00 | 0.00 | 0.29 | 1.68 |
time (sec) |
N/A | 0.441 | 0.737 | 2.425 | 0.040 | 0.117 | 0.000 | 0.000 | 0.181 | 26.949 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 51 | 47 | 52 | 59 | 53 | 0 | 0 | 23 | 67 |
N.S. |
1 | 0.98 | 0.90 | 1.00 | 1.13 | 1.02 | 0.00 | 0.00 | 0.44 | 1.29 |
time (sec) |
N/A | 0.402 | 0.424 | 0.983 | 0.041 | 0.087 | 0.000 | 0.000 | 0.164 | 26.300 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 22 | 26 | 28 | 28 | 0 | 0 | 21 | 27 |
N.S. |
1 | 1.00 | 0.88 | 1.04 | 1.12 | 1.12 | 0.00 | 0.00 | 0.84 | 1.08 |
time (sec) |
N/A | 0.331 | 0.103 | 0.818 | 0.034 | 0.120 | 0.000 | 0.000 | 0.179 | 0.204 |
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 | 49 | 50 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.351 | 0.350 | 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 | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 201 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 4.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.369 | 3.457 | 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(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 63 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.514 | 0.765 | 0.000 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 63 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.514 | 0.489 | 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 | 73 | 73 | 63 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.512 | 0.409 | 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 | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 61 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.471 | 0.054 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |