A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36 }
B grade: { }
C grade: { }
F grade: { }
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36 }
B grade: { }
C grade: { }
F grade: { }
A grade: { 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36 }
B grade: { }
C grade: { }
A grade: { 4, 9, 14, 15, 19, 23, 27, 28, 32, 36 }
B grade: { }
C grade: { 1, 2, 3, 6, 7, 8, 11, 12, 13, 16, 17, 18, 20, 21, 22, 24, 25, 26, 29, 30, 31, 33, 34, 35 }
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36 }
B grade: { }
C grade: { }
F grade: { }
A grade: { 3, 4, 8, 9, 13, 14, 15, 18, 19, 22, 23, 26, 27, 28, 31, 32, 35, 36 }
C grade: { }
F grade: { 1, 2, 5, 6, 7, 10, 11, 16, 17, 20, 21, 24, 29, 30, 33, 34 }
A grade: { 4, 9, 14, 15, 19, 23, 27, 28, 32, 36 }
B grade: { }
C grade: { 1, 2, 3, 6, 7, 8, 11, 12, 13, 16, 17, 18, 20, 21, 22, 24, 25, 26, 29, 30, 31, 33, 34, 35 }
A grade: { 4, 9, 14, 15, 19, 23, 27, 28, 32, 36 }
B grade: { 3, 8, 11, 12, 13, 31 }
C grade: { }
F grade: { 1, 2, 5, 6, 7, 10, 16, 17, 18, 20, 21, 22, 24, 25, 26, 29, 30, 33, 34, 35 }
Detailed conclusion table per each integral is given by 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 just an F.
In this table,the column normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\)
Problem 1 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 249 | 157 | 204 | 1558 | 172 | 0 | 227 | -1 |
normalized size | 1 | 1.00 | 0.63 | 0.82 | 6.26 | 0.69 | 0.00 | 0.91 | -0.00 |
time (sec) | N/A | 0.243 | 0.718 | 0.025 | 1.687 | 0.462 | 0.000 | 0.202 | 0.000 |
Problem 2 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 123 | 111 | 100 | 580 | 118 | 0 | 183 | -1 |
normalized size | 1 | 1.00 | 0.90 | 0.81 | 4.72 | 0.96 | 0.00 | 1.49 | -0.01 |
time (sec) | N/A | 0.037 | 0.384 | 0.023 | 1.760 | 0.414 | 0.000 | 1.220 | 0.000 |
Problem 3 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | A | C | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 84 | 82 | 112 | 102 | 88 | 135 | 99 |
normalized size | 1 | 1.00 | 0.87 | 0.85 | 1.15 | 1.05 | 0.91 | 1.39 | 1.02 |
time (sec) | N/A | 0.021 | 0.174 | 0.025 | 0.335 | 0.443 | 0.590 | 0.192 | 0.056 |
Problem 4 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | A | A | A | A | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.06 |
time (sec) | N/A | 0.008 | 4.207 | 0.122 | 0.000 | 0.469 | 0.000 | 0.000 | 0.000 |
Problem 5 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | F | F | A | F | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 110 | 0 | 0 | 117 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.00 | 0.00 | 1.06 | 0.00 | 0.00 | -0.01 |
time (sec) | N/A | 0.083 | 0.796 | 0.541 | 0.000 | 0.463 | 0.000 | 0.000 | 0.000 |
Problem 6 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 251 | 165 | 202 | 1556 | 179 | 0 | 229 | -1 |
normalized size | 1 | 1.00 | 0.66 | 0.80 | 6.20 | 0.71 | 0.00 | 0.91 | -0.00 |
time (sec) | N/A | 0.204 | 0.717 | 0.026 | 2.847 | 0.430 | 0.000 | 0.180 | 0.000 |
Problem 7 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 124 | 117 | 99 | 578 | 126 | 0 | 185 | -1 |
normalized size | 1 | 1.00 | 0.94 | 0.80 | 4.66 | 1.02 | 0.00 | 1.49 | -0.01 |
time (sec) | N/A | 0.044 | 0.325 | 0.028 | 3.136 | 0.424 | 0.000 | 0.208 | 0.000 |
Problem 8 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | A | C | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 89 | 80 | 112 | 107 | 94 | 137 | 105 |
normalized size | 1 | 1.00 | 0.91 | 0.82 | 1.14 | 1.09 | 0.96 | 1.40 | 1.07 |
time (sec) | N/A | 0.025 | 0.187 | 0.026 | 0.590 | 0.420 | 0.581 | 0.264 | 6.144 |
Problem 9 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | A | A | A | A | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) | N/A | 0.008 | 4.860 | 0.115 | 0.000 | 0.410 | 0.000 | 0.000 | 0.000 |
Problem 10 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | F | F | A | F | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 115 | 0 | 0 | 124 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.05 | 0.00 | 0.00 | 1.13 | 0.00 | 0.00 | -0.01 |
time (sec) | N/A | 0.084 | 0.812 | 0.620 | 0.000 | 0.465 | 0.000 | 0.000 | 0.000 |
Problem 11 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | F | C | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 66 | 59 | 156 | 59 | 0 | 75 | 64 |
normalized size | 1 | 1.00 | 0.80 | 0.72 | 1.90 | 0.72 | 0.00 | 0.91 | 0.78 |
time (sec) | N/A | 0.033 | 0.120 | 0.023 | 1.210 | 0.413 | 0.000 | 0.134 | 6.656 |
Problem 12 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | B | C | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 39 | 30 | 123 | 32 | 160 | 65 | 32 |
normalized size | 1 | 1.00 | 0.95 | 0.73 | 3.00 | 0.78 | 3.90 | 1.59 | 0.78 |
time (sec) | N/A | 0.013 | 0.048 | 0.025 | 0.700 | 0.452 | 1.417 | 0.184 | 0.061 |
Problem 13 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | A | C | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 20 | 70 | 22 | 29 | 39 | 19 |
normalized size | 1 | 1.00 | 1.00 | 0.83 | 2.92 | 0.92 | 1.21 | 1.62 | 0.79 |
time (sec) | N/A | 0.006 | 0.026 | 0.022 | 0.415 | 0.407 | 0.531 | 1.231 | 0.042 |
Problem 14 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | A | A | A | A | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.06 |
time (sec) | N/A | 0.008 | 14.168 | 0.139 | 0.000 | 0.432 | 0.000 | 0.000 | 0.000 |
Problem 15 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | A | A | A | A | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) | N/A | 0.025 | 11.401 | 0.145 | 0.000 | 0.407 | 0.000 | 0.000 | 0.000 |
Problem 16 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 248 | 170 | 191 | 1603 | 178 | 0 | 214 | -1 |
normalized size | 1 | 1.00 | 0.69 | 0.77 | 6.46 | 0.72 | 0.00 | 0.86 | -0.00 |
time (sec) | N/A | 0.227 | 0.666 | 0.076 | 1.507 | 0.447 | 0.000 | 0.225 | 0.000 |
Problem 17 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 126 | 118 | 95 | 608 | 124 | 0 | 170 | -1 |
normalized size | 1 | 1.00 | 0.94 | 0.75 | 4.83 | 0.98 | 0.00 | 1.35 | -0.01 |
time (sec) | N/A | 0.073 | 0.279 | 0.060 | 3.114 | 0.425 | 0.000 | 0.416 | 0.000 |
Problem 18 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | A | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 97 | 72 | 124 | 93 | 83 | 122 | -1 |
normalized size | 1 | 1.00 | 0.97 | 0.72 | 1.24 | 0.93 | 0.83 | 1.22 | -0.01 |
time (sec) | N/A | 0.050 | 0.104 | 0.060 | 1.065 | 0.426 | 1.168 | 0.794 | 0.000 |
Problem 19 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | A | A | A | A | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) | N/A | 0.027 | 6.875 | 0.285 | 0.000 | 0.419 | 0.000 | 0.000 | 0.000 |
Problem 20 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 248 | 175 | 199 | 1603 | 187 | 0 | 216 | -1 |
normalized size | 1 | 1.00 | 0.71 | 0.80 | 6.46 | 0.75 | 0.00 | 0.87 | -0.00 |
time (sec) | N/A | 0.220 | 0.710 | 0.073 | 2.608 | 0.465 | 0.000 | 0.924 | 0.000 |
Problem 21 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 126 | 122 | 99 | 608 | 133 | 0 | 172 | -1 |
normalized size | 1 | 1.00 | 0.97 | 0.79 | 4.83 | 1.06 | 0.00 | 1.37 | -0.01 |
time (sec) | N/A | 0.066 | 0.289 | 0.059 | 3.360 | 0.451 | 0.000 | 0.237 | 0.000 |
Problem 22 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | A | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 102 | 76 | 124 | 96 | 88 | 124 | -1 |
normalized size | 1 | 1.00 | 1.02 | 0.76 | 1.24 | 0.96 | 0.88 | 1.24 | -0.01 |
time (sec) | N/A | 0.048 | 0.109 | 0.060 | 0.459 | 0.419 | 1.217 | 0.587 | 0.000 |
Problem 23 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | A | A | A | A | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) | N/A | 0.028 | 7.190 | 0.286 | 0.000 | 0.405 | 0.000 | 0.000 | 0.000 |
Problem 24 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 77 | 64 | 171 | 57 | 0 | 64 | -1 |
normalized size | 1 | 1.00 | 0.91 | 0.75 | 2.01 | 0.67 | 0.00 | 0.75 | -0.01 |
time (sec) | N/A | 0.062 | 0.146 | 0.072 | 1.182 | 0.401 | 0.000 | 0.717 | 0.000 |
Problem 25 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | B | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 42 | 35 | 135 | 37 | 121 | 54 | -1 |
normalized size | 1 | 1.00 | 0.91 | 0.76 | 2.93 | 0.80 | 2.63 | 1.17 | -0.02 |
time (sec) | N/A | 0.030 | 0.056 | 0.058 | 0.535 | 0.403 | 1.909 | 0.190 | 0.000 |
Problem 26 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | A | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 20 | 34 | 19 | 22 | 26 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.74 | 1.26 | 0.70 | 0.81 | 0.96 | -0.04 |
time (sec) | N/A | 0.015 | 0.013 | 0.056 | 0.428 | 0.397 | 0.992 | 0.173 | 0.000 |
Problem 27 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | A | A | A | A | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) | N/A | 0.028 | 10.485 | 0.270 | 0.000 | 0.434 | 0.000 | 0.000 | 0.000 |
Problem 28 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | A | A | A | A | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) | N/A | 0.049 | 10.634 | 0.328 | 0.000 | 0.409 | 0.000 | 0.000 | 0.000 |
Problem 29 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 285 | 186 | 399 | 2259 | 231 | 0 | 569 | -1 |
normalized size | 1 | 1.00 | 0.65 | 1.40 | 7.93 | 0.81 | 0.00 | 2.00 | -0.00 |
time (sec) | N/A | 0.271 | 1.326 | 0.029 | 2.244 | 0.429 | 0.000 | 0.391 | 0.000 |
Problem 30 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 140 | 128 | 184 | 695 | 135 | 0 | 327 | -1 |
normalized size | 1 | 1.00 | 0.91 | 1.31 | 4.96 | 0.96 | 0.00 | 2.34 | -0.01 |
time (sec) | N/A | 0.056 | 0.656 | 0.025 | 0.901 | 0.423 | 0.000 | 0.191 | 0.000 |
Problem 31 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | A | C | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 84 | 82 | 112 | 102 | 88 | 135 | 99 |
normalized size | 1 | 1.00 | 0.87 | 0.85 | 1.15 | 1.05 | 0.91 | 1.39 | 1.02 |
time (sec) | N/A | 0.022 | 0.098 | 0.023 | 0.327 | 0.414 | 0.609 | 0.194 | 0.002 |
Problem 32 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | A | A | A | A | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) | N/A | 0.011 | 7.748 | 0.209 | 0.000 | 0.397 | 0.000 | 0.000 | 0.000 |
Problem 33 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 291 | 291 | 215 | 378 | 2344 | 257 | 0 | 538 | -1 |
normalized size | 1 | 1.00 | 0.74 | 1.30 | 8.05 | 0.88 | 0.00 | 1.85 | -0.00 |
time (sec) | N/A | 0.337 | 1.216 | 0.074 | 2.094 | 0.457 | 0.000 | 0.570 | 0.000 |
Problem 34 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 150 | 140 | 170 | 735 | 149 | 0 | 304 | -1 |
normalized size | 1 | 1.00 | 0.93 | 1.13 | 4.90 | 0.99 | 0.00 | 2.03 | -0.01 |
time (sec) | N/A | 0.093 | 0.456 | 0.060 | 0.878 | 0.432 | 0.000 | 1.340 | 0.000 |
Problem 35 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | A | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 97 | 72 | 124 | 93 | 83 | 122 | -1 |
normalized size | 1 | 1.00 | 0.97 | 0.72 | 1.24 | 0.93 | 0.83 | 1.22 | -0.01 |
time (sec) | N/A | 0.048 | 0.074 | 0.055 | 0.424 | 0.436 | 1.180 | 0.269 | 0.000 |
Problem 36 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | A | A | A | A | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) | N/A | 0.037 | 7.396 | 0.419 | 0.000 | 0.436 | 0.000 | 0.000 | 0.000 |
The following table is specific to Rubi. It gives additional statistics for each integral. the column steps is the number of steps used by Rubi to obtain the antiderivative. The rules column is the number of unique rules used. The integrand size column is the leaf size of the integrand. Finally the ratio \(\frac {\text {number of rules}}{\text {integrand size}}\) is given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [24] had the largest ratio of [.4667]
# | grade |
|
|
|
|
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\) | |||||||||||
1 | A | 8 | 6 | 1.00 | 15 | 0.400 | |||||||||||
2 | A | 4 | 4 | 1.00 | 13 | 0.308 | |||||||||||
3 | A | 3 | 3 | 1.00 | 11 | 0.273 | |||||||||||
4 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||
5 | A | 5 | 4 | 1.00 | 33 | 0.121 | |||||||||||
6 | A | 8 | 6 | 1.00 | 16 | 0.375 | |||||||||||
7 | A | 4 | 4 | 1.00 | 14 | 0.286 | |||||||||||
8 | A | 3 | 3 | 1.00 | 12 | 0.250 | |||||||||||
9 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||
10 | A | 5 | 4 | 1.00 | 35 | 0.114 | |||||||||||
11 | A | 6 | 6 | 1.00 | 13 | 0.462 | |||||||||||
12 | A | 3 | 3 | 1.00 | 11 | 0.273 | |||||||||||
13 | A | 2 | 2 | 1.00 | 9 | 0.222 | |||||||||||
14 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||
15 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||
16 | A | 10 | 7 | 1.00 | 17 | 0.412 | |||||||||||
17 | A | 6 | 5 | 1.00 | 15 | 0.333 | |||||||||||
18 | A | 5 | 4 | 1.00 | 13 | 0.308 | |||||||||||
19 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||
20 | A | 10 | 7 | 1.00 | 18 | 0.389 | |||||||||||
21 | A | 6 | 5 | 1.00 | 16 | 0.312 | |||||||||||
22 | A | 5 | 4 | 1.00 | 14 | 0.286 | |||||||||||
23 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||
24 | A | 8 | 7 | 1.00 | 15 | 0.467 | |||||||||||
25 | A | 5 | 4 | 1.00 | 13 | 0.308 | |||||||||||
26 | A | 4 | 3 | 1.00 | 11 | 0.273 | |||||||||||
27 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||
28 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||
29 | A | 8 | 6 | 1.00 | 19 | 0.316 | |||||||||||
30 | A | 4 | 4 | 1.00 | 17 | 0.235 | |||||||||||
31 | A | 3 | 3 | 1.00 | 11 | 0.273 | |||||||||||
32 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||
33 | A | 10 | 7 | 1.00 | 21 | 0.333 | |||||||||||
34 | A | 6 | 5 | 1.00 | 19 | 0.263 | |||||||||||
35 | A | 5 | 4 | 1.00 | 13 | 0.308 | |||||||||||
36 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||