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 | C | A | A | C | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 324 | 35 | 35 | 446 | 35 | 87 | 48 | 35 | 49 |
N.S. |
1 | 8.76 | 0.95 | 0.95 | 12.05 | 0.95 | 2.35 | 1.30 | 0.95 | 1.32 |
time (sec) |
N/A | 1.365 | 0.044 | 0.090 | 0.173 | 0.088 | 0.097 | 0.133 | 0.229 | 0.332 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | C | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 349 | 41 | 41 | 558 | 40 | 92 | 66 | 40 | 53 |
N.S. |
1 | 7.76 | 0.91 | 0.91 | 12.40 | 0.89 | 2.04 | 1.47 | 0.89 | 1.18 |
time (sec) |
N/A | 1.390 | 0.347 | 0.072 | 0.248 | 0.081 | 0.077 | 0.137 | 0.156 | 0.162 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 377 | 48 | 52 | 527 | 52 | 112 | 91 | 51 | 52 |
N.S. |
1 | 5.71 | 0.73 | 0.79 | 7.98 | 0.79 | 1.70 | 1.38 | 0.77 | 0.79 |
time (sec) |
N/A | 1.494 | 1.172 | 0.092 | 0.228 | 0.091 | 0.114 | 0.144 | 0.156 | 0.185 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 0 | 39 | 41 | 52 | 40 | 124 | 95 | 40 | 69 |
N.S. |
1 | 0.00 | 0.93 | 0.98 | 1.24 | 0.95 | 2.95 | 2.26 | 0.95 | 1.64 |
time (sec) |
N/A | 0.000 | 0.076 | 0.123 | 0.110 | 0.274 | 0.106 | 0.158 | 0.154 | 0.121 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 0 | 43 | 43 | 55 | 43 | 121 | 98 | 43 | 71 |
N.S. |
1 | 0.00 | 0.96 | 0.96 | 1.22 | 0.96 | 2.69 | 2.18 | 0.96 | 1.58 |
time (sec) |
N/A | 0.000 | 0.063 | 0.101 | 0.113 | 0.199 | 0.125 | 0.161 | 0.149 | 0.094 |
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 | 69 | 0 | 50 | 53 | 68 | 55 | 158 | 132 | 52 | 57 |
N.S. |
1 | 0.00 | 0.72 | 0.77 | 0.99 | 0.80 | 2.29 | 1.91 | 0.75 | 0.83 |
time (sec) |
N/A | 0.000 | 0.076 | 0.116 | 0.110 | 0.190 | 0.219 | 0.172 | 0.158 | 0.209 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 24 | 76 | 92 | 75 | 94 | 79 | 75 | 76 |
N.S. |
1 | 1.00 | 0.31 | 0.97 | 1.18 | 0.96 | 1.21 | 1.01 | 0.96 | 0.97 |
time (sec) |
N/A | 0.349 | 0.056 | 0.161 | 0.028 | 0.080 | 0.068 | 0.131 | 0.156 | 0.144 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 24 | 64 | 77 | 63 | 80 | 67 | 63 | 63 |
N.S. |
1 | 1.00 | 0.37 | 0.98 | 1.18 | 0.97 | 1.23 | 1.03 | 0.97 | 0.97 |
time (sec) |
N/A | 0.326 | 0.052 | 0.095 | 0.033 | 0.082 | 0.062 | 0.142 | 0.154 | 0.100 |
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 | 86 | 110 | 53 | 52 | 62 | 51 | 66 | 55 | 51 | 52 |
N.S. |
1 | 1.28 | 0.62 | 0.60 | 0.72 | 0.59 | 0.77 | 0.64 | 0.59 | 0.60 |
time (sec) |
N/A | 0.555 | 0.055 | 0.065 | 0.033 | 0.087 | 0.062 | 0.121 | 0.153 | 0.106 |
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 | 62 | 77 | 41 | 40 | 47 | 39 | 53 | 43 | 39 | 39 |
N.S. |
1 | 1.24 | 0.66 | 0.65 | 0.76 | 0.63 | 0.85 | 0.69 | 0.63 | 0.63 |
time (sec) |
N/A | 0.441 | 0.051 | 0.049 | 0.035 | 0.085 | 0.051 | 0.117 | 0.154 | 0.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 29 | 28 | 32 | 27 | 39 | 689 | 27 | 27 |
N.S. |
1 | 1.00 | 0.66 | 0.64 | 0.73 | 0.61 | 0.89 | 15.66 | 0.61 | 0.61 |
time (sec) |
N/A | 0.335 | 0.048 | 0.035 | 0.029 | 0.079 | 0.049 | 0.127 | 0.160 | 0.079 |
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 | 20 | 20 | 19 | 18 | 18 | 22 | 18 | 18 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.90 | 0.90 | 1.10 | 0.90 | 0.90 | 0.90 |
time (sec) |
N/A | 0.259 | 0.035 | 0.028 | 0.025 | 0.083 | 0.039 | 0.107 | 0.158 | 0.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 16 | 13 | 13 | 0 | 0 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 0.87 | 0.87 | 0.00 | 0.00 | 0.87 | 0.87 |
time (sec) |
N/A | 0.259 | 0.041 | 0.039 | 0.074 | 0.080 | 0.000 | 0.000 | 0.161 | 0.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 32 | 35 | 18 | 35 | 0 | 0 | 33 | 32 |
N.S. |
1 | 1.00 | 0.91 | 1.00 | 0.51 | 1.00 | 0.00 | 0.00 | 0.94 | 0.91 |
time (sec) |
N/A | 0.327 | 0.049 | 0.047 | 0.072 | 0.079 | 0.000 | 0.000 | 0.160 | 0.108 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 59 | 48 | 52 | 22 | 48 | 0 | 0 | 52 | 57 |
N.S. |
1 | 1.02 | 0.83 | 0.90 | 0.38 | 0.83 | 0.00 | 0.00 | 0.90 | 0.98 |
time (sec) |
N/A | 0.412 | 0.061 | 0.072 | 0.081 | 0.085 | 0.000 | 0.000 | 0.161 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 83 | 59 | 72 | 22 | 59 | 0 | 0 | 71 | 69 |
N.S. |
1 | 1.02 | 0.73 | 0.89 | 0.27 | 0.73 | 0.00 | 0.00 | 0.88 | 0.85 |
time (sec) |
N/A | 0.500 | 0.073 | 0.099 | 0.075 | 0.083 | 0.000 | 0.000 | 0.154 | 0.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 91 | 22 | 71 | 0 | 0 | 90 | 90 |
N.S. |
1 | 1.00 | 1.00 | 3.79 | 0.92 | 2.96 | 0.00 | 0.00 | 3.75 | 3.75 |
time (sec) |
N/A | 0.269 | 0.047 | 0.160 | 0.070 | 0.081 | 0.000 | 0.000 | 0.160 | 0.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 110 | 22 | 83 | 0 | 0 | 109 | 102 |
N.S. |
1 | 1.00 | 1.00 | 4.58 | 0.92 | 3.46 | 0.00 | 0.00 | 4.54 | 4.25 |
time (sec) |
N/A | 0.267 | 0.049 | 0.234 | 0.068 | 0.084 | 0.000 | 0.000 | 0.160 | 0.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 34 | 123 | 127 | 113 | 0 | 116 | 167 | 154 |
N.S. |
1 | 1.00 | 1.00 | 3.62 | 3.74 | 3.32 | 0.00 | 3.41 | 4.91 | 4.53 |
time (sec) |
N/A | 0.267 | 0.075 | 0.297 | 0.027 | 0.076 | 0.000 | 0.106 | 0.156 | 0.155 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 34 | 111 | 112 | 101 | 0 | 104 | 143 | 139 |
N.S. |
1 | 1.00 | 1.00 | 3.26 | 3.29 | 2.97 | 0.00 | 3.06 | 4.21 | 4.09 |
time (sec) |
N/A | 0.263 | 0.067 | 0.169 | 0.029 | 0.082 | 0.000 | 0.109 | 0.167 | 0.125 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 164 | 95 | 99 | 97 | 89 | 0 | 92 | 119 | 116 |
N.S. |
1 | 1.28 | 0.74 | 0.77 | 0.76 | 0.70 | 0.00 | 0.72 | 0.93 | 0.91 |
time (sec) |
N/A | 0.662 | 0.110 | 0.112 | 0.027 | 0.083 | 0.000 | 0.112 | 0.156 | 0.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 129 | 83 | 87 | 82 | 77 | 0 | 80 | 95 | 98 |
N.S. |
1 | 1.23 | 0.79 | 0.83 | 0.78 | 0.73 | 0.00 | 0.76 | 0.90 | 0.93 |
time (sec) |
N/A | 0.541 | 0.096 | 0.080 | 0.039 | 0.095 | 0.000 | 0.115 | 0.150 | 0.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 94 | 71 | 75 | 67 | 65 | 0 | 68 | 71 | 75 |
N.S. |
1 | 1.15 | 0.87 | 0.91 | 0.82 | 0.79 | 0.00 | 0.83 | 0.87 | 0.91 |
time (sec) |
N/A | 0.423 | 0.088 | 0.056 | 0.035 | 0.080 | 0.000 | 0.116 | 0.149 | 0.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 59 | 54 | 53 | 49 | 0 | 57 | 50 | 54 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.90 | 0.83 | 0.00 | 0.97 | 0.85 | 0.92 |
time (sec) |
N/A | 0.321 | 0.072 | 0.040 | 0.032 | 0.111 | 0.000 | 0.114 | 0.151 | 0.084 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 37 | 26 | 25 | 32 | 0 | 26 | 26 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.70 | 0.68 | 0.86 | 0.00 | 0.70 | 0.70 | 0.70 |
time (sec) |
N/A | 0.244 | 0.053 | 0.026 | 0.032 | 0.096 | 0.000 | 0.135 | 0.145 | 0.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 49 | 44 | 28 | 40 | 0 | 0 | 17 | 44 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.57 | 0.82 | 0.00 | 0.00 | 0.35 | 0.90 |
time (sec) |
N/A | 0.312 | 0.080 | 0.042 | 0.074 | 0.088 | 0.000 | 0.000 | 0.165 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 62 | 67 | 28 | 57 | 0 | 0 | 17 | 70 |
N.S. |
1 | 1.00 | 0.85 | 0.92 | 0.38 | 0.78 | 0.00 | 0.00 | 0.23 | 0.96 |
time (sec) |
N/A | 0.396 | 0.112 | 0.063 | 0.072 | 0.082 | 0.000 | 0.000 | 0.157 | 0.121 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 97 | 77 | 86 | 28 | 73 | 0 | 0 | 17 | 109 |
N.S. |
1 | 1.01 | 0.80 | 0.90 | 0.29 | 0.76 | 0.00 | 0.00 | 0.18 | 1.14 |
time (sec) |
N/A | 0.483 | 0.106 | 0.079 | 0.075 | 0.091 | 0.000 | 0.000 | 0.159 | 0.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 121 | 89 | 98 | 28 | 85 | 0 | 0 | 17 | 131 |
N.S. |
1 | 1.02 | 0.75 | 0.82 | 0.24 | 0.71 | 0.00 | 0.00 | 0.14 | 1.10 |
time (sec) |
N/A | 0.573 | 0.118 | 0.127 | 0.077 | 0.078 | 0.000 | 0.000 | 0.168 | 0.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 34 | 110 | 28 | 97 | 0 | 0 | 17 | 153 |
N.S. |
1 | 1.00 | 1.00 | 3.24 | 0.82 | 2.85 | 0.00 | 0.00 | 0.50 | 4.50 |
time (sec) |
N/A | 0.262 | 0.081 | 0.185 | 0.074 | 0.084 | 0.000 | 0.000 | 0.163 | 0.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 34 | 122 | 28 | 109 | 0 | 0 | 17 | 175 |
N.S. |
1 | 1.00 | 1.00 | 3.59 | 0.82 | 3.21 | 0.00 | 0.00 | 0.50 | 5.15 |
time (sec) |
N/A | 0.261 | 0.077 | 0.285 | 0.076 | 0.084 | 0.000 | 0.000 | 0.159 | 0.127 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 24 | 76 | 92 | 75 | 94 | 0 | 75 | 76 |
N.S. |
1 | 1.00 | 0.31 | 0.97 | 1.18 | 0.96 | 1.21 | 0.00 | 0.96 | 0.97 |
time (sec) |
N/A | 0.331 | 0.081 | 0.425 | 0.034 | 0.088 | 0.075 | 0.000 | 0.156 | 0.134 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 24 | 64 | 77 | 63 | 80 | 105 | 63 | 63 |
N.S. |
1 | 1.00 | 0.37 | 0.98 | 1.18 | 0.97 | 1.23 | 1.62 | 0.97 | 0.97 |
time (sec) |
N/A | 0.317 | 0.065 | 0.250 | 0.033 | 0.085 | 0.066 | 0.137 | 0.157 | 0.100 |
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 | 84 | 110 | 53 | 52 | 62 | 51 | 66 | 83 | 51 | 51 |
N.S. |
1 | 1.31 | 0.63 | 0.62 | 0.74 | 0.61 | 0.79 | 0.99 | 0.61 | 0.61 |
time (sec) |
N/A | 0.572 | 0.062 | 0.140 | 0.031 | 0.083 | 0.062 | 0.122 | 0.161 | 0.103 |
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 | 67 | 77 | 41 | 40 | 47 | 39 | 53 | 61 | 39 | 39 |
N.S. |
1 | 1.15 | 0.61 | 0.60 | 0.70 | 0.58 | 0.79 | 0.91 | 0.58 | 0.58 |
time (sec) |
N/A | 0.454 | 0.054 | 0.079 | 0.027 | 0.086 | 0.054 | 0.105 | 0.160 | 0.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 29 | 28 | 32 | 27 | 39 | 689 | 27 | 27 |
N.S. |
1 | 1.00 | 0.66 | 0.64 | 0.73 | 0.61 | 0.89 | 15.66 | 0.61 | 0.61 |
time (sec) |
N/A | 0.346 | 0.047 | 0.046 | 0.028 | 0.093 | 0.053 | 0.130 | 0.157 | 0.066 |
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 | 20 | 20 | 19 | 18 | 18 | 22 | 18 | 18 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.90 | 0.90 | 1.10 | 0.90 | 0.90 | 0.90 |
time (sec) |
N/A | 0.264 | 0.021 | 0.033 | 0.029 | 0.084 | 0.040 | 0.128 | 0.153 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 41 | 13 | 13 | 0 | 0 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 2.73 | 0.87 | 0.87 | 0.00 | 0.00 | 0.87 | 0.87 |
time (sec) |
N/A | 0.258 | 0.042 | 0.033 | 0.076 | 0.087 | 0.000 | 0.000 | 0.156 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 32 | 97 | 18 | 35 | 0 | 0 | 33 | 32 |
N.S. |
1 | 1.00 | 0.91 | 2.77 | 0.51 | 1.00 | 0.00 | 0.00 | 0.94 | 0.91 |
time (sec) |
N/A | 0.328 | 0.052 | 0.049 | 0.078 | 0.080 | 0.000 | 0.000 | 0.154 | 0.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 59 | 48 | 141 | 22 | 48 | 0 | 0 | 52 | 57 |
N.S. |
1 | 1.02 | 0.83 | 2.43 | 0.38 | 0.83 | 0.00 | 0.00 | 0.90 | 0.98 |
time (sec) |
N/A | 0.412 | 0.067 | 0.090 | 0.075 | 0.083 | 0.000 | 0.000 | 0.157 | 0.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 83 | 59 | 177 | 22 | 59 | 0 | 0 | 71 | 69 |
N.S. |
1 | 1.02 | 0.73 | 2.19 | 0.27 | 0.73 | 0.00 | 0.00 | 0.88 | 0.85 |
time (sec) |
N/A | 0.504 | 0.073 | 0.174 | 0.081 | 0.074 | 0.000 | 0.000 | 0.162 | 0.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 213 | 22 | 71 | 0 | 0 | 90 | 90 |
N.S. |
1 | 1.00 | 1.00 | 8.88 | 0.92 | 2.96 | 0.00 | 0.00 | 3.75 | 3.75 |
time (sec) |
N/A | 0.270 | 0.048 | 0.332 | 0.071 | 0.072 | 0.000 | 0.000 | 0.159 | 0.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 249 | 22 | 83 | 0 | 0 | 109 | 102 |
N.S. |
1 | 1.00 | 1.00 | 10.38 | 0.92 | 3.46 | 0.00 | 0.00 | 4.54 | 4.25 |
time (sec) |
N/A | 0.273 | 0.048 | 0.593 | 0.074 | 0.076 | 0.000 | 0.000 | 0.169 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 34 | 106 | 28 | 49 | 0 | 0 | 37 | 71 |
N.S. |
1 | 1.00 | 1.00 | 3.12 | 0.82 | 1.44 | 0.00 | 0.00 | 1.09 | 2.09 |
time (sec) |
N/A | 0.278 | 0.082 | 0.053 | 0.072 | 0.114 | 0.000 | 0.000 | 0.161 | 0.070 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 34 | 109 | 28 | 47 | 0 | 0 | 33 | 75 |
N.S. |
1 | 1.00 | 1.00 | 3.21 | 0.82 | 1.38 | 0.00 | 0.00 | 0.97 | 2.21 |
time (sec) |
N/A | 0.273 | 0.085 | 0.047 | 0.068 | 0.082 | 0.000 | 0.000 | 0.161 | 0.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 34 | 75 | 28 | 29 | 0 | 0 | 15 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.21 | 0.82 | 0.85 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.265 | 0.077 | 0.035 | 0.069 | 0.089 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 78 | 26 | 29 | 0 | 0 | 13 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.44 | 0.81 | 0.91 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.245 | 0.084 | 0.027 | 0.073 | 0.092 | 0.000 | 0.000 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 34 | 100 | 28 | 38 | 0 | 0 | 17 | 63 |
N.S. |
1 | 1.00 | 1.00 | 2.94 | 0.82 | 1.12 | 0.00 | 0.00 | 0.50 | 1.85 |
time (sec) |
N/A | 0.263 | 0.102 | 0.039 | 0.068 | 0.098 | 0.000 | 0.000 | 0.154 | 0.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 34 | 102 | 28 | 41 | 0 | 0 | 17 | 70 |
N.S. |
1 | 1.00 | 1.00 | 3.00 | 0.82 | 1.21 | 0.00 | 0.00 | 0.50 | 2.06 |
time (sec) |
N/A | 0.263 | 0.097 | 0.043 | 0.071 | 0.092 | 0.000 | 0.000 | 0.149 | 0.088 |
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 | 11 | 11 | 9 | 8 | 8 | 7 | 8 | 9 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.73 | 0.73 | 0.64 | 0.73 | 0.82 | 0.73 |
time (sec) |
N/A | 0.228 | 0.019 | 0.031 | 0.026 | 0.082 | 0.042 | 0.114 | 0.155 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 121 | 22 | 80 | 0 | 0 | 103 | 99 |
N.S. |
1 | 1.00 | 1.00 | 5.50 | 1.00 | 3.64 | 0.00 | 0.00 | 4.68 | 4.50 |
time (sec) |
N/A | 0.256 | 0.008 | 0.122 | 0.075 | 0.077 | 0.000 | 0.000 | 0.148 | 0.143 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 99 | 21 | 68 | 0 | 0 | 84 | 87 |
N.S. |
1 | 1.00 | 1.00 | 4.71 | 1.00 | 3.24 | 0.00 | 0.00 | 4.00 | 4.14 |
time (sec) |
N/A | 0.253 | 0.006 | 0.098 | 0.075 | 0.074 | 0.000 | 0.000 | 0.161 | 0.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 76 | 53 | 77 | 22 | 56 | 0 | 0 | 65 | 66 |
N.S. |
1 | 0.96 | 0.67 | 0.97 | 0.28 | 0.71 | 0.00 | 0.00 | 0.82 | 0.84 |
time (sec) |
N/A | 0.443 | 0.029 | 0.083 | 0.079 | 0.079 | 0.000 | 0.000 | 0.165 | 0.108 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 52 | 40 | 55 | 21 | 43 | 0 | 0 | 46 | 54 |
N.S. |
1 | 0.93 | 0.71 | 0.98 | 0.38 | 0.77 | 0.00 | 0.00 | 0.82 | 0.96 |
time (sec) |
N/A | 0.361 | 0.022 | 0.076 | 0.081 | 0.096 | 0.000 | 0.000 | 0.150 | 0.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 31 | 18 | 30 | 0 | 0 | 27 | 27 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 0.64 | 1.07 | 0.00 | 0.00 | 0.96 | 0.96 |
time (sec) |
N/A | 0.291 | 0.011 | 0.063 | 0.074 | 0.081 | 0.000 | 0.000 | 0.147 | 0.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 15 | 13 | 13 | 0 | 0 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.15 | 1.00 | 1.00 | 0.00 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.247 | 0.005 | 0.064 | 0.075 | 0.080 | 0.000 | 0.000 | 0.151 | 0.074 |
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 | 18 | 19 | 18 | 20 | 20 | 20 | 20 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.11 | 1.11 | 1.11 | 1.11 | 1.00 |
time (sec) |
N/A | 0.248 | 0.007 | 0.032 | 0.027 | 0.076 | 0.047 | 0.131 | 0.149 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 27 | 32 | 21 | 31 | 22 | 0 | 29 | 27 |
N.S. |
1 | 1.00 | 0.69 | 0.82 | 0.54 | 0.79 | 0.56 | 0.00 | 0.74 | 0.69 |
time (sec) |
N/A | 0.323 | 0.010 | 0.039 | 0.079 | 0.075 | 0.047 | 0.000 | 0.156 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 70 | 41 | 44 | 22 | 43 | 39 | 0 | 43 | 45 |
N.S. |
1 | 1.15 | 0.67 | 0.72 | 0.36 | 0.70 | 0.64 | 0.00 | 0.70 | 0.74 |
time (sec) |
N/A | 0.419 | 0.013 | 0.051 | 0.076 | 0.090 | 0.060 | 0.000 | 0.152 | 0.087 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 101 | 53 | 56 | 21 | 55 | 53 | 0 | 55 | 57 |
N.S. |
1 | 1.23 | 0.65 | 0.68 | 0.26 | 0.67 | 0.65 | 0.00 | 0.67 | 0.70 |
time (sec) |
N/A | 0.530 | 0.014 | 0.059 | 0.082 | 0.074 | 0.063 | 0.000 | 0.153 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 22 | 68 | 22 | 67 | 66 | 0 | 67 | 69 |
N.S. |
1 | 1.00 | 0.34 | 1.05 | 0.34 | 1.03 | 1.02 | 0.00 | 1.03 | 1.06 |
time (sec) |
N/A | 0.315 | 0.006 | 0.072 | 0.077 | 0.084 | 0.066 | 0.000 | 0.148 | 0.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 21 | 80 | 21 | 79 | 80 | 0 | 79 | 81 |
N.S. |
1 | 1.00 | 0.27 | 1.04 | 0.27 | 1.03 | 1.04 | 0.00 | 1.03 | 1.05 |
time (sec) |
N/A | 0.340 | 0.006 | 0.086 | 0.080 | 0.073 | 0.066 | 0.000 | 0.152 | 0.126 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 123 | 22 | 84 | 0 | 0 | 105 | 102 |
N.S. |
1 | 1.00 | 1.00 | 5.12 | 0.92 | 3.50 | 0.00 | 0.00 | 4.38 | 4.25 |
time (sec) |
N/A | 0.273 | 0.008 | 0.323 | 0.071 | 0.072 | 0.000 | 0.000 | 0.149 | 0.230 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 101 | 22 | 72 | 0 | 0 | 86 | 90 |
N.S. |
1 | 1.00 | 1.00 | 4.21 | 0.92 | 3.00 | 0.00 | 0.00 | 3.58 | 3.75 |
time (sec) |
N/A | 0.274 | 0.005 | 0.201 | 0.071 | 0.088 | 0.000 | 0.000 | 0.157 | 0.182 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 83 | 57 | 79 | 22 | 60 | 0 | 0 | 67 | 69 |
N.S. |
1 | 1.02 | 0.70 | 0.98 | 0.27 | 0.74 | 0.00 | 0.00 | 0.83 | 0.85 |
time (sec) |
N/A | 0.503 | 0.024 | 0.125 | 0.078 | 0.080 | 0.000 | 0.000 | 0.156 | 0.163 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 59 | 44 | 57 | 22 | 47 | 0 | 0 | 48 | 57 |
N.S. |
1 | 1.02 | 0.76 | 0.98 | 0.38 | 0.81 | 0.00 | 0.00 | 0.83 | 0.98 |
time (sec) |
N/A | 0.412 | 0.021 | 0.085 | 0.079 | 0.076 | 0.000 | 0.000 | 0.161 | 0.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 32 | 35 | 18 | 35 | 0 | 0 | 30 | 33 |
N.S. |
1 | 1.00 | 0.91 | 1.00 | 0.51 | 1.00 | 0.00 | 0.00 | 0.86 | 0.94 |
time (sec) |
N/A | 0.319 | 0.009 | 0.056 | 0.075 | 0.080 | 0.000 | 0.000 | 0.156 | 0.146 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 16 | 13 | 13 | 0 | 0 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 0.87 | 0.87 | 0.00 | 0.00 | 0.87 | 0.87 |
time (sec) |
N/A | 0.258 | 0.005 | 0.046 | 0.075 | 0.078 | 0.000 | 0.000 | 0.161 | 0.074 |
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 | 20 | 20 | 19 | 18 | 22 | 27 | 22 | 22 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.90 | 1.10 | 1.35 | 1.10 | 1.10 | 0.90 |
time (sec) |
N/A | 0.257 | 0.007 | 0.043 | 0.028 | 0.076 | 0.050 | 0.115 | 0.158 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 32 | 35 | 22 | 34 | 29 | 0 | 34 | 36 |
N.S. |
1 | 1.00 | 0.73 | 0.80 | 0.50 | 0.77 | 0.66 | 0.00 | 0.77 | 0.82 |
time (sec) |
N/A | 0.338 | 0.012 | 0.062 | 0.077 | 0.074 | 0.064 | 0.000 | 0.167 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 77 | 45 | 47 | 22 | 47 | 44 | 0 | 48 | 47 |
N.S. |
1 | 1.24 | 0.73 | 0.76 | 0.35 | 0.76 | 0.71 | 0.00 | 0.77 | 0.76 |
time (sec) |
N/A | 0.438 | 0.014 | 0.095 | 0.074 | 0.077 | 0.063 | 0.000 | 0.158 | 0.087 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 110 | 58 | 59 | 22 | 60 | 58 | 0 | 60 | 60 |
N.S. |
1 | 1.28 | 0.67 | 0.69 | 0.26 | 0.70 | 0.67 | 0.00 | 0.70 | 0.70 |
time (sec) |
N/A | 0.543 | 0.015 | 0.142 | 0.076 | 0.072 | 0.069 | 0.000 | 0.155 | 0.102 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 24 | 71 | 22 | 71 | 71 | 0 | 72 | 72 |
N.S. |
1 | 1.00 | 0.35 | 1.03 | 0.32 | 1.03 | 1.03 | 0.00 | 1.04 | 1.04 |
time (sec) |
N/A | 0.320 | 0.006 | 0.213 | 0.081 | 0.074 | 0.098 | 0.000 | 0.163 | 0.116 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 24 | 83 | 22 | 84 | 85 | 0 | 84 | 84 |
N.S. |
1 | 1.00 | 0.29 | 1.01 | 0.27 | 1.02 | 1.04 | 0.00 | 1.02 | 1.02 |
time (sec) |
N/A | 0.341 | 0.006 | 0.299 | 0.078 | 0.094 | 0.102 | 0.000 | 0.155 | 0.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 34 | 124 | 28 | 110 | 0 | 0 | 196 | 173 |
N.S. |
1 | 1.00 | 1.00 | 3.65 | 0.82 | 3.24 | 0.00 | 0.00 | 5.76 | 5.09 |
time (sec) |
N/A | 0.274 | 0.008 | 0.378 | 0.083 | 0.077 | 0.000 | 0.000 | 0.159 | 0.160 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 34 | 112 | 28 | 98 | 0 | 0 | 171 | 151 |
N.S. |
1 | 1.00 | 1.00 | 3.29 | 0.82 | 2.88 | 0.00 | 0.00 | 5.03 | 4.44 |
time (sec) |
N/A | 0.271 | 0.007 | 0.239 | 0.075 | 0.077 | 0.000 | 0.000 | 0.160 | 0.129 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 121 | 86 | 100 | 28 | 86 | 0 | 0 | 146 | 129 |
N.S. |
1 | 1.02 | 0.72 | 0.84 | 0.24 | 0.72 | 0.00 | 0.00 | 1.23 | 1.08 |
time (sec) |
N/A | 0.643 | 0.044 | 0.155 | 0.075 | 0.076 | 0.000 | 0.000 | 0.165 | 0.116 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 97 | 74 | 88 | 28 | 74 | 0 | 0 | 121 | 107 |
N.S. |
1 | 1.01 | 0.77 | 0.92 | 0.29 | 0.77 | 0.00 | 0.00 | 1.26 | 1.11 |
time (sec) |
N/A | 0.547 | 0.035 | 0.100 | 0.075 | 0.079 | 0.000 | 0.000 | 0.156 | 0.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 60 | 67 | 28 | 56 | 0 | 0 | 95 | 71 |
N.S. |
1 | 1.00 | 0.82 | 0.92 | 0.38 | 0.77 | 0.00 | 0.00 | 1.30 | 0.97 |
time (sec) |
N/A | 0.452 | 0.028 | 0.065 | 0.075 | 0.077 | 0.000 | 0.000 | 0.150 | 0.180 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 49 | 44 | 26 | 42 | 0 | 0 | 69 | 44 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.53 | 0.86 | 0.00 | 0.00 | 1.41 | 0.90 |
time (sec) |
N/A | 0.355 | 0.015 | 0.042 | 0.076 | 0.077 | 0.000 | 0.000 | 0.172 | 0.144 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 39 | 28 | 34 | 34 | 0 | 0 | 45 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.72 | 0.87 | 0.87 | 0.00 | 0.00 | 1.15 | 0.72 |
time (sec) |
N/A | 0.305 | 0.009 | 0.054 | 0.084 | 0.081 | 0.000 | 0.000 | 0.167 | 0.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 63 | 58 | 28 | 58 | 0 | 0 | 19 | 58 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.44 | 0.92 | 0.00 | 0.00 | 0.30 | 0.92 |
time (sec) |
N/A | 0.402 | 0.023 | 0.083 | 0.249 | 0.080 | 0.000 | 0.000 | 0.158 | 0.135 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 98 | 74 | 79 | 28 | 76 | 0 | 0 | 19 | 79 |
N.S. |
1 | 1.14 | 0.86 | 0.92 | 0.33 | 0.88 | 0.00 | 0.00 | 0.22 | 0.92 |
time (sec) |
N/A | 0.518 | 0.061 | 0.132 | 0.134 | 0.083 | 0.000 | 0.000 | 0.159 | 0.151 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 133 | 86 | 91 | 28 | 88 | 0 | 0 | 19 | 102 |
N.S. |
1 | 1.22 | 0.79 | 0.83 | 0.26 | 0.81 | 0.00 | 0.00 | 0.17 | 0.94 |
time (sec) |
N/A | 0.632 | 0.068 | 0.207 | 0.084 | 0.088 | 0.000 | 0.000 | 0.159 | 0.175 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 168 | 100 | 103 | 28 | 100 | 0 | 0 | 19 | 121 |
N.S. |
1 | 1.27 | 0.76 | 0.78 | 0.21 | 0.76 | 0.00 | 0.00 | 0.14 | 0.92 |
time (sec) |
N/A | 0.770 | 0.096 | 0.315 | 0.091 | 0.087 | 0.000 | 0.000 | 0.154 | 0.174 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 34 | 115 | 28 | 112 | 0 | 0 | 19 | 142 |
N.S. |
1 | 1.00 | 1.00 | 3.38 | 0.82 | 3.29 | 0.00 | 0.00 | 0.56 | 4.18 |
time (sec) |
N/A | 0.274 | 0.009 | 0.477 | 0.077 | 0.083 | 0.000 | 0.000 | 0.155 | 0.195 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 34 | 127 | 28 | 124 | 0 | 0 | 19 | 159 |
N.S. |
1 | 1.00 | 1.00 | 3.74 | 0.82 | 3.65 | 0.00 | 0.00 | 0.56 | 4.68 |
time (sec) |
N/A | 0.276 | 0.010 | 0.690 | 0.081 | 0.075 | 0.000 | 0.000 | 0.156 | 0.210 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 249 | 22 | 84 | 0 | 0 | 105 | 102 |
N.S. |
1 | 1.00 | 1.00 | 10.38 | 0.92 | 3.50 | 0.00 | 0.00 | 4.38 | 4.25 |
time (sec) |
N/A | 0.272 | 0.008 | 0.934 | 0.078 | 0.088 | 0.000 | 0.000 | 0.150 | 0.210 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 213 | 22 | 72 | 0 | 0 | 86 | 90 |
N.S. |
1 | 1.00 | 1.00 | 8.88 | 0.92 | 3.00 | 0.00 | 0.00 | 3.58 | 3.75 |
time (sec) |
N/A | 0.273 | 0.006 | 0.532 | 0.080 | 0.070 | 0.000 | 0.000 | 0.154 | 0.177 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 83 | 57 | 177 | 22 | 60 | 0 | 0 | 67 | 69 |
N.S. |
1 | 1.02 | 0.70 | 2.19 | 0.27 | 0.74 | 0.00 | 0.00 | 0.83 | 0.85 |
time (sec) |
N/A | 0.508 | 0.025 | 0.293 | 0.080 | 0.074 | 0.000 | 0.000 | 0.151 | 0.145 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 59 | 44 | 141 | 22 | 47 | 0 | 0 | 48 | 57 |
N.S. |
1 | 1.02 | 0.76 | 2.43 | 0.38 | 0.81 | 0.00 | 0.00 | 0.83 | 0.98 |
time (sec) |
N/A | 0.430 | 0.018 | 0.153 | 0.081 | 0.073 | 0.000 | 0.000 | 0.149 | 0.130 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 32 | 97 | 18 | 35 | 0 | 0 | 30 | 33 |
N.S. |
1 | 1.00 | 0.91 | 2.77 | 0.51 | 1.00 | 0.00 | 0.00 | 0.86 | 0.94 |
time (sec) |
N/A | 0.333 | 0.008 | 0.072 | 0.077 | 0.078 | 0.000 | 0.000 | 0.155 | 0.126 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 41 | 13 | 13 | 0 | 0 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 2.73 | 0.87 | 0.87 | 0.00 | 0.00 | 0.87 | 0.87 |
time (sec) |
N/A | 0.260 | 0.005 | 0.051 | 0.075 | 0.074 | 0.000 | 0.000 | 0.159 | 0.074 |
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 | 20 | 20 | 19 | 18 | 22 | 27 | 22 | 22 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.90 | 1.10 | 1.35 | 1.10 | 1.10 | 0.90 |
time (sec) |
N/A | 0.263 | 0.007 | 0.060 | 0.026 | 0.068 | 0.048 | 0.130 | 0.158 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 32 | 35 | 22 | 34 | 29 | 0 | 34 | 36 |
N.S. |
1 | 1.00 | 0.73 | 0.80 | 0.50 | 0.77 | 0.66 | 0.00 | 0.77 | 0.82 |
time (sec) |
N/A | 0.343 | 0.010 | 0.113 | 0.077 | 0.078 | 0.081 | 0.000 | 0.157 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 77 | 45 | 47 | 22 | 47 | 44 | 0 | 48 | 48 |
N.S. |
1 | 1.15 | 0.67 | 0.70 | 0.33 | 0.70 | 0.66 | 0.00 | 0.72 | 0.72 |
time (sec) |
N/A | 0.436 | 0.013 | 0.212 | 0.082 | 0.068 | 0.066 | 0.000 | 0.158 | 0.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 110 | 58 | 59 | 22 | 60 | 58 | 0 | 60 | 60 |
N.S. |
1 | 1.33 | 0.70 | 0.71 | 0.27 | 0.72 | 0.70 | 0.00 | 0.72 | 0.72 |
time (sec) |
N/A | 0.552 | 0.015 | 0.364 | 0.075 | 0.082 | 0.076 | 0.000 | 0.156 | 0.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 24 | 71 | 22 | 71 | 71 | 0 | 72 | 72 |
N.S. |
1 | 1.00 | 0.35 | 1.03 | 0.32 | 1.03 | 1.03 | 0.00 | 1.04 | 1.04 |
time (sec) |
N/A | 0.325 | 0.006 | 0.604 | 0.078 | 0.073 | 0.082 | 0.000 | 0.163 | 0.123 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 24 | 83 | 22 | 84 | 85 | 0 | 84 | 84 |
N.S. |
1 | 1.00 | 0.29 | 1.01 | 0.27 | 1.02 | 1.04 | 0.00 | 1.02 | 1.02 |
time (sec) |
N/A | 0.340 | 0.006 | 0.921 | 0.076 | 0.079 | 0.096 | 0.000 | 0.157 | 0.136 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 34 | 120 | 28 | 55 | 0 | 0 | 96 | 88 |
N.S. |
1 | 1.00 | 1.00 | 3.53 | 0.82 | 1.62 | 0.00 | 0.00 | 2.82 | 2.59 |
time (sec) |
N/A | 0.276 | 0.007 | 0.121 | 0.074 | 0.068 | 0.000 | 0.000 | 0.160 | 0.119 |