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 | C | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 230 | 183 | 34 | 221 | 767 | 109 | 241 | 239 | 599 |
N.S. |
1 | 1.28 | 1.02 | 0.19 | 1.23 | 4.26 | 0.61 | 1.34 | 1.33 | 3.33 |
time (sec) |
N/A | 0.739 | 0.088 | 0.105 | 0.111 | 0.080 | 0.331 | 0.116 | 0.185 | 17.225 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 230 | 184 | 35 | 221 | 767 | 110 | 241 | 239 | 603 |
N.S. |
1 | 1.27 | 1.02 | 0.19 | 1.22 | 4.24 | 0.61 | 1.33 | 1.32 | 3.33 |
time (sec) |
N/A | 0.668 | 0.054 | 0.101 | 0.116 | 0.087 | 0.341 | 0.129 | 0.187 | 17.353 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 95 | 36 | 109 | 755 | 110 | 230 | 101 | 579 |
N.S. |
1 | 1.00 | 1.12 | 0.42 | 1.28 | 8.88 | 1.29 | 2.71 | 1.19 | 6.81 |
time (sec) |
N/A | 0.341 | 0.033 | 0.102 | 0.110 | 0.085 | 0.339 | 0.116 | 0.199 | 17.405 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 95 | 37 | 109 | 755 | 110 | 228 | 101 | 579 |
N.S. |
1 | 1.00 | 1.12 | 0.44 | 1.28 | 8.88 | 1.29 | 2.68 | 1.19 | 6.81 |
time (sec) |
N/A | 0.341 | 0.026 | 0.100 | 0.107 | 0.086 | 0.340 | 0.113 | 0.192 | 0.260 |
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 | 40 | 40 | 33 | 35 | 39 | 33 | 41 | 52 | 31 | 29 |
N.S. |
1 | 1.00 | 0.82 | 0.88 | 0.98 | 0.82 | 1.02 | 1.30 | 0.78 | 0.72 |
time (sec) |
N/A | 0.291 | 0.018 | 0.103 | 0.103 | 0.064 | 0.052 | 0.108 | 0.188 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 51 | 44 | 40 | 39 | 42 | 49 | 40 | 33 | 21 |
N.S. |
1 | 1.89 | 1.63 | 1.48 | 1.44 | 1.56 | 1.81 | 1.48 | 1.22 | 0.78 |
time (sec) |
N/A | 0.320 | 0.016 | 0.095 | 0.103 | 0.062 | 0.046 | 0.113 | 0.184 | 17.165 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 32 | 13 | 25 | 29 | 32 | 29 | 23 | 12 |
N.S. |
1 | 1.00 | 2.00 | 0.81 | 1.56 | 1.81 | 2.00 | 1.81 | 1.44 | 0.75 |
time (sec) |
N/A | 0.241 | 0.018 | 0.093 | 0.105 | 0.064 | 0.041 | 0.131 | 0.180 | 0.108 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 13 | 12 | 12 | 15 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 0.75 | 0.94 | 0.75 | 0.75 | 0.75 |
time (sec) |
N/A | 0.233 | 0.007 | 0.092 | 0.104 | 0.059 | 0.044 | 0.110 | 0.185 | 17.122 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 60 | 204 | 100 | 148 | 138 | 0 | 67 | 57 |
N.S. |
1 | 1.00 | 0.80 | 2.72 | 1.33 | 1.97 | 1.84 | 0.00 | 0.89 | 0.76 |
time (sec) |
N/A | 0.341 | 0.025 | 0.200 | 0.112 | 0.095 | 0.175 | 0.000 | 0.192 | 17.667 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | A | A | B | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 106 | 91 | 204 | 70 | 151 | 131 | 0 | 54 | 43 |
N.S. |
1 | 2.08 | 1.78 | 4.00 | 1.37 | 2.96 | 2.57 | 0.00 | 1.06 | 0.84 |
time (sec) |
N/A | 0.402 | 0.026 | 0.209 | 0.107 | 0.092 | 0.180 | 0.000 | 0.178 | 17.672 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 60 | 83 | 302 | 137 | 87 | 92 | 69 | 57 |
N.S. |
1 | 1.00 | 0.80 | 1.11 | 4.03 | 1.83 | 1.16 | 1.23 | 0.92 | 0.76 |
time (sec) |
N/A | 0.335 | 0.040 | 0.129 | 0.111 | 0.069 | 0.093 | 0.116 | 0.185 | 17.144 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 90 | 75 | 75 | 302 | 140 | 80 | 100 | 50 | 41 |
N.S. |
1 | 2.09 | 1.74 | 1.74 | 7.02 | 3.26 | 1.86 | 2.33 | 1.16 | 0.95 |
time (sec) |
N/A | 0.393 | 0.025 | 0.119 | 0.109 | 0.066 | 0.094 | 0.129 | 0.185 | 0.095 |
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 | 13 | 13 | 25 | 18 | 17 | 17 | 22 | 19 | 17 | 9 |
N.S. |
1 | 1.00 | 1.92 | 1.38 | 1.31 | 1.31 | 1.69 | 1.46 | 1.31 | 0.69 |
time (sec) |
N/A | 0.240 | 0.010 | 0.112 | 0.113 | 0.069 | 0.068 | 0.108 | 0.182 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 225 | 80 | 224 | 0 | 162 | 272 | 0 | 164 | 0 |
N.S. |
1 | 1.04 | 0.37 | 1.04 | 0.00 | 0.75 | 1.26 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.801 | 10.054 | 1.111 | 0.000 | 0.077 | 2.553 | 0.000 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 192 | 78 | 200 | 0 | 135 | 177 | 0 | 122 | 0 |
N.S. |
1 | 1.03 | 0.42 | 1.08 | 0.00 | 0.73 | 0.95 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.678 | 10.047 | 1.092 | 0.000 | 0.077 | 1.687 | 0.000 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 159 | 77 | 182 | 0 | 109 | 85 | 0 | 84 | 0 |
N.S. |
1 | 1.01 | 0.49 | 1.15 | 0.00 | 0.69 | 0.54 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.575 | 7.917 | 1.076 | 0.000 | 0.071 | 1.000 | 0.000 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 123 | 77 | 154 | 0 | 91 | 82 | 0 | 52 | 0 |
N.S. |
1 | 1.00 | 0.63 | 1.25 | 0.00 | 0.74 | 0.67 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.490 | 10.046 | 0.698 | 0.000 | 0.071 | 0.853 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 158 | 100 | 199 | 0 | 120 | 82 | 0 | 72 | 0 |
N.S. |
1 | 1.01 | 0.64 | 1.28 | 0.00 | 0.77 | 0.53 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.577 | 10.066 | 0.723 | 0.000 | 0.074 | 2.977 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 199 | 125 | 245 | 0 | 192 | 82 | 0 | 96 | 0 |
N.S. |
1 | 1.06 | 0.66 | 1.30 | 0.00 | 1.02 | 0.44 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.689 | 10.130 | 0.725 | 0.000 | 0.081 | 9.889 | 0.000 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 135 | 45 | 34 | 0 | 96 | 231 | 0 | 128 | 0 |
N.S. |
1 | 1.08 | 0.36 | 0.27 | 0.00 | 0.77 | 1.85 | 0.00 | 1.02 | 0.00 |
time (sec) |
N/A | 0.578 | 8.741 | 1.273 | 0.000 | 0.078 | 2.124 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 104 | 45 | 34 | 0 | 85 | 153 | 0 | 100 | 0 |
N.S. |
1 | 1.05 | 0.45 | 0.34 | 0.00 | 0.86 | 1.55 | 0.00 | 1.01 | 0.00 |
time (sec) |
N/A | 0.455 | 7.324 | 1.232 | 0.000 | 0.078 | 1.460 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 44 | 33 | 0 | 72 | 75 | 0 | 72 | 0 |
N.S. |
1 | 1.00 | 0.60 | 0.45 | 0.00 | 0.99 | 1.03 | 0.00 | 0.99 | 0.00 |
time (sec) |
N/A | 0.389 | 5.608 | 1.217 | 0.000 | 0.077 | 0.846 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 49 | 34 | 0 | 56 | 68 | 0 | 46 | 0 |
N.S. |
1 | 1.00 | 1.26 | 0.87 | 0.00 | 1.44 | 1.74 | 0.00 | 1.18 | 0.00 |
time (sec) |
N/A | 0.315 | 10.025 | 0.763 | 0.000 | 0.074 | 0.721 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 63 | 34 | 0 | 80 | 68 | 0 | 54 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.50 | 0.00 | 1.18 | 1.00 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.378 | 10.040 | 1.422 | 0.000 | 0.075 | 2.249 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 101 | 70 | 34 | 0 | 122 | 68 | 0 | 66 | 0 |
N.S. |
1 | 1.05 | 0.73 | 0.35 | 0.00 | 1.27 | 0.71 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.452 | 10.124 | 1.418 | 0.000 | 0.074 | 3.133 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 226 | 45 | 36 | 0 | 125 | 236 | 0 | 166 | 0 |
N.S. |
1 | 1.88 | 0.38 | 0.30 | 0.00 | 1.04 | 1.97 | 0.00 | 1.38 | 0.00 |
time (sec) |
N/A | 0.707 | 9.284 | 1.682 | 0.000 | 0.074 | 2.506 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 160 | 45 | 36 | 0 | 110 | 155 | 0 | 128 | 0 |
N.S. |
1 | 1.72 | 0.48 | 0.39 | 0.00 | 1.18 | 1.67 | 0.00 | 1.38 | 0.00 |
time (sec) |
N/A | 0.558 | 7.528 | 1.646 | 0.000 | 0.084 | 1.663 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 101 | 45 | 36 | 0 | 93 | 73 | 0 | 90 | 0 |
N.S. |
1 | 1.53 | 0.68 | 0.55 | 0.00 | 1.41 | 1.11 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.429 | 6.616 | 1.589 | 0.000 | 0.076 | 0.968 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 45 | 36 | 0 | 71 | 70 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 2.81 | 2.25 | 0.00 | 4.44 | 4.38 | 0.00 | 1.56 | 0.00 |
time (sec) |
N/A | 0.253 | 10.031 | 0.951 | 0.000 | 0.068 | 0.810 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 68 | 64 | 36 | 0 | 81 | 70 | 0 | 39 | 0 |
N.S. |
1 | 1.10 | 1.03 | 0.58 | 0.00 | 1.31 | 1.13 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.364 | 10.045 | 1.023 | 0.000 | 0.071 | 2.070 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 127 | 73 | 36 | 0 | 165 | 70 | 0 | 56 | 0 |
N.S. |
1 | 1.38 | 0.79 | 0.39 | 0.00 | 1.79 | 0.76 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.502 | 10.086 | 0.951 | 0.000 | 0.072 | 5.281 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 193 | 81 | 36 | 0 | 246 | 70 | 0 | 71 | 0 |
N.S. |
1 | 1.62 | 0.68 | 0.30 | 0.00 | 2.07 | 0.59 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.626 | 10.095 | 0.932 | 0.000 | 0.076 | 12.944 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 226 | 45 | 36 | 0 | 126 | 236 | 0 | 166 | 0 |
N.S. |
1 | 1.88 | 0.38 | 0.30 | 0.00 | 1.05 | 1.97 | 0.00 | 1.38 | 0.00 |
time (sec) |
N/A | 0.706 | 9.230 | 1.862 | 0.000 | 0.078 | 2.466 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 160 | 45 | 36 | 0 | 109 | 155 | 0 | 128 | 0 |
N.S. |
1 | 1.72 | 0.48 | 0.39 | 0.00 | 1.17 | 1.67 | 0.00 | 1.38 | 0.00 |
time (sec) |
N/A | 0.566 | 7.751 | 1.882 | 0.000 | 0.074 | 1.662 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 101 | 45 | 36 | 0 | 94 | 73 | 0 | 90 | 0 |
N.S. |
1 | 1.53 | 0.68 | 0.55 | 0.00 | 1.42 | 1.11 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.429 | 6.128 | 1.824 | 0.000 | 0.066 | 0.961 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 45 | 36 | 0 | 69 | 70 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 1.29 | 1.03 | 0.00 | 1.97 | 2.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.310 | 10.031 | 1.184 | 0.000 | 0.064 | 0.832 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 48 | 64 | 36 | 0 | 77 | 70 | 0 | 40 | 0 |
N.S. |
1 | 1.02 | 1.36 | 0.77 | 0.00 | 1.64 | 1.49 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.302 | 10.039 | 1.174 | 0.000 | 0.075 | 2.339 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 134 | 73 | 36 | 0 | 166 | 70 | 0 | 53 | 0 |
N.S. |
1 | 1.44 | 0.78 | 0.39 | 0.00 | 1.78 | 0.75 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.504 | 10.073 | 1.158 | 0.000 | 0.072 | 3.996 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 186 | 81 | 36 | 0 | 239 | 70 | 0 | 72 | 0 |
N.S. |
1 | 1.55 | 0.68 | 0.30 | 0.00 | 1.99 | 0.58 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.605 | 10.074 | 1.171 | 0.000 | 0.079 | 14.560 | 0.000 | 0.243 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 259 | 90 | 36 | 0 | 326 | 70 | 0 | 85 | 0 |
N.S. |
1 | 1.76 | 0.61 | 0.24 | 0.00 | 2.22 | 0.48 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.782 | 10.137 | 1.230 | 0.000 | 0.076 | 35.459 | 0.000 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 319 | 327 | 80 | 238 | 0 | 160 | 262 | 0 | 154 | 0 |
N.S. |
1 | 1.03 | 0.25 | 0.75 | 0.00 | 0.50 | 0.82 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.758 | 10.051 | 1.084 | 0.000 | 0.072 | 2.456 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 290 | 295 | 78 | 214 | 0 | 134 | 170 | 0 | 114 | 0 |
N.S. |
1 | 1.02 | 0.27 | 0.74 | 0.00 | 0.46 | 0.59 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.661 | 10.043 | 1.073 | 0.000 | 0.070 | 1.624 | 0.000 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 263 | 77 | 196 | 0 | 107 | 82 | 0 | 78 | 0 |
N.S. |
1 | 1.01 | 0.30 | 0.75 | 0.00 | 0.41 | 0.31 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.560 | 7.947 | 1.048 | 0.000 | 0.072 | 0.918 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 228 | 77 | 169 | 0 | 89 | 78 | 0 | 48 | 0 |
N.S. |
1 | 1.00 | 0.34 | 0.74 | 0.00 | 0.39 | 0.34 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.475 | 10.044 | 0.683 | 0.000 | 0.069 | 0.817 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 262 | 262 | 99 | 212 | 0 | 119 | 78 | 0 | 70 | 0 |
N.S. |
1 | 1.00 | 0.38 | 0.81 | 0.00 | 0.45 | 0.30 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.568 | 10.064 | 0.735 | 0.000 | 0.073 | 2.375 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 302 | 122 | 256 | 0 | 195 | 78 | 0 | 92 | 0 |
N.S. |
1 | 1.03 | 0.42 | 0.88 | 0.00 | 0.67 | 0.27 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.667 | 10.117 | 0.717 | 0.000 | 0.081 | 9.673 | 0.000 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 223 | 45 | 34 | 0 | 94 | 221 | 0 | 112 | 0 |
N.S. |
1 | 1.06 | 0.21 | 0.16 | 0.00 | 0.45 | 1.05 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.624 | 8.638 | 1.090 | 0.000 | 0.073 | 1.920 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 194 | 45 | 34 | 0 | 82 | 146 | 0 | 88 | 0 |
N.S. |
1 | 1.04 | 0.24 | 0.18 | 0.00 | 0.44 | 0.78 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.530 | 7.554 | 0.991 | 0.000 | 0.072 | 1.321 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 165 | 44 | 33 | 0 | 70 | 71 | 0 | 64 | 0 |
N.S. |
1 | 1.01 | 0.27 | 0.20 | 0.00 | 0.43 | 0.44 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.463 | 5.609 | 1.016 | 0.000 | 0.077 | 0.784 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 134 | 49 | 34 | 0 | 54 | 65 | 0 | 40 | 0 |
N.S. |
1 | 1.02 | 0.37 | 0.26 | 0.00 | 0.41 | 0.49 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.382 | 10.024 | 0.629 | 0.000 | 0.076 | 0.659 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 159 | 61 | 34 | 0 | 76 | 65 | 0 | 50 | 0 |
N.S. |
1 | 1.01 | 0.39 | 0.22 | 0.00 | 0.48 | 0.41 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.432 | 10.037 | 1.198 | 0.000 | 0.072 | 1.678 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 191 | 68 | 34 | 0 | 120 | 65 | 0 | 60 | 0 |
N.S. |
1 | 1.04 | 0.37 | 0.18 | 0.00 | 0.65 | 0.35 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.527 | 10.079 | 1.143 | 0.000 | 0.169 | 2.827 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 238 | 249 | 47 | 38 | 0 | 127 | 226 | 0 | 158 | 0 |
N.S. |
1 | 1.05 | 0.20 | 0.16 | 0.00 | 0.53 | 0.95 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.650 | 8.785 | 1.359 | 0.000 | 0.075 | 2.315 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 218 | 47 | 38 | 0 | 111 | 148 | 0 | 122 | 0 |
N.S. |
1 | 1.03 | 0.22 | 0.18 | 0.00 | 0.52 | 0.70 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.569 | 7.488 | 1.317 | 0.000 | 0.077 | 1.540 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 186 | 47 | 38 | 0 | 95 | 70 | 0 | 86 | 0 |
N.S. |
1 | 1.00 | 0.25 | 0.20 | 0.00 | 0.51 | 0.38 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.478 | 5.917 | 1.332 | 0.000 | 0.068 | 0.899 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 47 | 38 | 0 | 73 | 66 | 0 | 55 | 0 |
N.S. |
1 | 1.00 | 0.53 | 0.43 | 0.00 | 0.82 | 0.74 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.302 | 10.026 | 0.855 | 0.000 | 0.068 | 0.775 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 183 | 65 | 38 | 0 | 108 | 66 | 0 | 71 | 0 |
N.S. |
1 | 0.98 | 0.35 | 0.20 | 0.00 | 0.58 | 0.35 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.481 | 10.044 | 0.898 | 0.000 | 0.069 | 2.340 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 218 | 74 | 38 | 0 | 162 | 66 | 0 | 87 | 0 |
N.S. |
1 | 1.03 | 0.35 | 0.18 | 0.00 | 0.76 | 0.31 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.574 | 10.080 | 0.875 | 0.000 | 0.070 | 8.513 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 238 | 249 | 83 | 38 | 0 | 210 | 66 | 0 | 103 | 0 |
N.S. |
1 | 1.05 | 0.35 | 0.16 | 0.00 | 0.88 | 0.28 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.625 | 10.091 | 0.855 | 0.000 | 0.074 | 31.680 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 218 | 47 | 38 | 0 | 111 | 148 | 0 | 122 | 0 |
N.S. |
1 | 1.03 | 0.22 | 0.18 | 0.00 | 0.52 | 0.70 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.553 | 7.322 | 1.118 | 0.000 | 0.067 | 1.567 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 187 | 47 | 38 | 0 | 95 | 70 | 0 | 86 | 0 |
N.S. |
1 | 1.01 | 0.25 | 0.20 | 0.00 | 0.51 | 0.38 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.480 | 5.793 | 1.123 | 0.000 | 0.073 | 0.927 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 152 | 47 | 38 | 0 | 73 | 66 | 0 | 54 | 0 |
N.S. |
1 | 1.00 | 0.31 | 0.25 | 0.00 | 0.48 | 0.43 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.399 | 10.028 | 0.683 | 0.000 | 0.065 | 0.778 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 119 | 65 | 38 | 0 | 105 | 66 | 0 | 70 | 0 |
N.S. |
1 | 1.00 | 0.55 | 0.32 | 0.00 | 0.88 | 0.55 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.360 | 10.033 | 0.710 | 0.000 | 0.071 | 2.349 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 216 | 74 | 38 | 0 | 162 | 66 | 0 | 86 | 0 |
N.S. |
1 | 1.02 | 0.35 | 0.18 | 0.00 | 0.77 | 0.31 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.566 | 10.072 | 0.671 | 0.000 | 0.071 | 8.547 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 237 | 248 | 83 | 38 | 0 | 210 | 66 | 0 | 102 | 0 |
N.S. |
1 | 1.05 | 0.35 | 0.16 | 0.00 | 0.89 | 0.28 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.643 | 10.080 | 0.661 | 0.000 | 0.070 | 31.862 | 0.000 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 0 | 74 | 88 | 0 | 106 | 206 | 0 | 158 | 0 |
N.S. |
1 | 0.00 | 0.43 | 0.51 | 0.00 | 0.62 | 1.20 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.000 | 9.188 | 2.000 | 0.000 | 0.077 | 2.467 | 0.000 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 0 | 74 | 88 | 0 | 91 | 134 | 0 | 122 | 0 |
N.S. |
1 | 0.00 | 0.51 | 0.61 | 0.00 | 0.63 | 0.92 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.000 | 7.674 | 1.734 | 0.000 | 0.066 | 1.703 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 0 | 74 | 88 | 0 | 74 | 63 | 0 | 86 | 0 |
N.S. |
1 | 0.00 | 0.62 | 0.74 | 0.00 | 0.62 | 0.53 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.000 | 5.954 | 1.992 | 0.000 | 0.067 | 0.955 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 74 | 88 | 0 | 56 | 61 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 1.72 | 2.05 | 0.00 | 1.30 | 1.42 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.300 | 10.031 | 0.980 | 0.000 | 0.067 | 0.803 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 0 | 90 | 88 | 0 | 83 | 60 | 0 | 38 | 0 |
N.S. |
1 | 0.00 | 0.78 | 0.76 | 0.00 | 0.72 | 0.52 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.000 | 10.041 | 1.001 | 0.000 | 0.072 | 1.924 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 0 | 98 | 88 | 0 | 169 | 61 | 0 | 53 | 0 |
N.S. |
1 | 0.00 | 0.68 | 0.61 | 0.00 | 1.17 | 0.42 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.000 | 10.069 | 1.035 | 0.000 | 0.076 | 5.074 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 0 | 106 | 88 | 0 | 249 | 60 | 0 | 70 | 0 |
N.S. |
1 | 0.00 | 0.62 | 0.52 | 0.00 | 1.46 | 0.35 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.000 | 10.088 | 0.999 | 0.000 | 0.075 | 13.222 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 0 | 74 | 88 | 0 | 90 | 134 | 0 | 122 | 0 |
N.S. |
1 | 0.00 | 0.51 | 0.61 | 0.00 | 0.62 | 0.92 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.000 | 7.653 | 2.023 | 0.000 | 0.068 | 1.680 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 0 | 74 | 88 | 0 | 75 | 63 | 0 | 86 | 0 |
N.S. |
1 | 0.00 | 0.62 | 0.74 | 0.00 | 0.63 | 0.53 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.000 | 6.334 | 2.205 | 0.000 | 0.068 | 0.972 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 63 | 74 | 88 | 0 | 53 | 60 | 0 | 24 | 0 |
N.S. |
1 | 0.71 | 0.83 | 0.99 | 0.00 | 0.60 | 0.67 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.358 | 10.106 | 1.266 | 0.000 | 0.067 | 0.819 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 0 | 90 | 88 | 0 | 81 | 60 | 0 | 39 | 0 |
N.S. |
1 | 0.00 | 1.23 | 1.21 | 0.00 | 1.11 | 0.82 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.000 | 10.037 | 1.299 | 0.000 | 0.069 | 1.677 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 0 | 98 | 88 | 0 | 169 | 60 | 0 | 54 | 0 |
N.S. |
1 | 0.00 | 0.68 | 0.61 | 0.00 | 1.17 | 0.41 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.000 | 10.056 | 1.264 | 0.000 | 0.075 | 3.819 | 0.000 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 0 | 106 | 88 | 0 | 247 | 60 | 0 | 71 | 0 |
N.S. |
1 | 0.00 | 0.62 | 0.51 | 0.00 | 1.44 | 0.35 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.000 | 10.068 | 1.282 | 0.000 | 0.081 | 11.938 | 0.000 | 0.242 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | B | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 0 | 114 | 88 | 0 | 329 | 60 | 0 | 86 | 0 |
N.S. |
1 | 0.00 | 0.58 | 0.45 | 0.00 | 1.67 | 0.30 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.000 | 10.109 | 1.328 | 0.000 | 0.077 | 35.263 | 0.000 | 0.255 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 244 | 254 | 76 | 90 | 0 | 138 | 236 | 0 | 161 | 0 |
N.S. |
1 | 1.04 | 0.31 | 0.37 | 0.00 | 0.57 | 0.97 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.683 | 8.889 | 2.427 | 0.000 | 0.068 | 2.556 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 222 | 76 | 90 | 0 | 122 | 155 | 0 | 125 | 0 |
N.S. |
1 | 1.02 | 0.35 | 0.41 | 0.00 | 0.56 | 0.71 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.573 | 7.568 | 2.154 | 0.000 | 0.062 | 1.685 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 189 | 76 | 90 | 0 | 106 | 73 | 0 | 89 | 0 |
N.S. |
1 | 0.99 | 0.40 | 0.47 | 0.00 | 0.56 | 0.38 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.489 | 6.190 | 2.431 | 0.000 | 0.063 | 0.994 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 76 | 90 | 0 | 87 | 70 | 0 | 58 | 0 |
N.S. |
1 | 1.00 | 0.84 | 1.00 | 0.00 | 0.97 | 0.78 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.305 | 10.042 | 1.374 | 0.000 | 0.064 | 0.829 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 187 | 91 | 90 | 0 | 115 | 70 | 0 | 73 | 0 |
N.S. |
1 | 0.98 | 0.48 | 0.47 | 0.00 | 0.61 | 0.37 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.487 | 10.049 | 1.365 | 0.000 | 0.063 | 2.888 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 222 | 99 | 90 | 0 | 168 | 70 | 0 | 90 | 0 |
N.S. |
1 | 1.02 | 0.46 | 0.41 | 0.00 | 0.77 | 0.32 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.574 | 10.054 | 1.339 | 0.000 | 0.070 | 9.015 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 244 | 254 | 107 | 90 | 0 | 215 | 70 | 0 | 105 | 0 |
N.S. |
1 | 1.04 | 0.44 | 0.37 | 0.00 | 0.88 | 0.29 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.656 | 10.086 | 1.328 | 0.000 | 0.070 | 33.281 | 0.000 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 222 | 76 | 90 | 0 | 121 | 156 | 0 | 125 | 0 |
N.S. |
1 | 1.02 | 0.35 | 0.41 | 0.00 | 0.56 | 0.72 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.585 | 7.571 | 1.849 | 0.000 | 0.061 | 1.722 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 190 | 76 | 90 | 0 | 105 | 73 | 0 | 89 | 0 |
N.S. |
1 | 1.00 | 0.40 | 0.47 | 0.00 | 0.55 | 0.38 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.489 | 6.112 | 2.072 | 0.000 | 0.064 | 0.982 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 156 | 76 | 90 | 0 | 84 | 71 | 0 | 57 | 0 |
N.S. |
1 | 1.00 | 0.49 | 0.58 | 0.00 | 0.54 | 0.46 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.416 | 10.034 | 1.028 | 0.000 | 0.063 | 0.847 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 123 | 91 | 90 | 0 | 111 | 70 | 0 | 72 | 0 |
N.S. |
1 | 1.01 | 0.75 | 0.74 | 0.00 | 0.91 | 0.57 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.378 | 10.028 | 1.064 | 0.000 | 0.067 | 2.946 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 220 | 99 | 90 | 0 | 167 | 71 | 0 | 89 | 0 |
N.S. |
1 | 1.02 | 0.46 | 0.42 | 0.00 | 0.77 | 0.33 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.576 | 10.041 | 1.056 | 0.000 | 0.065 | 9.043 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 243 | 253 | 107 | 90 | 0 | 216 | 70 | 0 | 104 | 0 |
N.S. |
1 | 1.04 | 0.44 | 0.37 | 0.00 | 0.89 | 0.29 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.657 | 10.048 | 1.038 | 0.000 | 0.073 | 33.346 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 285 | 115 | 90 | 0 | 263 | 71 | 0 | 121 | 0 |
N.S. |
1 | 1.06 | 0.43 | 0.33 | 0.00 | 0.97 | 0.26 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.731 | 10.070 | 1.076 | 0.000 | 0.068 | 89.756 | 0.000 | 0.236 | 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 | 106 | 106 | 106 | 96 | 94 | 94 | 110 | 98 | 101 | 95 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.89 | 0.89 | 1.04 | 0.92 | 0.95 | 0.90 |
time (sec) |
N/A | 0.436 | 0.016 | 0.103 | 0.026 | 0.057 | 0.026 | 0.137 | 0.179 | 0.049 |
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 | 79 | 79 | 79 | 72 | 71 | 71 | 78 | 73 | 77 | 71 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.90 | 0.90 | 0.99 | 0.92 | 0.97 | 0.90 |
time (sec) |
N/A | 0.393 | 0.012 | 0.100 | 0.026 | 0.055 | 0.023 | 0.107 | 0.173 | 0.033 |
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 | 56 | 56 | 56 | 49 | 48 | 48 | 56 | 50 | 53 | 49 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.86 | 0.86 | 1.00 | 0.89 | 0.95 | 0.88 |
time (sec) |
N/A | 0.340 | 0.009 | 0.100 | 0.026 | 0.060 | 0.020 | 0.111 | 0.179 | 0.025 |
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 | 32 | 32 | 32 | 27 | 26 | 26 | 29 | 26 | 29 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.81 | 0.81 | 0.91 | 0.81 | 0.91 | 0.81 |
time (sec) |
N/A | 0.291 | 0.002 | 0.059 | 0.027 | 0.060 | 0.017 | 0.108 | 0.180 | 0.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 55 | 47 | 0 | 131 | 104 | 50 | 70 | 45 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.00 | 2.38 | 1.89 | 0.91 | 1.27 | 0.82 |
time (sec) |
N/A | 0.333 | 0.026 | 0.115 | 0.000 | 0.071 | 0.150 | 0.130 | 0.181 | 17.015 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 85 | 78 | 70 | 0 | 222 | 138 | 72 | 139 | 68 |
N.S. |
1 | 1.15 | 1.05 | 0.95 | 0.00 | 3.00 | 1.86 | 0.97 | 1.88 | 0.92 |
time (sec) |
N/A | 0.364 | 0.038 | 0.116 | 0.000 | 0.073 | 0.231 | 0.103 | 0.181 | 17.013 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 106 | 92 | 92 | 0 | 306 | 219 | 86 | 221 | 97 |
N.S. |
1 | 1.14 | 0.99 | 0.99 | 0.00 | 3.29 | 2.35 | 0.92 | 2.38 | 1.04 |
time (sec) |
N/A | 0.395 | 0.045 | 0.113 | 0.000 | 0.081 | 0.357 | 0.104 | 0.179 | 17.019 |