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 | F | A | A | F(-1) | A | F(-1) | F(-1) | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 27 | 24 | 0 | 179 | 0 | 0 | 130 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.89 | 0.00 | 6.63 | 0.00 | 0.00 | 4.81 | 0.00 |
time (sec) |
N/A | 0.000 | 0.073 | 1.687 | 0.000 | 0.131 | 0.000 | 0.000 | 200.030 | 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 | 23 | 44 | 20 | 22 | 19 | 19 | 20 | 19 | 26 | 21 |
N.S. |
1 | 1.91 | 0.87 | 0.96 | 0.83 | 0.83 | 0.87 | 0.83 | 1.13 | 0.91 |
time (sec) |
N/A | 0.226 | 0.457 | 0.137 | 0.091 | 0.098 | 0.111 | 0.118 | 0.239 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 27 | 27 | 25 | 35 | 24 | 0 | 32 | 0 | 23 |
N.S. |
1 | 0.96 | 0.96 | 0.89 | 1.25 | 0.86 | 0.00 | 1.14 | 0.00 | 0.82 |
time (sec) |
N/A | 0.457 | 0.098 | 14.932 | 0.135 | 0.095 | 0.000 | 0.848 | 0.400 | 3.861 |
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 | 29 | 45 | 33 | 27 | 39 | 44 | 22 | 40 | 50 | 42 |
N.S. |
1 | 1.55 | 1.14 | 0.93 | 1.34 | 1.52 | 0.76 | 1.38 | 1.72 | 1.45 |
time (sec) |
N/A | 0.492 | 0.164 | 1.352 | 0.141 | 0.083 | 0.072 | 0.171 | 0.201 | 2.812 |
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 | 25 | 15 | 13 | 11 | 10 | 10 | 10 | 10 | 11 | 10 |
N.S. |
1 | 0.60 | 0.52 | 0.44 | 0.40 | 0.40 | 0.40 | 0.40 | 0.44 | 0.40 |
time (sec) |
N/A | 0.143 | 0.004 | 0.072 | 0.032 | 0.092 | 0.038 | 0.111 | 0.204 | 0.029 |
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 | 19 | 25 | 18 | 19 | 167 | 15 | 15 | 15 | 70 | 16 |
N.S. |
1 | 1.32 | 0.95 | 1.00 | 8.79 | 0.79 | 0.79 | 0.79 | 3.68 | 0.84 |
time (sec) |
N/A | 0.572 | 0.046 | 0.715 | 0.166 | 0.086 | 0.140 | 0.127 | 0.195 | 2.823 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | F(-1) | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 277 | 22 | 115 | 91 | 251 | 0 | 0 | 139 | 115 |
N.S. |
1 | 12.59 | 1.00 | 5.23 | 4.14 | 11.41 | 0.00 | 0.00 | 6.32 | 5.23 |
time (sec) |
N/A | 2.536 | 0.686 | 0.434 | 0.152 | 0.154 | 0.000 | 0.000 | 0.390 | 3.399 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | F | A | A | A | F(-1) | A | B | B |
verified | N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 1969 | 0 | 32 | 30 | 32 | 0 | 32 | 99 | 28 |
N.S. |
1 | 61.53 | 0.00 | 1.00 | 0.94 | 1.00 | 0.00 | 1.00 | 3.09 | 0.88 |
time (sec) |
N/A | 18.849 | 0.000 | 1.047 | 0.496 | 0.100 | 0.000 | 0.308 | 0.405 | 3.238 |
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 | 17 | 16 | 16 | 15 | 17 | 16 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.00 | 0.94 | 1.06 | 1.00 | 1.00 |
time (sec) |
N/A | 0.213 | 0.006 | 0.054 | 0.026 | 0.085 | 0.046 | 0.110 | 0.191 | 0.096 |
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 | 13 | 9 | 9 | 10 | 9 | 9 | 8 | 10 | 9 | 9 |
N.S. |
1 | 0.69 | 0.69 | 0.77 | 0.69 | 0.69 | 0.62 | 0.77 | 0.69 | 0.69 |
time (sec) |
N/A | 0.143 | 0.002 | 0.215 | 0.025 | 0.082 | 0.036 | 0.106 | 0.196 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 27 | 25 | 19 | 30 | 23 | 19 | 23 | 26 | 18 |
N.S. |
1 | 1.04 | 0.96 | 0.73 | 1.15 | 0.88 | 0.73 | 0.88 | 1.00 | 0.69 |
time (sec) |
N/A | 0.232 | 0.047 | 0.792 | 0.056 | 0.102 | 0.262 | 0.112 | 0.203 | 2.647 |
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 | 18 | 16 | 16 | 13 | 14 | 16 | 12 | 14 | 16 | 12 |
N.S. |
1 | 0.89 | 0.89 | 0.72 | 0.78 | 0.89 | 0.67 | 0.78 | 0.89 | 0.67 |
time (sec) |
N/A | 0.154 | 0.002 | 0.095 | 0.025 | 0.093 | 0.040 | 0.105 | 0.205 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 24 | 26 | 43 | 30 | 22 | 25 | 25 | 25 |
N.S. |
1 | 0.00 | 1.00 | 1.08 | 1.79 | 1.25 | 0.92 | 1.04 | 1.04 | 1.04 |
time (sec) |
N/A | 0.000 | 0.110 | 12.033 | 0.165 | 0.089 | 7.999 | 0.135 | 0.209 | 2.749 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 21 | 20 | 20 | 20 | 17 | 20 | 21 | 19 |
N.S. |
1 | 0.00 | 0.95 | 0.91 | 0.91 | 0.91 | 0.77 | 0.91 | 0.95 | 0.86 |
time (sec) |
N/A | 0.000 | 0.098 | 0.994 | 0.066 | 0.093 | 0.060 | 0.108 | 0.215 | 3.000 |
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 | 12 | 16 | 12 | 18 | 17 | 17 | 17 | 17 | 71 | 17 |
N.S. |
1 | 1.33 | 1.00 | 1.50 | 1.42 | 1.42 | 1.42 | 1.42 | 5.92 | 1.42 |
time (sec) |
N/A | 0.166 | 0.010 | 0.127 | 0.024 | 0.089 | 0.090 | 36.476 | 0.213 | 0.040 |
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 | 23 | 30 | 20 | 18 | 123 | 17 | 15 | 23 | 58 | 24 |
N.S. |
1 | 1.30 | 0.87 | 0.78 | 5.35 | 0.74 | 0.65 | 1.00 | 2.52 | 1.04 |
time (sec) |
N/A | 0.608 | 0.137 | 0.484 | 0.121 | 0.088 | 0.097 | 0.120 | 0.221 | 2.745 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 26 | 36 | 43 | 43 | 27 | 62 | 64 | 39 |
N.S. |
1 | 0.00 | 1.00 | 1.38 | 1.65 | 1.65 | 1.04 | 2.38 | 2.46 | 1.50 |
time (sec) |
N/A | 0.000 | 0.538 | 0.932 | 0.079 | 0.087 | 0.125 | 0.219 | 0.205 | 2.575 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 39 | 39 | 38 | 38 | 36 | 39 | 941 | 0 |
N.S. |
1 | 0.00 | 1.56 | 1.56 | 1.52 | 1.52 | 1.44 | 1.56 | 37.64 | 0.00 |
time (sec) |
N/A | 0.000 | 0.417 | 0.932 | 0.065 | 0.094 | 0.114 | 0.171 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 45 | 45 | 44 | 44 | 42 | 44 | 47 | 47 |
N.S. |
1 | 0.00 | 1.45 | 1.45 | 1.42 | 1.42 | 1.35 | 1.42 | 1.52 | 1.52 |
time (sec) |
N/A | 0.000 | 0.027 | 0.951 | 0.163 | 0.081 | 0.365 | 0.201 | 0.208 | 2.835 |
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 | 21 | 23 | 23 | 18 | 19 | 19 | 15 | 19 | 21 | 19 |
N.S. |
1 | 1.10 | 1.10 | 0.86 | 0.90 | 0.90 | 0.71 | 0.90 | 1.00 | 0.90 |
time (sec) |
N/A | 0.217 | 0.383 | 0.217 | 0.071 | 0.093 | 0.094 | 0.128 | 0.656 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 18 | 15 | 13 | 22 | 17 | 14 | 17 | 18 | 12 |
N.S. |
1 | 0.75 | 0.62 | 0.54 | 0.92 | 0.71 | 0.58 | 0.71 | 0.75 | 0.50 |
time (sec) |
N/A | 0.189 | 0.019 | 0.261 | 0.052 | 0.086 | 0.051 | 0.118 | 0.207 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | A | A | A | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 176 | 24 | 29 | 26 | 27 | 32 | 31 | 483 | 0 |
N.S. |
1 | 7.33 | 1.00 | 1.21 | 1.08 | 1.12 | 1.33 | 1.29 | 20.12 | 0.00 |
time (sec) |
N/A | 0.907 | 5.086 | 2.039 | 0.179 | 0.092 | 0.258 | 0.142 | 0.219 | 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 | 19 | 32 | 17 | 17 | 23 | 17 | 17 | 23 | 29 | 17 |
N.S. |
1 | 1.68 | 0.89 | 0.89 | 1.21 | 0.89 | 0.89 | 1.21 | 1.53 | 0.89 |
time (sec) |
N/A | 0.474 | 0.024 | 0.253 | 0.025 | 0.088 | 0.078 | 0.133 | 0.206 | 2.643 |
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 | 25 | 26 | 26 | 20 | 25 | 31 | 22 | 42 | 52 | 60 |
N.S. |
1 | 1.04 | 1.04 | 0.80 | 1.00 | 1.24 | 0.88 | 1.68 | 2.08 | 2.40 |
time (sec) |
N/A | 0.497 | 0.032 | 0.839 | 0.169 | 0.085 | 0.104 | 0.144 | 0.209 | 2.829 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 63 | 40 | 40 | 53 | 53 | 65 | 51 |
N.S. |
1 | 1.00 | 1.00 | 3.00 | 1.90 | 1.90 | 2.52 | 2.52 | 3.10 | 2.43 |
time (sec) |
N/A | 0.457 | 0.027 | 0.517 | 0.066 | 0.093 | 0.368 | 0.143 | 1.285 | 2.885 |
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 | 22 | 28 | 26 | 25 | 24 | 24 | 24 | 24 | 36 | 25 |
N.S. |
1 | 1.27 | 1.18 | 1.14 | 1.09 | 1.09 | 1.09 | 1.09 | 1.64 | 1.14 |
time (sec) |
N/A | 0.199 | 0.149 | 0.190 | 0.034 | 0.095 | 0.053 | 0.126 | 0.203 | 0.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 25 | 12 | 31 | 11 | 15 | 0 | 53 | 11 |
N.S. |
1 | 0.00 | 0.81 | 0.39 | 1.00 | 0.35 | 0.48 | 0.00 | 1.71 | 0.35 |
time (sec) |
N/A | 0.000 | 8.519 | 2.433 | 0.298 | 0.099 | 16.129 | 0.000 | 200.027 | 2.628 |
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 | 19 | 17 | 12 | 12 | 15 | 15 | 10 | 15 | 16 | 11 |
N.S. |
1 | 0.89 | 0.63 | 0.63 | 0.79 | 0.79 | 0.53 | 0.79 | 0.84 | 0.58 |
time (sec) |
N/A | 0.147 | 0.002 | 0.145 | 0.024 | 0.068 | 0.019 | 0.112 | 0.161 | 2.458 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 28 | 28 | 29 | 0 | 28 | 26 | 32 | 24 | 24 |
N.S. |
1 | 0.97 | 0.97 | 1.00 | 0.00 | 0.97 | 0.90 | 1.10 | 0.83 | 0.83 |
time (sec) |
N/A | 0.315 | 0.010 | 0.308 | 0.000 | 0.093 | 0.137 | 0.124 | 0.182 | 2.734 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 24 | 32 | 21 | 74 | 20 | 21 | 35 | 22 |
N.S. |
1 | 0.00 | 1.00 | 1.33 | 0.88 | 3.08 | 0.83 | 0.88 | 1.46 | 0.92 |
time (sec) |
N/A | 0.000 | 0.130 | 0.059 | 0.245 | 0.089 | 1.358 | 0.128 | 0.203 | 2.829 |
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 | 19 | 25 | 15 | 14 | 18 | 18 | 22 | 20 | 26 | 24 |
N.S. |
1 | 1.32 | 0.79 | 0.74 | 0.95 | 0.95 | 1.16 | 1.05 | 1.37 | 1.26 |
time (sec) |
N/A | 0.279 | 0.019 | 0.161 | 0.030 | 0.085 | 0.065 | 0.115 | 0.194 | 2.632 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 27 | 26 | 16 | 39 | 39 | 26 | 58 | 57 | 27 |
N.S. |
1 | 1.35 | 1.30 | 0.80 | 1.95 | 1.95 | 1.30 | 2.90 | 2.85 | 1.35 |
time (sec) |
N/A | 0.710 | 0.718 | 0.321 | 0.070 | 0.089 | 0.140 | 0.123 | 0.188 | 0.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 135 | 27 | 21 | 26 | 30 | 20 | 38 | 37 | 22 |
N.S. |
1 | 5.00 | 1.00 | 0.78 | 0.96 | 1.11 | 0.74 | 1.41 | 1.37 | 0.81 |
time (sec) |
N/A | 1.404 | 0.116 | 1.135 | 0.153 | 0.091 | 0.156 | 0.126 | 0.178 | 2.688 |
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 | 15 | 16 | 16 | 16 | 15 | 15 | 12 | 15 | 14 | 13 |
N.S. |
1 | 1.07 | 1.07 | 1.07 | 1.00 | 1.00 | 0.80 | 1.00 | 0.93 | 0.87 |
time (sec) |
N/A | 0.153 | 0.001 | 0.099 | 0.029 | 0.074 | 0.017 | 0.116 | 0.163 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | F(-1) | A | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 28 | 26 | 311 | 18 | 0 | 22 | 92 | 22 |
N.S. |
1 | 0.00 | 1.12 | 1.04 | 12.44 | 0.72 | 0.00 | 0.88 | 3.68 | 0.88 |
time (sec) |
N/A | 0.000 | 0.038 | 1.187 | 0.301 | 0.101 | 0.000 | 0.114 | 200.015 | 2.846 |
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 | 21 | 16 | 16 | 17 | 13 | 14 | 17 | 32 | 18 | 14 |
N.S. |
1 | 0.76 | 0.76 | 0.81 | 0.62 | 0.67 | 0.81 | 1.52 | 0.86 | 0.67 |
time (sec) |
N/A | 0.175 | 0.002 | 0.379 | 0.030 | 0.081 | 0.048 | 0.112 | 0.170 | 0.058 |
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 | 21 | 35 | 21 | 19 | 75 | 23 | 34 | 16 | 29 | 17 |
N.S. |
1 | 1.67 | 1.00 | 0.90 | 3.57 | 1.10 | 1.62 | 0.76 | 1.38 | 0.81 |
time (sec) |
N/A | 0.250 | 0.047 | 0.128 | 0.036 | 0.088 | 0.067 | 0.108 | 0.170 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 25 | 26 | 20 | 25 | 20 | 25 | 27 | 21 |
N.S. |
1 | 0.00 | 1.00 | 1.04 | 0.80 | 1.00 | 0.80 | 1.00 | 1.08 | 0.84 |
time (sec) |
N/A | 0.000 | 0.065 | 0.763 | 0.120 | 0.079 | 2.594 | 0.130 | 0.173 | 2.743 |
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 | 28 | 30 | 24 | 24 | 22 | 23 | 26 | 22 | 21 | 23 |
N.S. |
1 | 1.07 | 0.86 | 0.86 | 0.79 | 0.82 | 0.93 | 0.79 | 0.75 | 0.82 |
time (sec) |
N/A | 0.195 | 0.080 | 0.819 | 0.030 | 0.081 | 0.070 | 0.109 | 0.168 | 2.621 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | C | B | A | A | F | B | B |
verified | N/A | N/A | N/A | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 0 | 433 | 384 | 41 | 37 | 0 | 27 | 23 |
N.S. |
1 | 0.00 | 0.00 | 16.04 | 14.22 | 1.52 | 1.37 | 0.00 | 1.00 | 0.85 |
time (sec) |
N/A | 0.000 | 0.000 | 0.077 | 0.509 | 0.084 | 9.463 | 0.000 | 0.184 | 3.136 |
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 | 23 | 9 | 9 | 9 | 9 | 9 | 5 | 9 | 8 | 9 |
N.S. |
1 | 0.39 | 0.39 | 0.39 | 0.39 | 0.39 | 0.22 | 0.39 | 0.35 | 0.39 |
time (sec) |
N/A | 0.143 | 0.000 | 0.033 | 0.026 | 0.083 | 0.018 | 0.110 | 0.164 | 0.010 |
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 | 9 | 12 | 12 | 9 | 8 | 8 | 7 | 8 | 9 | 8 |
N.S. |
1 | 1.33 | 1.33 | 1.00 | 0.89 | 0.89 | 0.78 | 0.89 | 1.00 | 0.89 |
time (sec) |
N/A | 0.134 | 0.001 | 0.054 | 0.025 | 0.072 | 0.021 | 0.108 | 0.171 | 2.727 |
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 | 17 | 18 | 16 | 14 | 13 | 21 | 12 | 24 | 24 | 13 |
N.S. |
1 | 1.06 | 0.94 | 0.82 | 0.76 | 1.24 | 0.71 | 1.41 | 1.41 | 0.76 |
time (sec) |
N/A | 0.182 | 0.008 | 0.234 | 0.034 | 0.091 | 0.057 | 0.111 | 0.158 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F(-1) | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 34 | 61 | 19 | 61 | 31 | 0 | 31 | 56 | 49 |
N.S. |
1 | 1.48 | 2.65 | 0.83 | 2.65 | 1.35 | 0.00 | 1.35 | 2.43 | 2.13 |
time (sec) |
N/A | 1.049 | 2.266 | 21.264 | 0.345 | 0.104 | 0.000 | 0.148 | 200.032 | 3.020 |
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 | 18 | 14 | 14 | 15 | 18 | 14 | 20 | 19 | 14 | 14 |
N.S. |
1 | 0.78 | 0.78 | 0.83 | 1.00 | 0.78 | 1.11 | 1.06 | 0.78 | 0.78 |
time (sec) |
N/A | 0.144 | 0.001 | 0.169 | 0.028 | 0.093 | 0.030 | 0.113 | 0.202 | 0.152 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 114 | 26 | 24 | 29 | 23 | 26 | 0 | 27 | 28 |
N.S. |
1 | 4.07 | 0.93 | 0.86 | 1.04 | 0.82 | 0.93 | 0.00 | 0.96 | 1.00 |
time (sec) |
N/A | 0.295 | 0.042 | 1.359 | 0.149 | 0.102 | 1.830 | 0.000 | 0.203 | 2.797 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 28 | 32 | 29 | 29 | 27 | 34 | 33 | 0 |
N.S. |
1 | 0.00 | 1.12 | 1.28 | 1.16 | 1.16 | 1.08 | 1.36 | 1.32 | 0.00 |
time (sec) |
N/A | 0.000 | 0.758 | 0.665 | 0.085 | 0.090 | 0.152 | 0.135 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 20 | 19 | 18 | 18 | 17 | 18 | 19 | 18 |
N.S. |
1 | 0.00 | 1.00 | 0.95 | 0.90 | 0.90 | 0.85 | 0.90 | 0.95 | 0.90 |
time (sec) |
N/A | 0.000 | 0.076 | 2.740 | 0.100 | 0.093 | 0.149 | 0.115 | 0.201 | 2.916 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 43 | 30 | 41 | 44 | 26 | 46 | 53 | 38 |
N.S. |
1 | 0.00 | 1.23 | 0.86 | 1.17 | 1.26 | 0.74 | 1.31 | 1.51 | 1.09 |
time (sec) |
N/A | 0.000 | 1.807 | 0.498 | 0.142 | 0.080 | 0.083 | 0.113 | 0.208 | 2.788 |
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 | 29 | 27 | 27 | 25 | 20 | 24 | 20 | 24 | 25 | 20 |
N.S. |
1 | 0.93 | 0.93 | 0.86 | 0.69 | 0.83 | 0.69 | 0.83 | 0.86 | 0.69 |
time (sec) |
N/A | 0.328 | 0.059 | 0.648 | 0.079 | 0.080 | 0.072 | 0.113 | 0.991 | 2.662 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 59 | 83 | 410 | 82 | 65 | 92 | 115 | 68 |
N.S. |
1 | 0.00 | 2.57 | 3.61 | 17.83 | 3.57 | 2.83 | 4.00 | 5.00 | 2.96 |
time (sec) |
N/A | 0.000 | 1.514 | 42.541 | 0.157 | 0.085 | 0.221 | 0.154 | 0.200 | 2.894 |
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 | 25 | 28 | 22 | 19 | 18 | 18 | 14 | 18 | 27 | 20 |
N.S. |
1 | 1.12 | 0.88 | 0.76 | 0.72 | 0.72 | 0.56 | 0.72 | 1.08 | 0.80 |
time (sec) |
N/A | 0.209 | 0.051 | 0.106 | 0.030 | 0.076 | 0.066 | 0.107 | 0.200 | 0.065 |
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 | 23 | 23 | 27 | 20 | 21 | 34 | 17 | 22 | 40 | 21 |
N.S. |
1 | 1.00 | 1.17 | 0.87 | 0.91 | 1.48 | 0.74 | 0.96 | 1.74 | 0.91 |
time (sec) |
N/A | 0.281 | 0.012 | 0.094 | 0.030 | 0.076 | 0.059 | 0.115 | 0.196 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 279 | 19 | 208 | 310 | 183 | 226 | 196 | 258 | 184 |
N.S. |
1 | 14.68 | 1.00 | 10.95 | 16.32 | 9.63 | 11.89 | 10.32 | 13.58 | 9.68 |
time (sec) |
N/A | 0.641 | 0.037 | 38.340 | 0.035 | 0.091 | 0.263 | 0.116 | 0.209 | 2.725 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | F | B |
verified | N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 32 | 24 | 39 | 62 | 20 | 0 | 401 | 38 |
N.S. |
1 | 0.00 | 1.23 | 0.92 | 1.50 | 2.38 | 0.77 | 0.00 | 15.42 | 1.46 |
time (sec) |
N/A | 0.000 | 1.159 | 4.819 | 0.325 | 0.095 | 0.211 | 0.000 | 0.230 | 3.203 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 10 | 10 | 9 | 9 | 8 | 9 | 11 | 9 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.90 | 0.90 | 0.80 | 0.90 | 1.10 | 0.90 |
time (sec) |
N/A | 0.221 | 0.007 | 0.283 | 0.057 | 0.087 | 0.082 | 0.111 | 0.192 | 2.631 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 21 | 19 | 21 | 31 | 0 | 31 | 24 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.90 | 1.00 | 1.48 | 0.00 | 1.48 | 1.14 | 0.00 |
time (sec) |
N/A | 0.000 | 0.391 | 78.359 | 0.129 | 0.081 | 0.000 | 0.120 | 0.207 | 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 | 14 | 11 | 11 | 11 | 10 | 15 | 7 | 11 | 12 | 10 |
N.S. |
1 | 0.79 | 0.79 | 0.79 | 0.71 | 1.07 | 0.50 | 0.79 | 0.86 | 0.71 |
time (sec) |
N/A | 0.156 | 0.005 | 0.188 | 0.023 | 0.078 | 0.037 | 0.106 | 0.198 | 0.035 |
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 | 26 | 27 | 29 | 26 | 40 | 40 | 22 | 28 | 36 | 27 |
N.S. |
1 | 1.04 | 1.12 | 1.00 | 1.54 | 1.54 | 0.85 | 1.08 | 1.38 | 1.04 |
time (sec) |
N/A | 0.602 | 0.038 | 0.317 | 0.150 | 0.078 | 0.089 | 0.113 | 0.212 | 2.833 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 63 | 70 | 81 | 76 | 58 | 115 | 77 | 0 |
N.S. |
1 | 0.00 | 1.70 | 1.89 | 2.19 | 2.05 | 1.57 | 3.11 | 2.08 | 0.00 |
time (sec) |
N/A | 0.000 | 0.094 | 1.226 | 0.089 | 0.096 | 0.164 | 0.193 | 0.231 | 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 | 13 | 10 | 10 | 10 | 9 | 9 | 7 | 9 | 10 | 9 |
N.S. |
1 | 0.77 | 0.77 | 0.77 | 0.69 | 0.69 | 0.54 | 0.69 | 0.77 | 0.69 |
time (sec) |
N/A | 0.137 | 0.001 | 0.070 | 0.028 | 0.075 | 0.036 | 0.106 | 0.203 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 72 | 25 | 26 | 36 | 30 | 32 | 34 | 51 | 40 |
N.S. |
1 | 2.88 | 1.00 | 1.04 | 1.44 | 1.20 | 1.28 | 1.36 | 2.04 | 1.60 |
time (sec) |
N/A | 1.192 | 1.379 | 7.247 | 0.263 | 0.089 | 0.223 | 0.232 | 0.216 | 2.798 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 25 | 38 | 26 | 45 | 42 | 47 | 52 | 47 |
N.S. |
1 | 0.00 | 1.04 | 1.58 | 1.08 | 1.88 | 1.75 | 1.96 | 2.17 | 1.96 |
time (sec) |
N/A | 0.000 | 0.161 | 1.344 | 0.210 | 0.085 | 0.326 | 0.146 | 0.219 | 4.458 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 14 | 28 | 14 | 15 | 23 | 12 | 15 | 21 | 15 |
N.S. |
1 | 0.47 | 0.93 | 0.47 | 0.50 | 0.77 | 0.40 | 0.50 | 0.70 | 0.50 |
time (sec) |
N/A | 0.179 | 0.008 | 0.227 | 0.034 | 0.082 | 0.052 | 0.108 | 0.209 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 19 | 17 | 16 | 43 | 15 | 16 | 20 | 16 |
N.S. |
1 | 0.00 | 0.95 | 0.85 | 0.80 | 2.15 | 0.75 | 0.80 | 1.00 | 0.80 |
time (sec) |
N/A | 0.000 | 0.077 | 0.072 | 0.157 | 0.086 | 0.076 | 0.122 | 0.213 | 2.411 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 21 | 21 | 25 | 25 | 25 | 26 | 25 | 102 | 0 |
N.S. |
1 | 0.78 | 0.78 | 0.93 | 0.93 | 0.93 | 0.96 | 0.93 | 3.78 | 0.00 |
time (sec) |
N/A | 0.513 | 0.034 | 0.562 | 0.155 | 0.103 | 0.090 | 0.151 | 200.021 | 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 | 28 | 21 | 17 | 20 | 19 | 19 | 15 | 21 | 19 | 17 |
N.S. |
1 | 0.75 | 0.61 | 0.71 | 0.68 | 0.68 | 0.54 | 0.75 | 0.68 | 0.61 |
time (sec) |
N/A | 0.205 | 0.004 | 0.129 | 0.041 | 0.087 | 0.038 | 0.110 | 0.164 | 2.786 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 27 | 23 | 21 | 24 | 37 | 19 | 0 | 25 | 18 |
N.S. |
1 | 1.17 | 1.00 | 0.91 | 1.04 | 1.61 | 0.83 | 0.00 | 1.09 | 0.78 |
time (sec) |
N/A | 1.519 | 0.071 | 35.388 | 0.210 | 0.108 | 18.978 | 0.000 | 0.185 | 3.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 25 | 25 | 26 | 30 | 25 | 0 | 0 | 23 | 25 |
N.S. |
1 | 0.86 | 0.86 | 0.90 | 1.03 | 0.86 | 0.00 | 0.00 | 0.79 | 0.86 |
time (sec) |
N/A | 1.397 | 0.428 | 3.532 | 0.159 | 0.092 | 0.000 | 0.000 | 0.179 | 2.821 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 0 | 46 | 63 | 87 | 60 | 56 | 95 | 167 | 71 |
N.S. |
1 | 0.00 | 1.18 | 1.62 | 2.23 | 1.54 | 1.44 | 2.44 | 4.28 | 1.82 |
time (sec) |
N/A | 0.000 | 0.488 | 12.921 | 0.254 | 0.098 | 0.737 | 3.156 | 0.179 | 3.499 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | C | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 46 | 46 | 46 | 74 | 49 | 39 | 46 | 62 | 39 |
N.S. |
1 | 2.19 | 2.19 | 2.19 | 3.52 | 2.33 | 1.86 | 2.19 | 2.95 | 1.86 |
time (sec) |
N/A | 0.720 | 0.209 | 7.127 | 0.068 | 0.091 | 0.089 | 0.127 | 0.166 | 2.824 |
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 | 12 | 12 | 18 | 15 | 14 | 23 | 12 | 14 | 31 | 58 |
N.S. |
1 | 1.00 | 1.50 | 1.25 | 1.17 | 1.92 | 1.00 | 1.17 | 2.58 | 4.83 |
time (sec) |
N/A | 0.211 | 0.009 | 0.276 | 0.029 | 0.078 | 0.050 | 0.115 | 0.164 | 2.592 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 62 | 63 | 67 | 58 | 69 | 70 | 69 | 77 | 57 |
N.S. |
1 | 1.77 | 1.80 | 1.91 | 1.66 | 1.97 | 2.00 | 1.97 | 2.20 | 1.63 |
time (sec) |
N/A | 0.313 | 0.020 | 0.307 | 0.033 | 0.082 | 0.308 | 0.115 | 0.162 | 2.760 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 28 | 34 | 45 | 50 | 49 | 46 | 35 | 52 |
N.S. |
1 | 0.00 | 1.00 | 1.21 | 1.61 | 1.79 | 1.75 | 1.64 | 1.25 | 1.86 |
time (sec) |
N/A | 0.000 | 0.132 | 2.082 | 0.144 | 0.098 | 0.129 | 0.116 | 0.179 | 2.753 |
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 | 6 | 4 | 4 | 5 | 4 | 4 | 3 | 5 | 4 | 4 |
N.S. |
1 | 0.67 | 0.67 | 0.83 | 0.67 | 0.67 | 0.50 | 0.83 | 0.67 | 0.67 |
time (sec) |
N/A | 0.119 | 0.000 | 0.029 | 0.028 | 0.070 | 0.017 | 0.113 | 0.182 | 0.007 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 41 | 49 | 35 | 54 | 32 | 0 | 197 | 46 |
N.S. |
1 | 0.00 | 1.28 | 1.53 | 1.09 | 1.69 | 1.00 | 0.00 | 6.16 | 1.44 |
time (sec) |
N/A | 0.000 | 0.463 | 0.188 | 0.111 | 0.097 | 1.764 | 0.000 | 200.023 | 2.951 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 44 | 33 | 31 | 35 | 36 | 41 | 868 | 37 |
N.S. |
1 | 0.00 | 1.76 | 1.32 | 1.24 | 1.40 | 1.44 | 1.64 | 34.72 | 1.48 |
time (sec) |
N/A | 0.000 | 15.216 | 0.468 | 0.064 | 0.099 | 0.161 | 0.159 | 0.228 | 0.118 |
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 | 24 | 20 | 20 | 14 | 13 | 13 | 17 | 13 | 14 | 13 |
N.S. |
1 | 0.83 | 0.83 | 0.58 | 0.54 | 0.54 | 0.71 | 0.54 | 0.58 | 0.54 |
time (sec) |
N/A | 0.152 | 0.003 | 0.086 | 0.024 | 0.084 | 0.039 | 0.108 | 0.170 | 0.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | B | B | F(-2) | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 50 | 25 | 49 | 56 | 0 | 49 | 49 |
N.S. |
1 | 0.00 | 1.00 | 2.17 | 1.09 | 2.13 | 2.43 | 0.00 | 2.13 | 2.13 |
time (sec) |
N/A | 0.000 | 0.048 | 0.981 | 0.155 | 0.106 | 0.165 | 0.000 | 0.179 | 3.336 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 48 | 48 | 38 | 136 | 37 | 32 | 93 | 62 | 21 |
N.S. |
1 | 1.85 | 1.85 | 1.46 | 5.23 | 1.42 | 1.23 | 3.58 | 2.38 | 0.81 |
time (sec) |
N/A | 0.722 | 0.054 | 1.234 | 0.034 | 0.206 | 0.071 | 0.115 | 0.182 | 0.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | F | B | A | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 51 | 111 | 0 | 114 | 39 | 125 | 164 | 0 |
N.S. |
1 | 0.00 | 1.50 | 3.26 | 0.00 | 3.35 | 1.15 | 3.68 | 4.82 | 0.00 |
time (sec) |
N/A | 0.000 | 0.160 | 8.231 | 0.000 | 0.097 | 0.331 | 1.955 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 14 | 14 | 17 | 24 | 16 | 17 | 16 | 16 | 19 |
N.S. |
1 | 0.78 | 0.78 | 0.94 | 1.33 | 0.89 | 0.94 | 0.89 | 0.89 | 1.06 |
time (sec) |
N/A | 9.598 | 0.115 | 1.106 | 0.136 | 0.080 | 0.136 | 0.129 | 0.169 | 2.613 |
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 | 22 | 22 | 20 | 20 | 19 | 19 | 19 | 19 | 20 | 19 |
N.S. |
1 | 1.00 | 0.91 | 0.91 | 0.86 | 0.86 | 0.86 | 0.86 | 0.91 | 0.86 |
time (sec) |
N/A | 0.724 | 0.036 | 2.066 | 0.163 | 0.081 | 0.147 | 0.149 | 0.170 | 2.717 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 69 | 23 | 22 | 23 | 21 | 17 | 21 | 27 | 23 |
N.S. |
1 | 2.23 | 0.74 | 0.71 | 0.74 | 0.68 | 0.55 | 0.68 | 0.87 | 0.74 |
time (sec) |
N/A | 0.257 | 0.149 | 0.177 | 0.108 | 0.091 | 0.080 | 0.120 | 1.541 | 2.534 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 27 | 39 | 16 | 38 | 15 | 14 | 15 | 29 | 15 |
N.S. |
1 | 1.59 | 2.29 | 0.94 | 2.24 | 0.88 | 0.82 | 0.88 | 1.71 | 0.88 |
time (sec) |
N/A | 0.246 | 0.010 | 0.276 | 0.112 | 0.076 | 0.056 | 0.108 | 0.179 | 0.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 87 | 64 | 42 | 57 | 58 | 44 | 58 | 75 | 57 |
N.S. |
1 | 3.22 | 2.37 | 1.56 | 2.11 | 2.15 | 1.63 | 2.15 | 2.78 | 2.11 |
time (sec) |
N/A | 0.248 | 0.033 | 0.312 | 0.112 | 0.093 | 0.093 | 0.117 | 0.183 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 56 | 38 | 43 | 35 | 40 | 53 | 40 | 74 | 47 |
N.S. |
1 | 2.24 | 1.52 | 1.72 | 1.40 | 1.60 | 2.12 | 1.60 | 2.96 | 1.88 |
time (sec) |
N/A | 0.430 | 1.695 | 1.165 | 0.087 | 0.092 | 0.149 | 0.124 | 1.714 | 2.623 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | F(-2) | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 47 | 44 | 50 | 42 | 0 | 54 | 61 | 60 |
N.S. |
1 | 0.00 | 1.74 | 1.63 | 1.85 | 1.56 | 0.00 | 2.00 | 2.26 | 2.22 |
time (sec) |
N/A | 0.000 | 0.050 | 6.585 | 0.166 | 0.086 | 0.000 | 1.541 | 0.171 | 3.085 |
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 | 21 | 27 | 21 | 27 | 20 | 20 | 19 | 20 | 27 | 20 |
N.S. |
1 | 1.29 | 1.00 | 1.29 | 0.95 | 0.95 | 0.90 | 0.95 | 1.29 | 0.95 |
time (sec) |
N/A | 2.459 | 0.046 | 0.900 | 0.068 | 0.096 | 0.168 | 0.142 | 0.180 | 3.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 100 | 111 | 33 | 96 | 60 | 116 | 113 | 33 | 196 |
N.S. |
1 | 3.85 | 4.27 | 1.27 | 3.69 | 2.31 | 4.46 | 4.35 | 1.27 | 7.54 |
time (sec) |
N/A | 0.380 | 0.036 | 0.357 | 0.025 | 0.079 | 0.196 | 0.114 | 0.174 | 0.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 29 | 24 | 11 | 24 | 29 | 24 | 30 | 24 |
N.S. |
1 | 0.00 | 1.00 | 0.83 | 0.38 | 0.83 | 1.00 | 0.83 | 1.03 | 0.83 |
time (sec) |
N/A | 0.000 | 5.515 | 3.652 | 0.070 | 0.078 | 0.100 | 0.117 | 0.173 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | A | F(-2) | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 112 | 88 | 198 | 47 | 0 | 148 | 183 | 357 |
N.S. |
1 | 0.00 | 3.61 | 2.84 | 6.39 | 1.52 | 0.00 | 4.77 | 5.90 | 11.52 |
time (sec) |
N/A | 0.000 | 0.104 | 13.188 | 0.186 | 0.090 | 0.000 | 0.627 | 0.183 | 3.330 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 36 | 30 | 52 | 38 | 41 | 29 | 34 | 32 |
N.S. |
1 | 0.00 | 1.38 | 1.15 | 2.00 | 1.46 | 1.58 | 1.12 | 1.31 | 1.23 |
time (sec) |
N/A | 0.000 | 0.388 | 0.986 | 0.083 | 0.109 | 0.900 | 0.175 | 0.177 | 2.905 |
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 | 22 | 33 | 18 | 17 | 25 | 18 | 12 | 17 | 19 | 18 |
N.S. |
1 | 1.50 | 0.82 | 0.77 | 1.14 | 0.82 | 0.55 | 0.77 | 0.86 | 0.82 |
time (sec) |
N/A | 0.243 | 0.063 | 0.166 | 0.033 | 0.074 | 0.059 | 0.109 | 0.167 | 2.628 |
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 | 24 | 20 | 20 | 20 | 19 | 19 | 19 | 27 | 30 | 19 |
N.S. |
1 | 0.83 | 0.83 | 0.83 | 0.79 | 0.79 | 0.79 | 1.12 | 1.25 | 0.79 |
time (sec) |
N/A | 0.179 | 0.014 | 0.261 | 0.025 | 0.083 | 0.054 | 0.115 | 0.172 | 2.477 |
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 | 18 | 18 | 16 | 14 | 13 | 13 | 17 | 13 | 14 | 13 |
N.S. |
1 | 1.00 | 0.89 | 0.78 | 0.72 | 0.72 | 0.94 | 0.72 | 0.78 | 0.72 |
time (sec) |
N/A | 0.145 | 0.002 | 0.088 | 0.029 | 0.075 | 0.038 | 0.106 | 0.172 | 2.620 |
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 | 27 | 34 | 30 | 28 | 45 | 31 | 24 | 31 | 33 | 24 |
N.S. |
1 | 1.26 | 1.11 | 1.04 | 1.67 | 1.15 | 0.89 | 1.15 | 1.22 | 0.89 |
time (sec) |
N/A | 3.810 | 0.115 | 1.491 | 0.110 | 0.095 | 0.106 | 0.136 | 0.183 | 2.655 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 19 | 0 | 76 | 32 | 112 | 109 | 55 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.00 | 3.80 | 1.60 | 5.60 | 5.45 | 2.75 |
time (sec) |
N/A | 0.681 | 1.498 | 0.561 | 0.000 | 0.086 | 0.131 | 0.116 | 0.173 | 0.158 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 24 | 28 | 28 | 27 | 24 | 30 | 28 | 292 |
N.S. |
1 | 0.00 | 0.96 | 1.12 | 1.12 | 1.08 | 0.96 | 1.20 | 1.12 | 11.68 |
time (sec) |
N/A | 0.000 | 0.337 | 5.091 | 0.159 | 0.088 | 0.086 | 0.221 | 0.178 | 3.115 |
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 | 14 | 14 | 14 | 16 | 15 | 15 | 15 | 15 | 14 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.14 | 1.07 | 1.07 | 1.07 | 1.07 | 1.00 | 1.07 |
time (sec) |
N/A | 0.241 | 0.106 | 0.477 | 0.072 | 0.100 | 0.157 | 0.116 | 0.171 | 2.828 |