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 | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 48 | 24 | 28 | 35 | 43 | 31 | 24 | 44 | 25 |
N.S. |
1 | 2.00 | 1.00 | 1.17 | 1.46 | 1.79 | 1.29 | 1.00 | 1.83 | 1.04 |
time (sec) |
N/A | 0.295 | 0.014 | 0.392 | 0.034 | 0.080 | 0.130 | 0.123 | 0.171 | 3.764 |
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 | 26 | 95 | 21 | 25 | 29 | 23 | 0 | 29 | 35 | 32 |
N.S. |
1 | 3.65 | 0.81 | 0.96 | 1.12 | 0.88 | 0.00 | 1.12 | 1.35 | 1.23 |
time (sec) |
N/A | 0.550 | 0.435 | 1.302 | 0.160 | 0.096 | 0.000 | 0.152 | 0.291 | 3.803 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 27 | 29 | 0 | 52 | 0 | 27 | 74 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.94 | 0.00 | 1.68 | 0.00 | 0.87 | 2.39 | 0.00 |
time (sec) |
N/A | 0.929 | 0.123 | 0.254 | 0.000 | 0.077 | 0.000 | 0.152 | 0.751 | 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 | 31 | 36 | 30 | 28 | 40 | 40 | 48 | 40 | 41 | 40 |
N.S. |
1 | 1.16 | 0.97 | 0.90 | 1.29 | 1.29 | 1.55 | 1.29 | 1.32 | 1.29 |
time (sec) |
N/A | 0.360 | 0.055 | 0.425 | 0.139 | 0.101 | 0.080 | 0.155 | 0.164 | 3.708 |
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 | 19 | 0 | 22 | 20 | 32 | 32 | 17 | 32 | 37 | 19 |
N.S. |
1 | 0.00 | 1.16 | 1.05 | 1.68 | 1.68 | 0.89 | 1.68 | 1.95 | 1.00 |
time (sec) |
N/A | 0.000 | 0.175 | 0.131 | 0.150 | 0.076 | 0.056 | 0.119 | 0.199 | 3.690 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 22 | 0 | 24 | 22 | 50 | 84 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.00 | 1.00 | 0.92 | 2.08 | 3.50 | 1.17 |
time (sec) |
N/A | 0.598 | 0.303 | 0.254 | 0.000 | 0.090 | 0.089 | 0.121 | 0.184 | 0.114 |
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 | 6 | 6 | 6 | 5 | 5 | 7 | 5 | 6 | 5 |
N.S. |
1 | 0.38 | 0.38 | 0.38 | 0.31 | 0.31 | 0.44 | 0.31 | 0.38 | 0.31 |
time (sec) |
N/A | 0.124 | 0.000 | 0.008 | 0.030 | 0.061 | 0.014 | 0.122 | 0.189 | 0.002 |
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 | 19 | 0 | 19 | 20 | 20 | 19 | 17 | 50 | 19 | 19 |
N.S. |
1 | 0.00 | 1.00 | 1.05 | 1.05 | 1.00 | 0.89 | 2.63 | 1.00 | 1.00 |
time (sec) |
N/A | 0.000 | 0.062 | 0.116 | 0.077 | 0.074 | 0.155 | 0.123 | 0.185 | 0.545 |
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 | 15 | 13 | 12 | 11 | 11 | 10 | 11 | 13 | 11 |
N.S. |
1 | 1.07 | 0.93 | 0.86 | 0.79 | 0.79 | 0.71 | 0.79 | 0.93 | 0.79 |
time (sec) |
N/A | 0.147 | 0.002 | 0.047 | 0.029 | 0.079 | 0.046 | 0.119 | 0.199 | 3.765 |
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 | 16 | 16 | 12 | 11 | 11 | 17 | 12 | 12 | 11 |
N.S. |
1 | 0.80 | 0.80 | 0.60 | 0.55 | 0.55 | 0.85 | 0.60 | 0.60 | 0.55 |
time (sec) |
N/A | 0.134 | 0.001 | 0.059 | 0.043 | 0.067 | 0.033 | 0.116 | 0.176 | 0.136 |
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 | 29 | 36 | 30 | 43 | 69 | 29 | 24 | 25 | 40 | 35 |
N.S. |
1 | 1.24 | 1.03 | 1.48 | 2.38 | 1.00 | 0.83 | 0.86 | 1.38 | 1.21 |
time (sec) |
N/A | 0.532 | 0.052 | 0.345 | 0.070 | 0.088 | 0.063 | 0.133 | 0.180 | 3.697 |
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 | 16 | 14 | 13 | 21 | 12 | 13 | 29 | 13 |
N.S. |
1 | 1.00 | 0.76 | 0.67 | 0.62 | 1.00 | 0.57 | 0.62 | 1.38 | 0.62 |
time (sec) |
N/A | 0.228 | 0.009 | 0.066 | 0.039 | 0.073 | 0.046 | 0.116 | 0.184 | 3.644 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 0 | 14 | 30 | 32 | 32 | 32 | 67 | 47 | 43 |
N.S. |
1 | 0.00 | 1.00 | 2.14 | 2.29 | 2.29 | 2.29 | 4.79 | 3.36 | 3.07 |
time (sec) |
N/A | 0.000 | 0.029 | 0.128 | 0.046 | 0.083 | 1.552 | 0.138 | 0.237 | 3.781 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 47 | 25 | 44 | 61 | 25 | 41 | 83 | 26 | 0 |
N.S. |
1 | 1.81 | 0.96 | 1.69 | 2.35 | 0.96 | 1.58 | 3.19 | 1.00 | 0.00 |
time (sec) |
N/A | 1.127 | 5.042 | 1.277 | 0.152 | 0.082 | 2.366 | 0.194 | 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 | 14 | 14 | 14 | 18 | 22 | 22 | 14 | 17 | 37 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.29 | 1.57 | 1.57 | 1.00 | 1.21 | 2.64 | 1.21 |
time (sec) |
N/A | 0.358 | 0.014 | 0.211 | 0.081 | 0.067 | 0.061 | 0.129 | 0.181 | 3.732 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 32 | 31 | 28 | 28 | 27 | 0 | 31 | 28 |
N.S. |
1 | 0.00 | 1.14 | 1.11 | 1.00 | 1.00 | 0.96 | 0.00 | 1.11 | 1.00 |
time (sec) |
N/A | 0.000 | 1.823 | 2.391 | 0.113 | 0.088 | 1.883 | 0.000 | 0.182 | 3.876 |
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 | 21 | 21 | 20 | 22 | 22 | 27 | 22 | 18 | 20 |
N.S. |
1 | 1.17 | 1.17 | 1.11 | 1.22 | 1.22 | 1.50 | 1.22 | 1.00 | 1.11 |
time (sec) |
N/A | 0.141 | 0.002 | 0.045 | 0.034 | 0.062 | 0.020 | 0.124 | 0.195 | 3.699 |
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 | 13 | 0 | 13 | 13 | 12 | 13 | 8 | 12 | 19 | 12 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 0.92 | 1.00 | 0.62 | 0.92 | 1.46 | 0.92 |
time (sec) |
N/A | 0.000 | 0.180 | 0.080 | 0.074 | 0.073 | 0.050 | 0.123 | 0.191 | 3.806 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 48 | 53 | 51 | 51 | 47 | 51 | 56 | 57 | 47 |
N.S. |
1 | 1.60 | 1.77 | 1.70 | 1.70 | 1.57 | 1.70 | 1.87 | 1.90 | 1.57 |
time (sec) |
N/A | 0.239 | 0.014 | 0.104 | 0.037 | 0.081 | 0.330 | 0.120 | 0.177 | 3.694 |
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 | 27 | 27 | 28 | 28 | 26 | 28 | 27 | 90 |
N.S. |
1 | 0.00 | 1.08 | 1.08 | 1.12 | 1.12 | 1.04 | 1.12 | 1.08 | 3.60 |
time (sec) |
N/A | 0.000 | 0.075 | 0.074 | 0.091 | 0.083 | 0.094 | 0.208 | 0.236 | 3.962 |
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 | 27 | 0 | 27 | 23 | 31 | 38 | 41 | 0 | 327 | 31 |
N.S. |
1 | 0.00 | 1.00 | 0.85 | 1.15 | 1.41 | 1.52 | 0.00 | 12.11 | 1.15 |
time (sec) |
N/A | 0.000 | 1.136 | 5.541 | 0.208 | 0.089 | 0.174 | 0.000 | 0.204 | 4.061 |
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 | 14 | 18 | 17 | 15 | 17 | 13 | 8 | 17 | 14 | 13 |
N.S. |
1 | 1.29 | 1.21 | 1.07 | 1.21 | 0.93 | 0.57 | 1.21 | 1.00 | 0.93 |
time (sec) |
N/A | 0.163 | 0.003 | 0.046 | 0.032 | 0.071 | 0.050 | 0.118 | 0.178 | 3.660 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | F(-1) | A | B | F(-1) |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 0 | 23 | 23 | 31 | 0 | 29 | 27 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.72 | 0.72 | 0.97 | 0.00 | 0.91 | 0.84 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 2.235 | 0.191 | 0.090 | 0.000 | 0.144 | 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 | 20 | 0 | 19 | 17 | 16 | 23 | 17 | 18 | 19 | 16 |
N.S. |
1 | 0.00 | 0.95 | 0.85 | 0.80 | 1.15 | 0.85 | 0.90 | 0.95 | 0.80 |
time (sec) |
N/A | 0.000 | 0.046 | 0.156 | 0.067 | 0.074 | 0.091 | 0.128 | 0.185 | 0.180 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | B | B | B |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 25 | 20 | 0 | 22 | 22 | 42 | 27 | 20 |
N.S. |
1 | 0.00 | 0.89 | 0.71 | 0.00 | 0.79 | 0.79 | 1.50 | 0.96 | 0.71 |
time (sec) |
N/A | 0.000 | 0.258 | 0.114 | 0.000 | 0.079 | 0.109 | 0.130 | 0.201 | 0.083 |
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 | 7 | 6 | 6 | 7 | 6 | 6 | 5 | 7 | 6 | 6 |
N.S. |
1 | 0.86 | 0.86 | 1.00 | 0.86 | 0.86 | 0.71 | 1.00 | 0.86 | 0.86 |
time (sec) |
N/A | 0.135 | 0.001 | 0.018 | 0.033 | 0.066 | 0.028 | 0.125 | 0.174 | 0.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 30 | 30 | 43 | 48 | 44 | 111 | 112 | 88 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 1.43 | 1.60 | 1.47 | 3.70 | 3.73 | 2.93 |
time (sec) |
N/A | 0.000 | 0.032 | 0.333 | 0.527 | 0.071 | 0.113 | 0.127 | 200.026 | 3.891 |
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 | 27 | 0 | 41 | 38 | 55 | 41 | 39 | 106 | 67 | 98 |
N.S. |
1 | 0.00 | 1.52 | 1.41 | 2.04 | 1.52 | 1.44 | 3.93 | 2.48 | 3.63 |
time (sec) |
N/A | 0.000 | 4.514 | 0.324 | 0.323 | 0.083 | 0.262 | 0.133 | 0.499 | 3.928 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | F(-2) | A | F(-2) | A | B | F(-1) |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 0 | 36 | 0 | 33 | 0 | 63 | 61 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.06 | 0.00 | 0.97 | 0.00 | 1.85 | 1.79 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 50.970 | 0.000 | 0.114 | 0.000 | 0.501 | 0.179 | 0.000 |
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 | 13 | 11 | 11 | 10 | 26 | 9 | 10 | 26 | 9 | 11 |
N.S. |
1 | 0.85 | 0.85 | 0.77 | 2.00 | 0.69 | 0.77 | 2.00 | 0.69 | 0.85 |
time (sec) |
N/A | 0.142 | 0.003 | 0.041 | 0.031 | 0.079 | 0.038 | 0.120 | 0.157 | 3.910 |
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 | 20 | 20 | 18 | 21 | 20 | 19 | 20 | 22 | 22 |
N.S. |
1 | 0.83 | 0.83 | 0.75 | 0.88 | 0.83 | 0.79 | 0.83 | 0.92 | 0.92 |
time (sec) |
N/A | 0.204 | 0.054 | 0.154 | 0.055 | 0.079 | 0.059 | 0.121 | 0.158 | 3.602 |
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 | 27 | 0 | 26 | 31 | 59 | 57 | 22 | 77 | 178 | 41 |
N.S. |
1 | 0.00 | 0.96 | 1.15 | 2.19 | 2.11 | 0.81 | 2.85 | 6.59 | 1.52 |
time (sec) |
N/A | 0.000 | 0.095 | 0.307 | 0.480 | 0.083 | 0.294 | 1.020 | 0.188 | 4.044 |
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 | 22 | 46 | 41 | 36 | 37 | 37 | 41 | 37 | 25 | 38 |
N.S. |
1 | 2.09 | 1.86 | 1.64 | 1.68 | 1.68 | 1.86 | 1.68 | 1.14 | 1.73 |
time (sec) |
N/A | 0.412 | 0.014 | 0.326 | 0.035 | 0.076 | 0.582 | 0.128 | 0.192 | 0.213 |
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 | 8 | 8 | 6 | 5 | 10 | 5 | 10 | 6 | 12 |
N.S. |
1 | 0.53 | 0.53 | 0.40 | 0.33 | 0.67 | 0.33 | 0.67 | 0.40 | 0.80 |
time (sec) |
N/A | 0.127 | 0.000 | 0.019 | 0.027 | 0.066 | 0.014 | 0.119 | 0.184 | 0.002 |
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 | 35 | 19 | 21 | 20 | 82 | 30 | 15 | 19 | 31 | 18 |
N.S. |
1 | 0.54 | 0.60 | 0.57 | 2.34 | 0.86 | 0.43 | 0.54 | 0.89 | 0.51 |
time (sec) |
N/A | 0.309 | 0.015 | 0.349 | 0.160 | 0.083 | 0.076 | 0.119 | 0.192 | 3.916 |
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 | 18 | 20 | 17 | 18 | 18 | 17 | 18 | 16 | 16 |
N.S. |
1 | 0.95 | 1.05 | 0.89 | 0.95 | 0.95 | 0.89 | 0.95 | 0.84 | 0.84 |
time (sec) |
N/A | 0.153 | 0.001 | 0.042 | 0.027 | 0.063 | 0.018 | 0.122 | 0.211 | 0.039 |
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 | 27 | 25 | 23 | 28 | 22 | 26 | 22 | 21 | 20 |
N.S. |
1 | 1.12 | 1.04 | 0.96 | 1.17 | 0.92 | 1.08 | 0.92 | 0.88 | 0.83 |
time (sec) |
N/A | 1.006 | 0.186 | 0.161 | 0.150 | 0.081 | 0.157 | 0.148 | 0.208 | 4.177 |
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 | 21 | 0 | 29 | 26 | 32 | 32 | 26 | 25 | 32 | 25 |
N.S. |
1 | 0.00 | 1.38 | 1.24 | 1.52 | 1.52 | 1.24 | 1.19 | 1.52 | 1.19 |
time (sec) |
N/A | 0.000 | 1.017 | 6.371 | 0.145 | 0.082 | 0.056 | 0.128 | 0.226 | 0.207 |
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 | 9 | 9 | 10 | 9 | 9 | 7 | 9 | 10 | 9 |
N.S. |
1 | 0.60 | 0.60 | 0.67 | 0.60 | 0.60 | 0.47 | 0.60 | 0.67 | 0.60 |
time (sec) |
N/A | 0.143 | 0.001 | 0.030 | 0.031 | 0.076 | 0.036 | 0.121 | 0.226 | 3.621 |
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 | 16 | 0 | 19 | 21 | 24 | 24 | 19 | 2597 | 25 | 29 |
N.S. |
1 | 0.00 | 1.19 | 1.31 | 1.50 | 1.50 | 1.19 | 162.31 | 1.56 | 1.81 |
time (sec) |
N/A | 0.000 | 0.238 | 0.263 | 0.061 | 0.099 | 0.255 | 0.398 | 0.222 | 3.783 |
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 | 38 | 34 | 23 | 31 | 27 | 26 | 31 | 33 | 22 |
N.S. |
1 | 1.73 | 1.55 | 1.05 | 1.41 | 1.23 | 1.18 | 1.41 | 1.50 | 1.00 |
time (sec) |
N/A | 0.226 | 0.011 | 0.122 | 0.028 | 0.076 | 0.084 | 0.124 | 0.204 | 0.084 |
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 | 27 | 0 | 29 | 23 | 29 | 29 | 24 | 29 | 29 | 24 |
N.S. |
1 | 0.00 | 1.07 | 0.85 | 1.07 | 1.07 | 0.89 | 1.07 | 1.07 | 0.89 |
time (sec) |
N/A | 0.000 | 7.484 | 0.191 | 0.084 | 0.078 | 0.071 | 0.138 | 0.223 | 3.741 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | F | B | B | B | F | B | F(-1) |
verified | N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 440 | 0 | 339 | 364 | 600 | 0 | 957 | 0 |
N.S. |
1 | 0.00 | 11.89 | 0.00 | 9.16 | 9.84 | 16.22 | 0.00 | 25.86 | 0.00 |
time (sec) |
N/A | 0.000 | 0.245 | 0.000 | 0.122 | 0.103 | 13.353 | 0.000 | 0.318 | 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 | 17 | 13 | 9 | 9 | 15 | 8 | 7 | 8 | 9 | 8 |
N.S. |
1 | 0.76 | 0.53 | 0.53 | 0.88 | 0.47 | 0.41 | 0.47 | 0.53 | 0.47 |
time (sec) |
N/A | 0.182 | 0.030 | 0.056 | 0.060 | 0.076 | 0.044 | 0.125 | 0.230 | 0.046 |
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 | 25 | 62 | 25 | 23 | 129 | 22 | 27 | 27 | 52 | 23 |
N.S. |
1 | 2.48 | 1.00 | 0.92 | 5.16 | 0.88 | 1.08 | 1.08 | 2.08 | 0.92 |
time (sec) |
N/A | 0.570 | 0.036 | 0.259 | 0.041 | 0.081 | 0.121 | 0.122 | 0.199 | 3.888 |
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 | 11 | 10 | 10 | 10 | 10 | 10 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.71 | 0.71 | 0.71 | 0.71 | 0.71 | 0.71 |
time (sec) |
N/A | 0.158 | 0.003 | 0.039 | 0.029 | 0.072 | 0.044 | 0.117 | 0.216 | 3.593 |
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 | 24 | 16 | 19 | 13 | 18 | 14 | 18 | 25 | 13 |
N.S. |
1 | 1.41 | 0.94 | 1.12 | 0.76 | 1.06 | 0.82 | 1.06 | 1.47 | 0.76 |
time (sec) |
N/A | 0.278 | 0.073 | 0.136 | 0.099 | 0.077 | 0.063 | 0.128 | 0.887 | 3.619 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | F | B | F(-1) |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 0 | 43 | 39 | 35 | 41 | 0 | 37 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.30 | 1.18 | 1.06 | 1.24 | 0.00 | 1.12 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 4.493 | 0.163 | 0.091 | 0.203 | 0.000 | 0.190 | 0.000 |
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 | 25 | 127 | 78 | 88 | 82 | 77 | 90 | 81 | 85 | 82 |
N.S. |
1 | 5.08 | 3.12 | 3.52 | 3.28 | 3.08 | 3.60 | 3.24 | 3.40 | 3.28 |
time (sec) |
N/A | 0.349 | 0.171 | 0.882 | 0.114 | 0.078 | 0.109 | 0.124 | 0.235 | 0.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | A | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 17 | 15 | 16 | 50 | 17 | 14 | 144 | 14 |
N.S. |
1 | 0.00 | 0.74 | 0.65 | 0.70 | 2.17 | 0.74 | 0.61 | 6.26 | 0.61 |
time (sec) |
N/A | 0.000 | 0.417 | 1.391 | 0.225 | 0.088 | 0.698 | 0.125 | 0.213 | 3.672 |
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 | 27 | 19 | 17 | 21 | 16 | 15 | 24 | 20 | 16 |
N.S. |
1 | 1.50 | 1.06 | 0.94 | 1.17 | 0.89 | 0.83 | 1.33 | 1.11 | 0.89 |
time (sec) |
N/A | 0.227 | 0.068 | 0.161 | 0.102 | 0.100 | 0.057 | 0.116 | 0.182 | 0.139 |
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 | 16 | 16 | 15 | 14 | 16 | 15 | 16 | 18 | 14 |
N.S. |
1 | 0.80 | 0.80 | 0.75 | 0.70 | 0.80 | 0.75 | 0.80 | 0.90 | 0.70 |
time (sec) |
N/A | 0.164 | 0.004 | 0.084 | 0.029 | 0.095 | 0.049 | 0.122 | 0.179 | 0.067 |
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 | 23 | 15 | 12 | 15 | 15 | 10 | 15 | 11 | 12 |
N.S. |
1 | 1.53 | 1.00 | 0.80 | 1.00 | 1.00 | 0.67 | 1.00 | 0.73 | 0.80 |
time (sec) |
N/A | 0.142 | 0.000 | 0.033 | 0.025 | 0.063 | 0.018 | 0.123 | 0.215 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 26 | 22 | 34 | 34 | 15 | 0 | 36 | 21 |
N.S. |
1 | 0.00 | 0.81 | 0.69 | 1.06 | 1.06 | 0.47 | 0.00 | 1.12 | 0.66 |
time (sec) |
N/A | 0.000 | 0.053 | 1.725 | 0.074 | 0.086 | 0.084 | 0.000 | 0.182 | 3.943 |
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 | 29 | 48 | 50 | 28 | 27 | 38 | 39 | 28 | 41 | 29 |
N.S. |
1 | 1.66 | 1.72 | 0.97 | 0.93 | 1.31 | 1.34 | 0.97 | 1.41 | 1.00 |
time (sec) |
N/A | 0.203 | 0.015 | 0.096 | 0.035 | 0.078 | 0.155 | 0.122 | 0.182 | 0.108 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 21 | 15 | 12 | 11 | 31 | 12 | 11 | 43 | 11 |
N.S. |
1 | 1.31 | 0.94 | 0.75 | 0.69 | 1.94 | 0.75 | 0.69 | 2.69 | 0.69 |
time (sec) |
N/A | 0.193 | 0.021 | 0.039 | 0.035 | 0.081 | 0.080 | 0.125 | 0.213 | 0.081 |
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 | 8 | 23 | 7 | 17 | 17 | 15 | 15 | 17 | 6 |
N.S. |
1 | 0.27 | 0.77 | 0.23 | 0.57 | 0.57 | 0.50 | 0.50 | 0.57 | 0.20 |
time (sec) |
N/A | 0.129 | 0.003 | 0.046 | 0.027 | 0.071 | 0.048 | 0.121 | 0.198 | 0.098 |
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 | 23 | 22 | 26 | 26 | 27 | 182 | 29 | 26 |
N.S. |
1 | 0.00 | 0.88 | 0.85 | 1.00 | 1.00 | 1.04 | 7.00 | 1.12 | 1.00 |
time (sec) |
N/A | 0.000 | 1.493 | 0.263 | 0.177 | 0.079 | 0.103 | 0.357 | 0.179 | 3.765 |
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 | 23 | 0 | 33 | 40 | 39 | 39 | 29 | 38 | 38 | 41 |
N.S. |
1 | 0.00 | 1.43 | 1.74 | 1.70 | 1.70 | 1.26 | 1.65 | 1.65 | 1.78 |
time (sec) |
N/A | 0.000 | 0.113 | 1.649 | 0.073 | 0.098 | 0.080 | 0.115 | 0.182 | 3.757 |
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 | 36 | 16 | 15 | 16 | 16 | 16 |
N.S. |
1 | 0.76 | 0.76 | 0.81 | 1.71 | 0.76 | 0.71 | 0.76 | 0.76 | 0.76 |
time (sec) |
N/A | 0.171 | 0.005 | 0.121 | 0.034 | 0.080 | 0.046 | 0.121 | 0.186 | 3.671 |
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 | 21 | 19 | 17 | 20 | 20 | 34 | 20 | 17 | 18 |
N.S. |
1 | 1.05 | 0.95 | 0.85 | 1.00 | 1.00 | 1.70 | 1.00 | 0.85 | 0.90 |
time (sec) |
N/A | 0.141 | 0.001 | 0.048 | 0.032 | 0.074 | 0.026 | 0.121 | 0.220 | 0.222 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | F(-1) | A | F | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 0 | 26 | 44 | 24 | 0 | 40 | 64 | 42 |
N.S. |
1 | 0.00 | 0.00 | 0.90 | 1.52 | 0.83 | 0.00 | 1.38 | 2.21 | 1.45 |
time (sec) |
N/A | 0.000 | 0.000 | 0.275 | 0.225 | 0.086 | 0.000 | 0.185 | 200.033 | 3.755 |
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 | 26 | 36 | 21 | 41 | 35 | 35 | 19 | 35 | 36 | 0 |
N.S. |
1 | 1.38 | 0.81 | 1.58 | 1.35 | 1.35 | 0.73 | 1.35 | 1.38 | 0.00 |
time (sec) |
N/A | 0.592 | 0.113 | 1.461 | 0.121 | 0.086 | 0.083 | 0.126 | 0.178 | 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 | 11 | 0 | 9 | 8 | 7 | 7 | 7 | 7 | 9 | 7 |
N.S. |
1 | 0.00 | 0.82 | 0.73 | 0.64 | 0.64 | 0.64 | 0.64 | 0.82 | 0.64 |
time (sec) |
N/A | 0.000 | 0.003 | 0.038 | 0.078 | 0.084 | 0.072 | 0.118 | 0.165 | 0.057 |
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 | 19 | 18 | 16 | 20 | 18 | 18 | 9 |
N.S. |
1 | 0.90 | 0.90 | 0.95 | 0.90 | 0.80 | 1.00 | 0.90 | 0.90 | 0.45 |
time (sec) |
N/A | 0.171 | 0.003 | 0.090 | 0.033 | 0.092 | 0.054 | 0.122 | 0.171 | 3.545 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F(-1) | A | B | A | F | B | B |
verified | N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 31 | 0 | 36 | 82 | 27 | 0 | 68 | 36 |
N.S. |
1 | 0.00 | 1.00 | 0.00 | 1.16 | 2.65 | 0.87 | 0.00 | 2.19 | 1.16 |
time (sec) |
N/A | 0.000 | 0.211 | 0.000 | 0.231 | 0.101 | 0.721 | 0.000 | 6.874 | 4.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 18 | 48 | 70 | 692 | 91 | 141 | 111 | 103 | 62 |
N.S. |
1 | 1.06 | 2.82 | 4.12 | 40.71 | 5.35 | 8.29 | 6.53 | 6.06 | 3.65 |
time (sec) |
N/A | 0.329 | 0.157 | 0.286 | 0.062 | 0.093 | 0.105 | 0.136 | 0.180 | 3.926 |
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 | 11 | 25 | 11 | 12 | 27 | 11 | 8 | 15 | 12 | 11 |
N.S. |
1 | 2.27 | 1.00 | 1.09 | 2.45 | 1.00 | 0.73 | 1.36 | 1.09 | 1.00 |
time (sec) |
N/A | 0.182 | 0.039 | 0.078 | 0.027 | 0.067 | 0.048 | 0.127 | 0.179 | 3.550 |
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 | 30 | 32 | 25 | 23 | 23 | 24 | 23 | 28 | 25 |
N.S. |
1 | 1.50 | 1.60 | 1.25 | 1.15 | 1.15 | 1.20 | 1.15 | 1.40 | 1.25 |
time (sec) |
N/A | 0.167 | 0.022 | 0.186 | 0.034 | 0.084 | 0.046 | 0.123 | 0.180 | 3.550 |
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 | 15 | 23 | 16 | 17 | 17 | 15 | 17 | 15 | 16 |
N.S. |
1 | 0.94 | 1.44 | 1.00 | 1.06 | 1.06 | 0.94 | 1.06 | 0.94 | 1.00 |
time (sec) |
N/A | 0.144 | 0.002 | 0.042 | 0.030 | 0.067 | 0.017 | 0.122 | 0.196 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | B | A | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 85 | 77 | 76 | 51 | 47 | 41 | 89 | 95 | 42 |
N.S. |
1 | 2.66 | 2.41 | 2.38 | 1.59 | 1.47 | 1.28 | 2.78 | 2.97 | 1.31 |
time (sec) |
N/A | 0.716 | 0.066 | 0.014 | 0.074 | 0.085 | 0.167 | 0.137 | 0.197 | 3.661 |
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 | 4 | 2 | 2 | 3 | 2 | 2 | 2 | 3 | 2 | 2 |
N.S. |
1 | 0.50 | 0.50 | 0.75 | 0.50 | 0.50 | 0.50 | 0.75 | 0.50 | 0.50 |
time (sec) |
N/A | 0.120 | 0.000 | 0.018 | 0.025 | 0.069 | 0.016 | 0.119 | 0.178 | 0.008 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | A | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 77 | 32 | 134 | 57 | 33 | 63 | 88 | 52 | 48 |
N.S. |
1 | 2.26 | 0.94 | 3.94 | 1.68 | 0.97 | 1.85 | 2.59 | 1.53 | 1.41 |
time (sec) |
N/A | 5.484 | 0.121 | 17.912 | 0.086 | 0.079 | 1.031 | 0.411 | 0.189 | 3.915 |
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 | 28 | 36 | 32 | 30 | 34 | 35 | 24 | 41 | 45 | 30 |
N.S. |
1 | 1.29 | 1.14 | 1.07 | 1.21 | 1.25 | 0.86 | 1.46 | 1.61 | 1.07 |
time (sec) |
N/A | 0.389 | 0.055 | 0.218 | 0.055 | 0.098 | 0.081 | 0.124 | 0.193 | 3.638 |
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 | 21 | 19 | 21 | 21 | 20 | 21 | 18 | 21 |
N.S. |
1 | 0.89 | 1.11 | 1.00 | 1.11 | 1.11 | 1.05 | 1.11 | 0.95 | 1.11 |
time (sec) |
N/A | 0.135 | 0.000 | 0.050 | 0.033 | 0.074 | 0.018 | 0.117 | 0.185 | 3.593 |
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 | 25 | 17 | 15 | 14 | 14 | 12 | 14 | 11 | 12 |
N.S. |
1 | 1.39 | 0.94 | 0.83 | 0.78 | 0.78 | 0.67 | 0.78 | 0.61 | 0.67 |
time (sec) |
N/A | 0.160 | 0.023 | 0.066 | 0.030 | 0.072 | 0.038 | 0.120 | 0.180 | 0.044 |
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 | 27 | 0 | 23 | 21 | 65 | 29 | 36 | 52 | 37 | 20 |
N.S. |
1 | 0.00 | 0.85 | 0.78 | 2.41 | 1.07 | 1.33 | 1.93 | 1.37 | 0.74 |
time (sec) |
N/A | 0.000 | 0.033 | 1.997 | 0.165 | 0.074 | 0.096 | 0.126 | 0.181 | 4.228 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 14 | 0 | 13 | 12 | 13 | 63 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.00 | 0.87 | 0.80 | 0.87 | 4.20 | 0.87 |
time (sec) |
N/A | 0.385 | 0.163 | 0.116 | 0.000 | 0.095 | 0.092 | 0.118 | 0.232 | 3.627 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | A | A | B | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 0 | 45 | 273 | 53 | 44 | 115 | 57 | 53 |
N.S. |
1 | 0.00 | 0.00 | 1.32 | 8.03 | 1.56 | 1.29 | 3.38 | 1.68 | 1.56 |
time (sec) |
N/A | 0.000 | 0.000 | 0.260 | 0.161 | 0.105 | 0.421 | 0.221 | 0.186 | 3.910 |
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 | 26 | 25 | 19 | 22 | 22 | 19 | 22 | 20 | 20 |
N.S. |
1 | 1.53 | 1.47 | 1.12 | 1.29 | 1.29 | 1.12 | 1.29 | 1.18 | 1.18 |
time (sec) |
N/A | 0.160 | 0.001 | 0.052 | 0.035 | 0.083 | 0.020 | 0.120 | 0.178 | 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 | 16 | 25 | 15 | 20 | 19 | 24 | 19 | 25 | 17 | 12 |
N.S. |
1 | 1.56 | 0.94 | 1.25 | 1.19 | 1.50 | 1.19 | 1.56 | 1.06 | 0.75 |
time (sec) |
N/A | 0.177 | 0.003 | 0.565 | 0.033 | 0.088 | 0.029 | 0.126 | 0.179 | 0.070 |
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 | 29 | 0 | 33 | 32 | 37 | 37 | 42 | 37 | 37 | 31 |
N.S. |
1 | 0.00 | 1.14 | 1.10 | 1.28 | 1.28 | 1.45 | 1.28 | 1.28 | 1.07 |
time (sec) |
N/A | 0.000 | 0.010 | 0.075 | 0.026 | 0.073 | 0.275 | 0.125 | 0.193 | 3.595 |
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 | 34 | 0 | 32 | 30 | 30 | 28 | 27 | 0 | 1633 | 28 |
N.S. |
1 | 0.00 | 0.94 | 0.88 | 0.88 | 0.82 | 0.79 | 0.00 | 48.03 | 0.82 |
time (sec) |
N/A | 0.000 | 0.068 | 6.061 | 0.269 | 0.097 | 1.376 | 0.000 | 0.235 | 4.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 30 | 60 | 31 | 30 | 22 | 1059 | 30 | 0 |
N.S. |
1 | 0.00 | 1.00 | 2.00 | 1.03 | 1.00 | 0.73 | 35.30 | 1.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.076 | 73.724 | 0.296 | 0.092 | 0.392 | 15.219 | 0.233 | 0.000 |
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 | 28 | 44 | 43 | 38 | 72 | 36 | 48 | 39 | 42 | 48 |
N.S. |
1 | 1.57 | 1.54 | 1.36 | 2.57 | 1.29 | 1.71 | 1.39 | 1.50 | 1.71 |
time (sec) |
N/A | 0.494 | 0.050 | 0.495 | 0.090 | 0.095 | 0.288 | 0.123 | 0.195 | 3.641 |
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 | 30 | 31 | 29 | 35 | 157 | 66 | 68 | 75 | 77 | 95 |
N.S. |
1 | 1.03 | 0.97 | 1.17 | 5.23 | 2.20 | 2.27 | 2.50 | 2.57 | 3.17 |
time (sec) |
N/A | 16.450 | 0.098 | 21.130 | 0.271 | 0.088 | 0.520 | 1.975 | 0.399 | 4.124 |
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 | 19 | 21 | 16 | 15 | 15 | 17 | 15 | 15 | 15 |
N.S. |
1 | 0.79 | 0.88 | 0.67 | 0.62 | 0.62 | 0.71 | 0.62 | 0.62 | 0.62 |
time (sec) |
N/A | 0.343 | 0.021 | 0.057 | 0.031 | 0.092 | 0.070 | 0.124 | 0.181 | 3.730 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | F(-1) | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 22 | 23 | 62 | 20 | 0 | 0 | 22 | 19 |
N.S. |
1 | 0.00 | 0.79 | 0.82 | 2.21 | 0.71 | 0.00 | 0.00 | 0.79 | 0.68 |
time (sec) |
N/A | 0.000 | 0.046 | 8.714 | 0.675 | 0.086 | 0.000 | 0.000 | 0.183 | 4.095 |
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 | 11 | 9 | 9 | 9 | 8 | 8 | 8 | 8 | 9 | 8 |
N.S. |
1 | 0.82 | 0.82 | 0.82 | 0.73 | 0.73 | 0.73 | 0.73 | 0.82 | 0.73 |
time (sec) |
N/A | 0.184 | 0.005 | 0.138 | 0.056 | 0.104 | 0.081 | 0.122 | 0.185 | 3.865 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 23 | 48 | 0 | 42 | 44 | 69 | 55 | 42 |
N.S. |
1 | 0.00 | 0.82 | 1.71 | 0.00 | 1.50 | 1.57 | 2.46 | 1.96 | 1.50 |
time (sec) |
N/A | 0.000 | 0.075 | 1.368 | 0.000 | 0.088 | 11.414 | 0.130 | 0.184 | 3.926 |
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 | 19 | 100 | 105 | 81 | 87 | 87 | 94 | 87 | 87 | 81 |
N.S. |
1 | 5.26 | 5.53 | 4.26 | 4.58 | 4.58 | 4.95 | 4.58 | 4.58 | 4.26 |
time (sec) |
N/A | 0.258 | 0.020 | 0.105 | 0.035 | 0.071 | 0.036 | 0.119 | 0.172 | 3.537 |
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 | 38 | 38 | 31 | 27 | 27 | 36 | 27 | 33 | 30 |
N.S. |
1 | 1.58 | 1.58 | 1.29 | 1.12 | 1.12 | 1.50 | 1.12 | 1.38 | 1.25 |
time (sec) |
N/A | 0.176 | 0.003 | 0.069 | 0.033 | 0.069 | 0.023 | 0.123 | 0.180 | 3.595 |
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 | 24 | 0 | 22 | 42 | 24 | 21 | 17 | 29 | 1350 | 32 |
N.S. |
1 | 0.00 | 0.92 | 1.75 | 1.00 | 0.88 | 0.71 | 1.21 | 56.25 | 1.33 |
time (sec) |
N/A | 0.000 | 0.071 | 8.445 | 0.088 | 0.078 | 0.142 | 0.125 | 0.280 | 3.708 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 25 | 81 | 214 | 108 | 172 | 164 | 68 | 240 |
N.S. |
1 | 0.00 | 1.00 | 3.24 | 8.56 | 4.32 | 6.88 | 6.56 | 2.72 | 9.60 |
time (sec) |
N/A | 0.000 | 0.201 | 8.658 | 0.182 | 0.086 | 5.688 | 0.152 | 0.186 | 4.140 |
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 | 31 | 32 | 28 | 28 | 26 | 28 | 27 | 26 | 28 | 0 |
N.S. |
1 | 1.03 | 0.90 | 0.90 | 0.84 | 0.90 | 0.87 | 0.84 | 0.90 | 0.00 |
time (sec) |
N/A | 2.001 | 0.102 | 31.844 | 0.110 | 0.090 | 0.891 | 0.217 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 45 | 45 | 41 | 39 | 37 | 44 | 40 | 39 | 27 |
N.S. |
1 | 2.65 | 2.65 | 2.41 | 2.29 | 2.18 | 2.59 | 2.35 | 2.29 | 1.59 |
time (sec) |
N/A | 0.225 | 0.006 | 0.193 | 0.026 | 0.092 | 0.098 | 0.125 | 0.183 | 3.620 |
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 | 26 | 41 | 27 | 24 | 34 | 22 | 22 | 22 | 27 | 24 |
N.S. |
1 | 1.58 | 1.04 | 0.92 | 1.31 | 0.85 | 0.85 | 0.85 | 1.04 | 0.92 |
time (sec) |
N/A | 0.660 | 0.097 | 0.835 | 0.118 | 0.075 | 0.075 | 0.131 | 0.197 | 3.679 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | B | B | B | B | B | B | F(-1) |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 0 | 56 | 74 | 64 | 48 | 121 | 99 | 0 |
N.S. |
1 | 0.00 | 0.00 | 2.00 | 2.64 | 2.29 | 1.71 | 4.32 | 3.54 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.429 | 0.229 | 0.096 | 1.028 | 0.315 | 0.203 | 0.000 |
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 | 28 | 31 | 31 | 31 | 27 | 33 | 735 | 0 |
N.S. |
1 | 0.00 | 1.12 | 1.24 | 1.24 | 1.24 | 1.08 | 1.32 | 29.40 | 0.00 |
time (sec) |
N/A | 0.000 | 0.142 | 0.505 | 0.076 | 0.073 | 0.083 | 0.139 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | A | B | F(-1) | F | F | B |
verified | N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 0 | 26 | 68 | 0 | 0 | 0 | 80 |
N.S. |
1 | 0.00 | 1.00 | 0.00 | 1.13 | 2.96 | 0.00 | 0.00 | 0.00 | 3.48 |
time (sec) |
N/A | 0.000 | 0.060 | 0.000 | 0.303 | 0.098 | 0.000 | 0.000 | 0.905 | 5.437 |