Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 37 | 26 | 28 | 69 | 24 | 26 | 24 | 28 | 23 |
N.S. |
1 | 1.68 | 1.18 | 1.27 | 3.14 | 1.09 | 1.18 | 1.09 | 1.27 | 1.05 |
time (sec) |
N/A | 0.268 | 0.109 | 0.080 | 0.028 | 0.106 | 0.065 | 0.113 | 0.175 | 0.031 |
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 | 17 | 0 | 15 | 15 | 14 | 14 | 14 | 14 | 15 | 14 |
N.S. |
1 | 0.00 | 0.88 | 0.88 | 0.82 | 0.82 | 0.82 | 0.82 | 0.88 | 0.82 |
time (sec) |
N/A | 0.000 | 0.229 | 0.138 | 0.171 | 0.078 | 0.065 | 0.123 | 0.171 | 2.695 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | F(-2) | A | A | A | F | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 23 | 129 | 0 | 21 | 20 | 24 | 100 | 24 |
N.S. |
1 | 0.00 | 0.96 | 5.38 | 0.00 | 0.88 | 0.83 | 1.00 | 4.17 | 1.00 |
time (sec) |
N/A | 0.000 | 1.462 | 0.019 | 0.000 | 0.089 | 5.976 | 0.167 | 200.023 | 3.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 25 | 21 | 22 | 21 | 21 | 20 | 28 | 25 | 0 |
N.S. |
1 | 0.89 | 0.75 | 0.79 | 0.75 | 0.75 | 0.71 | 1.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.591 | 0.040 | 2.375 | 0.157 | 0.091 | 0.073 | 0.148 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 64 | 17 | 18 | 44 | 16 | 15 | 22 | 28 | 46 |
N.S. |
1 | 3.37 | 0.89 | 0.95 | 2.32 | 0.84 | 0.79 | 1.16 | 1.47 | 2.42 |
time (sec) |
N/A | 0.289 | 0.088 | 0.261 | 0.211 | 0.081 | 0.153 | 0.174 | 0.176 | 2.721 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 164 | 33 | 31 | 50 | 52 | 31 | 78 | 129 | 0 |
N.S. |
1 | 4.56 | 0.92 | 0.86 | 1.39 | 1.44 | 0.86 | 2.17 | 3.58 | 0.00 |
time (sec) |
N/A | 1.847 | 0.068 | 1.935 | 0.169 | 0.088 | 0.091 | 0.136 | 0.182 | 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 | 24 | 25 | 25 | 25 | 24 | 24 | 20 | 24 | 25 | 24 |
N.S. |
1 | 1.04 | 1.04 | 1.04 | 1.00 | 1.00 | 0.83 | 1.00 | 1.04 | 1.00 |
time (sec) |
N/A | 0.764 | 0.098 | 0.487 | 0.209 | 0.078 | 0.103 | 0.114 | 0.178 | 3.031 |
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 | 27 | 27 | 18 | 15 | 15 | 27 | 15 | 16 | 22 |
N.S. |
1 | 1.17 | 1.17 | 0.78 | 0.65 | 0.65 | 1.17 | 0.65 | 0.70 | 0.96 |
time (sec) |
N/A | 0.169 | 0.002 | 0.042 | 0.030 | 0.088 | 0.100 | 0.119 | 0.180 | 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 | 16 | 17 | 17 | 17 | 16 | 16 | 15 | 16 | 17 | 16 |
N.S. |
1 | 1.06 | 1.06 | 1.06 | 1.00 | 1.00 | 0.94 | 1.00 | 1.06 | 1.00 |
time (sec) |
N/A | 0.149 | 0.002 | 0.085 | 0.032 | 0.083 | 0.039 | 0.111 | 0.181 | 2.692 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | C | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 51 | 18 | 21 | 372 | 21 | 20 | 35 | 20 | 16 |
N.S. |
1 | 2.83 | 1.00 | 1.17 | 20.67 | 1.17 | 1.11 | 1.94 | 1.11 | 0.89 |
time (sec) |
N/A | 0.572 | 0.837 | 0.316 | 0.131 | 0.081 | 0.093 | 0.121 | 0.195 | 0.056 |
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 | 20 | 29 | 29 | 22 | 31 | 20 | 19 | 20 | 20 | 20 |
N.S. |
1 | 1.45 | 1.45 | 1.10 | 1.55 | 1.00 | 0.95 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.251 | 0.070 | 0.123 | 0.064 | 0.077 | 0.084 | 0.116 | 0.186 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 28 | 29 | 37 | 27 | 36 | 34 | 0 | 54 | 29 |
N.S. |
1 | 0.93 | 0.97 | 1.23 | 0.90 | 1.20 | 1.13 | 0.00 | 1.80 | 0.97 |
time (sec) |
N/A | 2.002 | 1.007 | 91.694 | 0.154 | 0.085 | 0.304 | 0.000 | 0.187 | 2.790 |
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 | 14 | 0 | 14 | 15 | 15 | 18 | 15 | 18 | 18 | 18 |
N.S. |
1 | 0.00 | 1.00 | 1.07 | 1.07 | 1.29 | 1.07 | 1.29 | 1.29 | 1.29 |
time (sec) |
N/A | 0.000 | 0.072 | 0.711 | 0.137 | 0.076 | 0.061 | 0.123 | 0.187 | 2.978 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 43 | 48 | 44 | 42 | 60 | 54 | 60 | 179 |
N.S. |
1 | 0.00 | 1.23 | 1.37 | 1.26 | 1.20 | 1.71 | 1.54 | 1.71 | 5.11 |
time (sec) |
N/A | 0.000 | 0.065 | 0.023 | 0.096 | 0.089 | 0.123 | 0.126 | 0.216 | 3.105 |
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 | 19 | 19 | 20 | 19 | 21 | 17 | 19 | 21 | 19 |
N.S. |
1 | 0.86 | 0.86 | 0.91 | 0.86 | 0.95 | 0.77 | 0.86 | 0.95 | 0.86 |
time (sec) |
N/A | 0.189 | 0.001 | 0.028 | 0.028 | 0.070 | 0.028 | 0.111 | 0.188 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 28 | 25 | 585 | 42 | 24 | 44 | 43 | 0 |
N.S. |
1 | 0.00 | 1.08 | 0.96 | 22.50 | 1.62 | 0.92 | 1.69 | 1.65 | 0.00 |
time (sec) |
N/A | 0.000 | 1.371 | 0.658 | 0.193 | 0.089 | 0.102 | 0.168 | 0.186 | 0.000 |
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 | 23 | 55 | 24 | 23 | 42 | 21 | 27 | 21 | 24 | 22 |
N.S. |
1 | 2.39 | 1.04 | 1.00 | 1.83 | 0.91 | 1.17 | 0.91 | 1.04 | 0.96 |
time (sec) |
N/A | 1.216 | 1.041 | 1.826 | 0.073 | 0.094 | 0.334 | 0.129 | 0.185 | 3.723 |
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 | 21 | 21 | 21 | 20 | 20 | 19 | 22 | 21 | 20 |
N.S. |
1 | 0.95 | 0.95 | 0.95 | 0.91 | 0.91 | 0.86 | 1.00 | 0.95 | 0.91 |
time (sec) |
N/A | 0.383 | 0.012 | 0.092 | 0.028 | 0.073 | 0.462 | 0.114 | 0.182 | 3.777 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 82 | 68 | 94 | 189 | 152 | 104 | 199 | 211 | 170 |
N.S. |
1 | 3.73 | 3.09 | 4.27 | 8.59 | 6.91 | 4.73 | 9.05 | 9.59 | 7.73 |
time (sec) |
N/A | 1.522 | 0.077 | 0.086 | 0.093 | 0.092 | 0.110 | 0.138 | 0.195 | 3.865 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | A | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 20 | 58 | 107 | 26 | 39 | 38 | 40 | 41 |
N.S. |
1 | 0.00 | 1.00 | 2.90 | 5.35 | 1.30 | 1.95 | 1.90 | 2.00 | 2.05 |
time (sec) |
N/A | 0.000 | 0.366 | 0.029 | 0.107 | 0.081 | 0.187 | 0.140 | 0.187 | 3.651 |
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 | 15 | 12 | 15 | 14 | 25 | 10 | 14 | 52 | 28 |
N.S. |
1 | 1.15 | 0.92 | 1.15 | 1.08 | 1.92 | 0.77 | 1.08 | 4.00 | 2.15 |
time (sec) |
N/A | 0.237 | 0.129 | 0.224 | 0.028 | 0.083 | 0.056 | 0.126 | 0.183 | 3.808 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 54 | 22 | 20 | 0 | 23 | 19 | 27 | 26 | 18 |
N.S. |
1 | 2.45 | 1.00 | 0.91 | 0.00 | 1.05 | 0.86 | 1.23 | 1.18 | 0.82 |
time (sec) |
N/A | 0.390 | 0.045 | 0.198 | 0.000 | 0.075 | 0.107 | 0.115 | 0.184 | 3.610 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 42 | 28 | 0 | 40 | 34 | 0 | 58 | 73 |
N.S. |
1 | 0.00 | 1.50 | 1.00 | 0.00 | 1.43 | 1.21 | 0.00 | 2.07 | 2.61 |
time (sec) |
N/A | 0.000 | 0.150 | 4.062 | 0.000 | 0.087 | 6.130 | 0.000 | 0.188 | 3.487 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 25 | 24 | 26 | 22 | 20 | 0 | 24 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.96 | 1.04 | 0.88 | 0.80 | 0.00 | 0.96 | 0.00 |
time (sec) |
N/A | 0.000 | 0.072 | 19.388 | 0.101 | 0.093 | 0.137 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 42 | 42 | 63 | 42 | 41 | 42 | 45 | 121 |
N.S. |
1 | 0.00 | 1.40 | 1.40 | 2.10 | 1.40 | 1.37 | 1.40 | 1.50 | 4.03 |
time (sec) |
N/A | 0.000 | 0.047 | 2.591 | 0.291 | 0.090 | 4.844 | 0.813 | 0.194 | 3.540 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 99 | 32 | 37 | 147 | 44 | 32 | 42 | 40 | 40 |
N.S. |
1 | 3.54 | 1.14 | 1.32 | 5.25 | 1.57 | 1.14 | 1.50 | 1.43 | 1.43 |
time (sec) |
N/A | 0.627 | 0.076 | 0.502 | 0.096 | 0.109 | 0.126 | 0.128 | 0.194 | 2.587 |
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 | 35 | 101 | 41 | 27 | 30 | 28 | 26 | 29 | 33 | 33 |
N.S. |
1 | 2.89 | 1.17 | 0.77 | 0.86 | 0.80 | 0.74 | 0.83 | 0.94 | 0.94 |
time (sec) |
N/A | 0.519 | 1.545 | 0.188 | 0.317 | 0.076 | 0.219 | 0.160 | 0.179 | 2.968 |
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 | 15 | 54 | 13 | 13 | 12 | 12 | 12 | 0 | 16 | 12 |
N.S. |
1 | 3.60 | 0.87 | 0.87 | 0.80 | 0.80 | 0.80 | 0.00 | 1.07 | 0.80 |
time (sec) |
N/A | 0.316 | 0.088 | 0.160 | 0.097 | 0.082 | 6.781 | 0.000 | 0.183 | 2.777 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | F | A | A | A | B | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 0 | 35 | 0 | 32 | 27 | 53 | 46 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.09 | 0.00 | 1.00 | 0.84 | 1.66 | 1.44 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 1.924 | 0.000 | 0.087 | 0.420 | 0.121 | 0.190 | 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 | 24 | 0 | 31 | 23 | 26 | 28 | 22 | 26 | 29 | 46 |
N.S. |
1 | 0.00 | 1.29 | 0.96 | 1.08 | 1.17 | 0.92 | 1.08 | 1.21 | 1.92 |
time (sec) |
N/A | 0.000 | 0.210 | 1.654 | 0.058 | 0.085 | 0.083 | 0.133 | 0.183 | 2.766 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 34 | 43 | 43 | 78 | 62 | 60 | 48 | 47 | 32 |
N.S. |
1 | 1.31 | 1.65 | 1.65 | 3.00 | 2.38 | 2.31 | 1.85 | 1.81 | 1.23 |
time (sec) |
N/A | 1.657 | 0.091 | 0.912 | 0.146 | 0.086 | 0.231 | 0.117 | 0.184 | 2.573 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | F | A | F(-1) | A | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 0 | 19 | 0 | 18 | 0 | 18 | 20 | 19 |
N.S. |
1 | 0.00 | 0.00 | 0.73 | 0.00 | 0.69 | 0.00 | 0.69 | 0.77 | 0.73 |
time (sec) |
N/A | 0.000 | 0.000 | 0.133 | 0.000 | 0.087 | 0.000 | 0.113 | 0.188 | 2.619 |
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 | 24 | 25 | 22 | 21 | 22 | 22 | 21 | 22 | 20 |
N.S. |
1 | 0.86 | 0.89 | 0.79 | 0.75 | 0.79 | 0.79 | 0.75 | 0.79 | 0.71 |
time (sec) |
N/A | 0.170 | 0.005 | 0.063 | 0.026 | 0.087 | 0.054 | 0.110 | 0.185 | 0.028 |
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 | 11 | 5 | 5 | 6 | 5 | 5 | 3 | 5 | 5 | 5 |
N.S. |
1 | 0.45 | 0.45 | 0.55 | 0.45 | 0.45 | 0.27 | 0.45 | 0.45 | 0.45 |
time (sec) |
N/A | 0.132 | 0.000 | 0.017 | 0.026 | 0.068 | 0.021 | 0.112 | 0.182 | 0.018 |
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 | 36 | 30 | 31 | 27 | 26 | 26 | 34 | 26 | 29 | 24 |
N.S. |
1 | 0.83 | 0.86 | 0.75 | 0.72 | 0.72 | 0.94 | 0.72 | 0.81 | 0.67 |
time (sec) |
N/A | 0.188 | 0.009 | 0.098 | 0.031 | 0.089 | 0.098 | 0.113 | 0.182 | 0.026 |
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 | 20 | 18 | 18 | 18 | 17 | 17 | 14 | 17 | 18 | 17 |
N.S. |
1 | 0.90 | 0.90 | 0.90 | 0.85 | 0.85 | 0.70 | 0.85 | 0.90 | 0.85 |
time (sec) |
N/A | 0.190 | 0.008 | 0.153 | 0.025 | 0.080 | 0.051 | 0.112 | 0.181 | 0.028 |
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 | 22 | 28 | 24 | 33 | 29 | 31 | 56 | 35 | 37 | 31 |
N.S. |
1 | 1.27 | 1.09 | 1.50 | 1.32 | 1.41 | 2.55 | 1.59 | 1.68 | 1.41 |
time (sec) |
N/A | 1.503 | 0.037 | 0.865 | 0.073 | 0.080 | 0.416 | 0.168 | 0.184 | 2.687 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | C | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 52 | 45 | 58 | 38 | 51 | 36 | 60 | 569 | 36 |
N.S. |
1 | 1.58 | 1.36 | 1.76 | 1.15 | 1.55 | 1.09 | 1.82 | 17.24 | 1.09 |
time (sec) |
N/A | 4.371 | 0.112 | 69.616 | 0.176 | 0.093 | 0.528 | 0.174 | 0.241 | 2.642 |
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 | 23 | 0 | 32 | 35 | 44 | 44 | 29 | 78 | 52 | 32 |
N.S. |
1 | 0.00 | 1.39 | 1.52 | 1.91 | 1.91 | 1.26 | 3.39 | 2.26 | 1.39 |
time (sec) |
N/A | 0.000 | 0.025 | 9.693 | 0.165 | 0.106 | 0.076 | 0.568 | 0.183 | 0.166 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 36 | 32 | 22 | 31 | 43 | 29 | 24 | 33 | 24 |
N.S. |
1 | 1.71 | 1.52 | 1.05 | 1.48 | 2.05 | 1.38 | 1.14 | 1.57 | 1.14 |
time (sec) |
N/A | 0.273 | 0.015 | 0.092 | 0.039 | 0.084 | 0.091 | 0.112 | 0.184 | 0.046 |
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 | 29 | 28 | 28 | 28 | 25 | 42 | 24 | 59 | 59 | 27 |
N.S. |
1 | 0.97 | 0.97 | 0.97 | 0.86 | 1.45 | 0.83 | 2.03 | 2.03 | 0.93 |
time (sec) |
N/A | 0.444 | 0.062 | 0.579 | 0.067 | 0.098 | 0.056 | 0.130 | 0.183 | 2.516 |
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 | 26 | 26 | 25 | 24 | 26 | 54 | 23 |
N.S. |
1 | 0.93 | 0.93 | 0.90 | 0.90 | 0.86 | 0.83 | 0.90 | 1.86 | 0.79 |
time (sec) |
N/A | 0.507 | 0.038 | 1.259 | 0.081 | 0.083 | 0.153 | 0.134 | 0.188 | 2.585 |
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 | 26 | 0 | 25 | 26 | 25 | 31 | 27 | 25 | 27 | 0 |
N.S. |
1 | 0.00 | 0.96 | 1.00 | 0.96 | 1.19 | 1.04 | 0.96 | 1.04 | 0.00 |
time (sec) |
N/A | 0.000 | 0.286 | 0.426 | 0.087 | 0.084 | 0.107 | 0.133 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | C | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 86 | 35 | 1157 | 71 | 43 | 76 | 88 | 119 | 46 |
N.S. |
1 | 2.77 | 1.13 | 37.32 | 2.29 | 1.39 | 2.45 | 2.84 | 3.84 | 1.48 |
time (sec) |
N/A | 3.894 | 0.059 | 0.148 | 0.154 | 0.090 | 0.306 | 0.148 | 0.184 | 2.586 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | F(-1) | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 29 | 22 | 90 | 76 | 0 | 103 | 112 | 0 |
N.S. |
1 | 0.00 | 1.12 | 0.85 | 3.46 | 2.92 | 0.00 | 3.96 | 4.31 | 0.00 |
time (sec) |
N/A | 0.000 | 2.060 | 1.743 | 0.112 | 0.095 | 0.000 | 0.132 | 0.183 | 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 | 26 | 0 | 29 | 31 | 35 | 30 | 34 | 30 | 25 | 23 |
N.S. |
1 | 0.00 | 1.12 | 1.19 | 1.35 | 1.15 | 1.31 | 1.15 | 0.96 | 0.88 |
time (sec) |
N/A | 0.000 | 2.860 | 0.832 | 0.087 | 0.078 | 0.086 | 0.146 | 0.188 | 2.658 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 82 | 13 | 12 | 22 | 11 | 0 | 19 | 13 | 78 |
N.S. |
1 | 6.31 | 1.00 | 0.92 | 1.69 | 0.85 | 0.00 | 1.46 | 1.00 | 6.00 |
time (sec) |
N/A | 0.654 | 0.464 | 0.086 | 0.073 | 0.093 | 0.000 | 0.122 | 0.182 | 2.714 |
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 | 16 | 16 | 13 | 57 | 16 | 12 | 14 | 14 | 14 |
N.S. |
1 | 0.76 | 0.76 | 0.62 | 2.71 | 0.76 | 0.57 | 0.67 | 0.67 | 0.67 |
time (sec) |
N/A | 0.191 | 0.069 | 0.075 | 0.109 | 0.081 | 0.058 | 0.114 | 0.187 | 2.911 |
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 | 27 | 30 | 23 | 22 | 22 | 19 | 22 | 27 | 24 |
N.S. |
1 | 1.17 | 1.30 | 1.00 | 0.96 | 0.96 | 0.83 | 0.96 | 1.17 | 1.04 |
time (sec) |
N/A | 0.163 | 0.005 | 0.102 | 0.034 | 0.081 | 0.044 | 0.111 | 0.184 | 2.831 |
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 | 24 | 55 | 30 | 26 | 25 | 32 | 31 | 25 | 23 | 21 |
N.S. |
1 | 2.29 | 1.25 | 1.08 | 1.04 | 1.33 | 1.29 | 1.04 | 0.96 | 0.88 |
time (sec) |
N/A | 0.200 | 0.023 | 0.128 | 0.032 | 0.090 | 0.072 | 0.108 | 0.190 | 2.761 |
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 | 11 | 8 | 8 | 9 | 8 | 8 | 7 | 9 | 8 | 8 |
N.S. |
1 | 0.73 | 0.73 | 0.82 | 0.73 | 0.73 | 0.64 | 0.82 | 0.73 | 0.73 |
time (sec) |
N/A | 0.143 | 0.001 | 0.023 | 0.026 | 0.073 | 0.029 | 0.112 | 0.189 | 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 | 19 | 10 | 10 | 10 | 9 | 9 | 10 | 9 | 10 | 9 |
N.S. |
1 | 0.53 | 0.53 | 0.53 | 0.47 | 0.47 | 0.53 | 0.47 | 0.53 | 0.47 |
time (sec) |
N/A | 0.134 | 0.000 | 0.050 | 0.025 | 0.078 | 0.014 | 0.121 | 0.196 | 0.001 |
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 | 25 | 23 | 19 | 18 | 24 | 15 | 18 | 33 | 21 |
N.S. |
1 | 1.09 | 1.00 | 0.83 | 0.78 | 1.04 | 0.65 | 0.78 | 1.43 | 0.91 |
time (sec) |
N/A | 0.312 | 0.033 | 0.130 | 0.026 | 0.079 | 0.134 | 0.126 | 0.183 | 2.570 |
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 | 6 | 6 | 7 | 6 | 6 | 5 | 7 | 6 | 6 |
N.S. |
1 | 0.46 | 0.46 | 0.54 | 0.46 | 0.46 | 0.38 | 0.54 | 0.46 | 0.46 |
time (sec) |
N/A | 0.146 | 0.001 | 0.022 | 0.027 | 0.066 | 0.029 | 0.112 | 0.186 | 0.008 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 34 | 32 | 357 | 30 | 27 | 0 | 62 | 46 |
N.S. |
1 | 0.00 | 1.03 | 0.97 | 10.82 | 0.91 | 0.82 | 0.00 | 1.88 | 1.39 |
time (sec) |
N/A | 0.000 | 0.151 | 0.967 | 0.232 | 0.088 | 11.844 | 0.000 | 0.187 | 3.148 |
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 | 17 | 16 | 14 | 14 | 14 | 14 | 14 | 15 | 14 |
N.S. |
1 | 0.77 | 0.73 | 0.64 | 0.64 | 0.64 | 0.64 | 0.64 | 0.68 | 0.64 |
time (sec) |
N/A | 0.325 | 0.018 | 0.061 | 0.035 | 0.082 | 0.044 | 0.116 | 0.186 | 0.038 |
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 | 16 | 22 | 22 | 16 | 79 | 21 | 15 | 25 | 25 | 21 |
N.S. |
1 | 1.38 | 1.38 | 1.00 | 4.94 | 1.31 | 0.94 | 1.56 | 1.56 | 1.31 |
time (sec) |
N/A | 0.421 | 0.019 | 1.123 | 0.032 | 0.097 | 0.083 | 0.121 | 0.195 | 2.728 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 98 | 51 | 44 | 81 | 40 | 48 | 41 | 44 | 42 |
N.S. |
1 | 2.97 | 1.55 | 1.33 | 2.45 | 1.21 | 1.45 | 1.24 | 1.33 | 1.27 |
time (sec) |
N/A | 0.355 | 0.012 | 0.510 | 0.038 | 0.081 | 0.136 | 0.115 | 0.182 | 2.626 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 58 | 24 | 16 | 15 | 30 | 15 | 34 | 43 | 19 |
N.S. |
1 | 3.05 | 1.26 | 0.84 | 0.79 | 1.58 | 0.79 | 1.79 | 2.26 | 1.00 |
time (sec) |
N/A | 0.403 | 0.287 | 0.366 | 0.160 | 0.085 | 0.070 | 0.116 | 0.194 | 0.087 |
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 | 21 | 21 | 30 | 34 | 19 | 30 | 37 | 20 |
N.S. |
1 | 0.00 | 0.84 | 0.84 | 1.20 | 1.36 | 0.76 | 1.20 | 1.48 | 0.80 |
time (sec) |
N/A | 0.000 | 0.127 | 0.556 | 0.062 | 0.084 | 0.076 | 0.125 | 0.183 | 3.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 42 | 40 | 28 | 40 | 23 | 27 | 28 | 23 | 16 |
N.S. |
1 | 2.62 | 2.50 | 1.75 | 2.50 | 1.44 | 1.69 | 1.75 | 1.44 | 1.00 |
time (sec) |
N/A | 0.235 | 0.015 | 0.391 | 0.028 | 0.088 | 0.067 | 0.110 | 0.189 | 2.902 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | F | A | A | F | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 0 | 40 | 0 | 42 | 34 | 0 | 41 | 38 |
N.S. |
1 | 0.00 | 0.00 | 1.54 | 0.00 | 1.62 | 1.31 | 0.00 | 1.58 | 1.46 |
time (sec) |
N/A | 0.000 | 0.000 | 3.551 | 0.000 | 0.097 | 0.443 | 0.000 | 0.212 | 3.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 22 | 22 | 28 | 51 | 28 | 54 | 25 | 75 | 29 |
N.S. |
1 | 1.22 | 1.22 | 1.56 | 2.83 | 1.56 | 3.00 | 1.39 | 4.17 | 1.61 |
time (sec) |
N/A | 0.283 | 0.021 | 0.374 | 0.160 | 0.086 | 0.401 | 0.122 | 0.193 | 2.739 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 61 | 51 | 24 | 183 | 16 | 31 | 58 | 66 | 16 |
N.S. |
1 | 2.77 | 2.32 | 1.09 | 8.32 | 0.73 | 1.41 | 2.64 | 3.00 | 0.73 |
time (sec) |
N/A | 0.376 | 0.038 | 0.441 | 0.121 | 0.100 | 0.129 | 0.133 | 0.187 | 3.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 36 | 36 | 29 | 64 | 36 | 42 | 35 | 37 | 192 |
N.S. |
1 | 1.29 | 1.29 | 1.04 | 2.29 | 1.29 | 1.50 | 1.25 | 1.32 | 6.86 |
time (sec) |
N/A | 1.262 | 0.758 | 3.244 | 0.150 | 0.081 | 0.164 | 0.114 | 0.191 | 3.161 |
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 | 21 | 21 | 21 | 20 | 23 | 14 | 23 | 23 | 20 |
N.S. |
1 | 0.95 | 0.95 | 0.95 | 0.91 | 1.05 | 0.64 | 1.05 | 1.05 | 0.91 |
time (sec) |
N/A | 0.192 | 0.010 | 0.209 | 0.030 | 0.088 | 0.050 | 0.112 | 0.188 | 2.717 |
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 | 18 | 11 | 11 | 16 | 10 | 14 | 10 | 16 | 14 |
N.S. |
1 | 1.50 | 0.92 | 0.92 | 1.33 | 0.83 | 1.17 | 0.83 | 1.33 | 1.17 |
time (sec) |
N/A | 0.161 | 0.027 | 0.047 | 0.027 | 0.078 | 0.044 | 0.111 | 0.184 | 0.036 |
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 | 32 | 0 | 33 | 31 | 28 | 28 | 42 | 43 | 31 | 0 |
N.S. |
1 | 0.00 | 1.03 | 0.97 | 0.88 | 0.88 | 1.31 | 1.34 | 0.97 | 0.00 |
time (sec) |
N/A | 0.000 | 4.045 | 0.331 | 0.113 | 0.088 | 0.140 | 0.681 | 0.202 | 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 | 30 | 0 | 23 | 28 | 23 | 23 | 24 | 23 | 35 | 26 |
N.S. |
1 | 0.00 | 0.77 | 0.93 | 0.77 | 0.77 | 0.80 | 0.77 | 1.17 | 0.87 |
time (sec) |
N/A | 0.000 | 1.428 | 0.606 | 0.143 | 0.087 | 0.279 | 0.119 | 0.229 | 2.699 |
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 | 22 | 0 | 20 | 20 | 18 | 18 | 17 | 18 | 20 | 0 |
N.S. |
1 | 0.00 | 0.91 | 0.91 | 0.82 | 0.82 | 0.77 | 0.82 | 0.91 | 0.00 |
time (sec) |
N/A | 0.000 | 0.194 | 0.739 | 0.085 | 0.079 | 0.121 | 0.137 | 0.185 | 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 | 17 | 14 | 12 | 10 | 13 | 13 | 10 | 13 | 8 | 12 |
N.S. |
1 | 0.82 | 0.71 | 0.59 | 0.76 | 0.76 | 0.59 | 0.76 | 0.47 | 0.71 |
time (sec) |
N/A | 0.138 | 0.000 | 0.024 | 0.026 | 0.059 | 0.021 | 0.119 | 0.190 | 2.583 |
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 | 29 | 0 | 30 | 24 | 23 | 36 | 22 | 45 | 50 | 0 |
N.S. |
1 | 0.00 | 1.03 | 0.83 | 0.79 | 1.24 | 0.76 | 1.55 | 1.72 | 0.00 |
time (sec) |
N/A | 0.000 | 3.690 | 0.311 | 0.096 | 0.090 | 0.079 | 0.134 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 0 | 46 | 43 | 28 | 31 | 40 | 42 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.70 | 1.59 | 1.04 | 1.15 | 1.48 | 1.56 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 1.582 | 0.087 | 0.082 | 0.110 | 0.136 | 0.197 | 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 | 11 | 9 | 9 | 8 | 7 | 7 | 5 | 7 | 11 | 8 |
N.S. |
1 | 0.82 | 0.82 | 0.73 | 0.64 | 0.64 | 0.45 | 0.64 | 1.00 | 0.73 |
time (sec) |
N/A | 0.181 | 0.007 | 0.027 | 0.032 | 0.071 | 0.047 | 0.108 | 0.195 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 33 | 20 | 29 | 40 | 26 | 34 | 32 | 35 | 33 |
N.S. |
1 | 1.27 | 0.77 | 1.12 | 1.54 | 1.00 | 1.31 | 1.23 | 1.35 | 1.27 |
time (sec) |
N/A | 0.247 | 0.021 | 0.386 | 0.060 | 0.081 | 0.080 | 0.117 | 0.192 | 2.676 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 29 | 30 | 0 | 29 | 26 | 29 | 94 | 31 |
N.S. |
1 | 0.00 | 0.88 | 0.91 | 0.00 | 0.88 | 0.79 | 0.88 | 2.85 | 0.94 |
time (sec) |
N/A | 0.000 | 0.073 | 0.845 | 0.000 | 0.082 | 0.146 | 0.146 | 0.196 | 2.938 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 69 | 12 | 11 | 39 | 13 | 10 | 13 | 13 | 13 |
N.S. |
1 | 3.45 | 0.60 | 0.55 | 1.95 | 0.65 | 0.50 | 0.65 | 0.65 | 0.65 |
time (sec) |
N/A | 0.418 | 0.017 | 0.131 | 0.032 | 0.077 | 0.049 | 0.115 | 0.198 | 2.645 |
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 | 14 | 24 | 21 | 22 | 148 | 21 | 24 | 21 | 175 | 21 |
N.S. |
1 | 1.71 | 1.50 | 1.57 | 10.57 | 1.50 | 1.71 | 1.50 | 12.50 | 1.50 |
time (sec) |
N/A | 0.421 | 0.043 | 2.112 | 0.165 | 0.085 | 0.073 | 0.133 | 0.187 | 0.354 |
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 | 27 | 24 | 26 | 25 | 26 | 19 | 25 | 26 | 27 |
N.S. |
1 | 0.84 | 0.75 | 0.81 | 0.78 | 0.81 | 0.59 | 0.78 | 0.81 | 0.84 |
time (sec) |
N/A | 0.222 | 0.006 | 0.053 | 0.031 | 0.068 | 0.044 | 0.108 | 0.190 | 2.791 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 0 | 42 | 53 | 45 | 36 | 51 | 52 | 48 |
N.S. |
1 | 0.00 | 0.00 | 1.14 | 1.43 | 1.22 | 0.97 | 1.38 | 1.41 | 1.30 |
time (sec) |
N/A | 0.000 | 0.000 | 110.589 | 0.194 | 0.090 | 0.538 | 0.221 | 0.410 | 0.373 |
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 | 10 | 15 | 15 | 9 | 14 | 14 | 17 | 14 | 12 | 8 |
N.S. |
1 | 1.50 | 1.50 | 0.90 | 1.40 | 1.40 | 1.70 | 1.40 | 1.20 | 0.80 |
time (sec) |
N/A | 0.144 | 0.001 | 0.036 | 0.028 | 0.077 | 0.019 | 0.116 | 0.189 | 2.560 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 25 | 23 | 102 | 21 | 24 | 80 | 25 | 149 |
N.S. |
1 | 0.00 | 0.96 | 0.88 | 3.92 | 0.81 | 0.92 | 3.08 | 0.96 | 5.73 |
time (sec) |
N/A | 0.000 | 0.185 | 0.687 | 0.180 | 0.077 | 0.124 | 0.251 | 0.187 | 3.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 31 | 27 | 78 | 23 | 26 | 24 | 23 | 30 | 30 |
N.S. |
1 | 1.11 | 0.96 | 2.79 | 0.82 | 0.93 | 0.86 | 0.82 | 1.07 | 1.07 |
time (sec) |
N/A | 0.647 | 0.028 | 103.882 | 0.191 | 0.083 | 0.351 | 0.137 | 0.198 | 2.958 |
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 | 21 | 22 | 63 | 21 | 22 | 24 | 24 | 21 |
N.S. |
1 | 0.00 | 0.81 | 0.85 | 2.42 | 0.81 | 0.85 | 0.92 | 0.92 | 0.81 |
time (sec) |
N/A | 0.000 | 0.090 | 0.421 | 0.212 | 0.097 | 0.228 | 0.214 | 0.185 | 2.719 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 35 | 30 | 65 | 31 | 24 | 31 | 363 | 29 |
N.S. |
1 | 0.00 | 1.17 | 1.00 | 2.17 | 1.03 | 0.80 | 1.03 | 12.10 | 0.97 |
time (sec) |
N/A | 0.000 | 5.045 | 0.139 | 0.147 | 0.092 | 0.098 | 0.119 | 0.325 | 2.734 |
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 | 34 | 27 | 27 | 31 | 31 | 24 | 31 | 28 | 26 |
N.S. |
1 | 1.36 | 1.08 | 1.08 | 1.24 | 1.24 | 0.96 | 1.24 | 1.12 | 1.04 |
time (sec) |
N/A | 0.187 | 0.133 | 0.145 | 0.028 | 0.083 | 0.088 | 0.115 | 0.190 | 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 | 13 | 10 | 19 | 7 | 8 | 8 | 7 | 13 | 7 | 6 |
N.S. |
1 | 0.77 | 1.46 | 0.54 | 0.62 | 0.62 | 0.54 | 1.00 | 0.54 | 0.46 |
time (sec) |
N/A | 0.144 | 0.002 | 0.059 | 0.030 | 0.067 | 0.042 | 0.114 | 0.186 | 2.718 |
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 | 32 | 0 | 49 | 46 | 44 | 44 | 42 | 46 | 52 | 0 |
N.S. |
1 | 0.00 | 1.53 | 1.44 | 1.38 | 1.38 | 1.31 | 1.44 | 1.62 | 0.00 |
time (sec) |
N/A | 0.000 | 0.137 | 60.465 | 0.284 | 0.082 | 5.357 | 1.177 | 0.409 | 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 | 21 | 21 | 21 | 16 | 15 | 17 | 17 | 17 | 15 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.76 | 0.71 | 0.81 | 0.81 | 0.81 | 0.71 | 0.71 |
time (sec) |
N/A | 0.221 | 0.005 | 0.067 | 0.025 | 0.070 | 0.040 | 0.113 | 0.184 | 0.024 |
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 | 32 | 0 | 31 | 30 | 50 | 66 | 34 | 54 | 49 | 48 |
N.S. |
1 | 0.00 | 0.97 | 0.94 | 1.56 | 2.06 | 1.06 | 1.69 | 1.53 | 1.50 |
time (sec) |
N/A | 0.000 | 0.065 | 0.128 | 0.088 | 0.085 | 0.104 | 0.144 | 0.283 | 3.251 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 174 | 32 | 36 | 368 | 86 | 105 | 103 | 89 | 31 |
N.S. |
1 | 6.69 | 1.23 | 1.38 | 14.15 | 3.31 | 4.04 | 3.96 | 3.42 | 1.19 |
time (sec) |
N/A | 0.828 | 1.302 | 0.293 | 0.052 | 0.081 | 0.105 | 0.124 | 0.185 | 3.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 66 | 23 | 106 | 113 | 60 | 130 | 394 | 0 |
N.S. |
1 | 0.00 | 2.36 | 0.82 | 3.79 | 4.04 | 2.14 | 4.64 | 14.07 | 0.00 |
time (sec) |
N/A | 0.000 | 3.730 | 3.258 | 0.105 | 0.088 | 0.185 | 0.394 | 0.199 | 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 | 30 | 26 | 29 | 22 | 19 | 19 | 44 | 19 | 24 | 17 |
N.S. |
1 | 0.87 | 0.97 | 0.73 | 0.63 | 0.63 | 1.47 | 0.63 | 0.80 | 0.57 |
time (sec) |
N/A | 0.177 | 0.003 | 0.087 | 0.026 | 0.081 | 0.082 | 0.115 | 0.199 | 3.077 |
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 | 35 | 0 | 34 | 28 | 27 | 29 | 29 | 0 | 107 | 27 |
N.S. |
1 | 0.00 | 0.97 | 0.80 | 0.77 | 0.83 | 0.83 | 0.00 | 3.06 | 0.77 |
time (sec) |
N/A | 0.000 | 0.163 | 0.103 | 0.495 | 0.089 | 22.717 | 0.000 | 200.034 | 3.411 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 299 | 158 | 47 | 606 | 45 | 51 | 45 | 165 | 400 |
N.S. |
1 | 11.50 | 6.08 | 1.81 | 23.31 | 1.73 | 1.96 | 1.73 | 6.35 | 15.38 |
time (sec) |
N/A | 0.827 | 0.257 | 1.769 | 0.119 | 0.094 | 0.105 | 0.120 | 0.196 | 0.724 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | B | C | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 217 | 111 | 128 | 219 | 131 | 122 | 230 | 225 | 207 |
N.S. |
1 | 7.48 | 3.83 | 4.41 | 7.55 | 4.52 | 4.21 | 7.93 | 7.76 | 7.14 |
time (sec) |
N/A | 1.609 | 0.053 | 7.668 | 0.097 | 0.084 | 0.128 | 0.127 | 0.169 | 3.584 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 66 | 60 | 80 | 67 | 151 | 76 | 16 | 186 | 84 |
N.S. |
1 | 3.00 | 2.73 | 3.64 | 3.05 | 6.86 | 3.45 | 0.73 | 8.45 | 3.82 |
time (sec) |
N/A | 0.467 | 0.037 | 0.592 | 0.038 | 0.076 | 0.551 | 0.118 | 0.168 | 3.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 39 | 39 | 39 | 36 | 36 | 36 | 38 | 232 | 36 |
N.S. |
1 | 1.86 | 1.86 | 1.86 | 1.71 | 1.71 | 1.71 | 1.81 | 11.05 | 1.71 |
time (sec) |
N/A | 0.504 | 0.035 | 0.569 | 0.035 | 0.083 | 5.219 | 0.130 | 0.173 | 3.026 |
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 | 20 | 11 | 9 | 8 | 9 | 9 | 7 | 9 | 7 | 7 |
N.S. |
1 | 0.55 | 0.45 | 0.40 | 0.45 | 0.45 | 0.35 | 0.45 | 0.35 | 0.35 |
time (sec) |
N/A | 0.132 | 0.000 | 0.018 | 0.029 | 0.059 | 0.021 | 0.114 | 0.171 | 0.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | A | B | A | A | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 3127 | 49 | 29 | 60 | 28 | 24 | 60 | 24 | 25 |
N.S. |
1 | 130.29 | 2.04 | 1.21 | 2.50 | 1.17 | 1.00 | 2.50 | 1.00 | 1.04 |
time (sec) |
N/A | 7.142 | 1.139 | 2.105 | 0.640 | 0.081 | 0.101 | 0.309 | 0.178 | 3.239 |