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Chapter 2
detailed summary tables of results

 2.1 List of integrals sorted by grade for each CAS
  2.1.1 Rubi
  2.1.2 Mathematica
  2.1.3 Maple
  2.1.4 Maxima
  2.1.5 FriCAS
  2.1.6 Sympy
  2.1.7 Giac
 2.2 Detailed conclusion table per each integral for all CAS systems
 2.3 Detailed conclusion table specific for Rubi results

2.1 List of integrals sorted by grade for each CAS

2.1.1 Rubi

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, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

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, 37, 38, 40, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 65, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 133, 136 }

B grade: { }

C grade: { 41, 63, 64, 66, 67, 131, 132, 134, 135 }

F grade: { 39, 47}

2.1.3 Maple

A grade: { 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 35, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 67, 68, 70, 71, 72, 73, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 95, 96, 97, 98, 99, 103, 107, 109, 110, 111, 112, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 132, 133, 135, 136 }

B grade: { 63, 66, 74, 131, 134 }

C grade: { 1, 69 }

F grade: { 26, 32, 33, 34, 36, 37, 38, 39, 47, 94, 100, 101, 102, 104, 105, 106, 108, 114 }

2.1.4 Maxima

A grade: { 9, 14, 15, 16, 17, 22, 25, 29, 30, 31, 40, 46, 48, 58, 62, 65, 68, 77, 82, 83, 84, 85, 90, 93, 97, 98, 99, 107, 109, 115, 126, 130, 133, 136

B grade: { }

C grade: { }

F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 18, 19, 20, 21, 23, 24, 26, 27, 28, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 59, 60, 61, 63, 64, 66, 67, 69, 70, 71, 72, 73, 74, 75, 76, 78, 79, 80, 81, 86, 87, 88, 89, 91, 92, 94, 95, 96, 100, 101, 102, 103, 104, 105, 106, 108, 110, 111, 112, 113, 114, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 127, 128, 129, 131, 132, 134, 135 }

2.1.5 FriCAS

A grade: { 9, 14, 15, 16, 17, 22, 25, 29, 30, 31, 40, 46, 48, 58, 62, 65, 68, 77, 82, 83, 84, 85, 90, 93, 97, 98, 99, 107, 109, 115, 126, 130, 133, 136 }

B grade: { }

C grade: { }

F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 18, 19, 20, 21, 23, 24, 26, 27, 28, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 59, 60, 61, 63, 64, 66, 67, 69, 70, 71, 72, 73, 74, 75, 76, 78, 79, 80, 81, 86, 87, 88, 89, 91, 92, 94, 95, 96, 100, 101, 102, 103, 104, 105, 106, 108, 110, 111, 112, 113, 114, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 127, 128, 129, 131, 132, 134, 135 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 7, 8, 9, 14, 15, 16, 17, 22, 25, 29, 30, 31, 40, 41, 46, 48, 58, 62, 65, 68, 70, 71, 72, 77, 82, 83, 84, 85, 90, 93, 97, 98, 99, 107, 109, 115, 116, 126, 130, 133, 136 }

B grade: { 69, 73, 75, 76 }

C grade: { }

F grade: { 6, 10, 11, 12, 13, 18, 19, 20, 21, 23, 24, 26, 27, 28, 32, 33, 34, 35, 36, 37, 38, 39, 42, 43, 44, 45, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 59, 60, 61, 63, 64, 66, 67, 74, 78, 79, 80, 81, 86, 87, 88, 89, 91, 92, 94, 95, 96, 100, 101, 102, 103, 104, 105, 106, 108, 110, 111, 112, 113, 114, 117, 118, 119, 120, 121, 122, 123, 124, 125, 127, 128, 129, 131, 132, 134, 135 }

2.1.7 Giac

A grade: { 2, 3, 4, 5, 7, 9, 10, 12, 14, 15, 16, 17, 22, 25, 29, 30, 31, 35, 40, 41, 43, 45, 46, 48, 49, 51, 53, 54, 58, 62, 65, 68, 70, 71, 72, 73, 76, 77, 78, 80, 82, 83, 84, 85, 86, 87, 88, 90, 93, 97, 98, 99, 103, 107, 109, 110, 112, 115, 116, 118, 120, 121, 122, 126, 130, 133, 136 }

B grade: { 61, 89, 125 }

C grade: { 8, 11, 13, 18, 19, 20, 21, 23, 24, 42, 44, 50, 52, 55, 56, 57, 59, 60, 64, 67, 75, 79, 81, 91, 92, 111, 113, 117, 119, 123, 124, 127, 128, 129, 132, 135 }

F grade: { 1, 6, 26, 27, 28, 32, 33, 34, 36, 37, 38, 39, 47, 63, 66, 69, 74, 94, 95, 96, 100, 101, 102, 104, 105, 106, 108, 114, 131, 134 }

2.2 Detailed conclusion table per each integral for all CAS systems

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
grade A A A C F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 86 86 82 37 0 0 46 0
normalized size 1 1. 0.95 0.43 0. 0. 0.53 0.
time (sec) N/A 0.074 0.054 0.171 0. 0. 0.958 0.
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 50 56 0 0 61 66
normalized size 1 1. 0.79 0.89 0. 0. 0.97 1.05
time (sec) N/A 0.068 0.036 0.056 0. 0. 1.272 1.295
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 41 44 0 0 46 51
normalized size 1 1. 0.84 0.9 0. 0. 0.94 1.04
time (sec) N/A 0.046 0.027 0.054 0. 0. 1.474 1.287
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 35 35 35 32 0 0 29 39
normalized size 1 1. 1. 0.91 0. 0. 0.83 1.11
time (sec) N/A 0.023 0.006 0.05 0. 0. 0.743 1.305
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 15 15 15 17 0 0 12 20
normalized size 1 1. 1. 1.13 0. 0. 0.8 1.33
time (sec) N/A 0.004 0.001 0.05 0. 0. 0.802 1.251
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 43 43 43 20 0 0 0 0
normalized size 1 1. 1. 0.47 0. 0. 0. 0.
time (sec) N/A 0.02 0.004 0.069 0. 0. 0. 0.
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 25 25 25 32 0 0 36 50
normalized size 1 1. 1. 1.28 0. 0. 1.44 2.
time (sec) N/A 0.045 0.01 0.054 0. 0. 1.169 1.203
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F A C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 46 48 0 0 41 201
normalized size 1 1. 1. 1.04 0. 0. 0.89 4.37
time (sec) N/A 0.065 0.013 0.052 0. 0. 0.891 1.353
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.031 2.513 0.059 0. 0. 0. 0.
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 149 149 107 149 0 0 0 119
normalized size 1 1. 0.72 1. 0. 0. 0. 0.8
time (sec) N/A 0.216 0.13 0.069 0. 0. 0. 1.287
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 112 112 78 84 0 0 0 105
normalized size 1 1. 0.7 0.75 0. 0. 0. 0.94
time (sec) N/A 0.135 0.073 0.149 0. 0. 0. 1.281
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 58 69 0 0 0 76
normalized size 1 1. 0.78 0.93 0. 0. 0. 1.03
time (sec) N/A 0.095 0.053 0.058 0. 0. 0. 1.325
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 32 32 32 32 0 0 0 66
normalized size 1 1. 1. 1. 0. 0. 0. 2.06
time (sec) N/A 0.051 0.008 0.05 0. 0. 0. 1.34
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.023 0.424 0.053 0. 0. 0. 0.
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.024 0.469 0.056 0. 0. 0. 0.
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.025 0.501 0.054 0. 0. 0. 0.
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 47 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.295 4.095 0.185 0. 0. 0. 0.
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 184 184 96 157 0 0 0 74
normalized size 1 1. 0.52 0.85 0. 0. 0. 0.4
time (sec) N/A 0.368 0.197 0.049 0. 0. 0. 1.286
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 118 118 63 99 0 0 0 74
normalized size 1 1. 0.53 0.84 0. 0. 0. 0.63
time (sec) N/A 0.277 0.141 0.053 0. 0. 0. 1.218
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 71 71 50 61 0 0 0 74
normalized size 1 1. 0.7 0.86 0. 0. 0. 1.04
time (sec) N/A 0.206 0.1 0.051 0. 0. 0. 1.264
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 26 26 41 24 0 0 0 62
normalized size 1 1. 1.58 0.92 0. 0. 0. 2.38
time (sec) N/A 0.005 0.036 0.049 0. 0. 0. 1.345
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.024 0.655 0.061 0. 0. 0. 0.
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 39 48 0 0 0 244
normalized size 1 1. 0.85 1.04 0. 0. 0. 5.3
time (sec) N/A 0.232 0.073 0.057 0. 0. 0. 1.318
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 111 111 84 86 0 0 0 1092
normalized size 1 1. 0.76 0.77 0. 0. 0. 9.84
time (sec) N/A 0.325 0.331 0.06 0. 0. 0. 1.337
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.044 5.25 0.148 0. 0. 0. 0.
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 329 329 158 0 0 0 0 0
normalized size 1 1. 0.48 0. 0. 0. 0. 0.
time (sec) N/A 1.495 1.711 0.056 0. 0. 0. 0.
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 154 154 95 135 0 0 0 0
normalized size 1 1. 0.62 0.88 0. 0. 0. 0.
time (sec) N/A 0.333 0.28 0.066 0. 0. 0. 0.
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 43 45 0 0 0 0
normalized size 1 1. 0.88 0.92 0. 0. 0. 0.
time (sec) N/A 0.065 0.009 0.049 0. 0. 0. 0.
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.034 3.302 0.051 0. 0. 0. 0.
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.034 5.059 0.056 0. 0. 0. 0.
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.034 2.753 0.059 0. 0. 0. 0.
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 137 137 106 0 0 0 0 0
normalized size 1 1. 0.77 0. 0. 0. 0. 0.
time (sec) N/A 0.276 1.726 0.097 0. 0. 0. 0.
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 137 137 106 0 0 0 0 0
normalized size 1 1. 0.77 0. 0. 0. 0. 0.
time (sec) N/A 0.263 1.694 0.095 0. 0. 0. 0.
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 128 128 102 0 0 0 0 0
normalized size 1 1. 0.8 0. 0. 0. 0. 0.
time (sec) N/A 0.238 1.642 0.069 0. 0. 0. 0.
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 54 54 95 72 0 0 0 80
normalized size 1 1. 1.76 1.33 0. 0. 0. 1.48
time (sec) N/A 0.031 0.064 0.075 0. 0. 0. 1.571
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 131 131 107 0 0 0 0 0
normalized size 1 1. 0.82 0. 0. 0. 0. 0.
time (sec) N/A 0.254 1.684 0.092 0. 0. 0. 0.
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 139 139 111 0 0 0 0 0
normalized size 1 1. 0.8 0. 0. 0. 0. 0.
time (sec) N/A 0.251 1.698 0.092 0. 0. 0. 0.
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 176 176 128 0 0 0 0 0
normalized size 1 1. 0.73 0. 0. 0. 0. 0.
time (sec) N/A 0.315 3.02 0.093 0. 0. 0. 0.
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 96 96 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.203 1.004 0.056 0. 0. 0. 0.
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 48 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.152 0.821 0.057 0. 0. 0. 0.
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F A A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 10 10 26 9 0 0 7 11
normalized size 1 1. 2.6 0.9 0. 0. 0.7 1.1
time (sec) N/A 0.021 0.014 0.041 0. 0. 1.06 1.146
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 26 26 26 23 0 0 0 55
normalized size 1 1. 1. 0.88 0. 0. 0. 2.12
time (sec) N/A 0.046 0.011 0.05 0. 0. 0. 1.224
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 61 61 44 58 0 0 0 62
normalized size 1 1. 0.72 0.95 0. 0. 0. 1.02
time (sec) N/A 0.081 0.079 0.062 0. 0. 0. 1.164
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 91 91 64 69 0 0 0 89
normalized size 1 1. 0.7 0.76 0. 0. 0. 0.98
time (sec) N/A 0.111 0.104 0.059 0. 0. 0. 1.161
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 126 126 93 138 0 0 0 104
normalized size 1 1. 0.74 1.1 0. 0. 0. 0.83
time (sec) N/A 0.194 0.177 0.059 0. 0. 0. 1.177
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 102 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.188 0.829 0.084 0. 0. 0. 0.
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 44 44 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.095 0.617 0.062 0. 0. 0. 0.
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.026 0.954 0.056 0. 0. 0. 0.
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 34 34 36 33 0 0 0 45
normalized size 1 1. 1.06 0.97 0. 0. 0. 1.32
time (sec) N/A 0.058 0.013 0.053 0. 0. 0. 1.182
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 61 61 42 44 0 0 0 74
normalized size 1 1. 0.69 0.72 0. 0. 0. 1.21
time (sec) N/A 0.066 0.049 0.056 0. 0. 0. 1.177
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 98 98 72 105 0 0 0 88
normalized size 1 1. 0.73 1.07 0. 0. 0. 0.9
time (sec) N/A 0.123 0.097 0.065 0. 0. 0. 1.172
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 128 128 94 111 0 0 0 115
normalized size 1 1. 0.73 0.87 0. 0. 0. 0.9
time (sec) N/A 0.179 0.105 0.078 0. 0. 0. 1.19
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 25 24 0 0 0 31
normalized size 1 1. 0.86 0.83 0. 0. 0. 1.07
time (sec) N/A 0.055 0.026 0.124 0. 0. 0. 1.201
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 25 24 0 0 0 31
normalized size 1 1. 0.86 0.83 0. 0. 0. 1.07
time (sec) N/A 0.056 0.026 0.131 0. 0. 0. 1.182
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F(-1) C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 187 187 123 171 0 0 0 223
normalized size 1 1. 0.66 0.91 0. 0. 0. 1.19
time (sec) N/A 0.708 0.326 0.063 0. 0. 0. 1.229
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 97 97 71 89 0 0 0 146
normalized size 1 1. 0.73 0.92 0. 0. 0. 1.51
time (sec) N/A 0.275 0.238 0.057 0. 0. 0. 1.19
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 34 34 33 31 0 0 0 77
normalized size 1 1. 0.97 0.91 0. 0. 0. 2.26
time (sec) N/A 0.054 0.017 0.049 0. 0. 0. 1.199
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.123 4.921 0.081 0. 0. 0. 0.
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F(-1) C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 218 218 134 209 0 0 0 231
normalized size 1 1. 0.61 0.96 0. 0. 0. 1.06
time (sec) N/A 0.66 0.343 0.068 0. 0. 0. 1.218
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 108 108 74 105 0 0 0 144
normalized size 1 1. 0.69 0.97 0. 0. 0. 1.33
time (sec) N/A 0.232 0.198 0.061 0. 0. 0. 1.202
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 45 43 0 0 0 128
normalized size 1 1. 0.98 0.93 0. 0. 0. 2.78
time (sec) N/A 0.075 0.021 0.055 0. 0. 0. 1.173
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.125 2.614 0.086 0. 0. 0. 0.
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 371 371 345 1212 0 0 0 0
normalized size 1 1. 0.93 3.27 0. 0. 0. 0.
time (sec) N/A 0.92 5.313 0.108 0. 0. 0. 0.
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F F C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 154 154 168 282 0 0 0 12880
normalized size 1 1. 1.09 1.83 0. 0. 0. 83.64
time (sec) N/A 0.228 1.971 0.072 0. 0. 0. 2.034
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.142 28.787 0.088 0. 0. 0. 0.
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 370 370 393 1208 0 0 0 0
normalized size 1 1. 1.06 3.26 0. 0. 0. 0.
time (sec) N/A 1.24 4.214 0.107 0. 0. 0. 0.
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F F C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 153 153 164 280 0 0 0 12439
normalized size 1 1. 1.07 1.83 0. 0. 0. 81.3
time (sec) N/A 0.223 1.745 0.079 0. 0. 0. 1.97
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.107 13.115 0.093 0. 0. 0. 0.
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 90 90 78 124 0 0 654 0
normalized size 1 1. 0.87 1.38 0. 0. 7.27 0.
time (sec) N/A 0.082 0.076 0.099 0. 0. 2.174 0.
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 53 56 0 0 85 66
normalized size 1 1. 0.84 0.89 0. 0. 1.35 1.05
time (sec) N/A 0.071 0.04 0.048 0. 0. 2.905 1.195
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 44 44 0 0 70 51
normalized size 1 1. 0.9 0.9 0. 0. 1.43 1.04
time (sec) N/A 0.048 0.029 0.05 0. 0. 2.435 1.171
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 35 35 35 32 0 0 53 39
normalized size 1 1. 1. 0.91 0. 0. 1.51 1.11
time (sec) N/A 0.024 0.008 0.05 0. 0. 1.749 1.165
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 16 19 0 0 31 22
normalized size 1 1. 1. 1.19 0. 0. 1.94 1.38
time (sec) N/A 0.004 0.001 0.045 0. 0. 1.684 1.191
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 61 61 94 158 0 0 0 0
normalized size 1 1. 1.54 2.59 0. 0. 0. 0.
time (sec) N/A 0.023 0.039 0.091 0. 0. 0. 0.
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F B C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 26 26 26 34 0 0 42 147
normalized size 1 1. 1. 1.31 0. 0. 1.62 5.65
time (sec) N/A 0.048 0.011 0.047 0. 0. 1.384 1.205
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 46 48 0 0 87 72
normalized size 1 1. 1. 1.04 0. 0. 1.89 1.57
time (sec) N/A 0.068 0.014 0.053 0. 0. 3.134 1.161
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.033 2.707 0.056 0. 0. 0. 0.
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 163 163 108 148 0 0 0 119
normalized size 1 1. 0.66 0.91 0. 0. 0. 0.73
time (sec) N/A 0.229 0.116 0.069 0. 0. 0. 1.183
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 112 112 78 84 0 0 0 104
normalized size 1 1. 0.7 0.75 0. 0. 0. 0.93
time (sec) N/A 0.138 0.081 0.073 0. 0. 0. 1.221
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 75 75 58 70 0 0 0 76
normalized size 1 1. 0.77 0.93 0. 0. 0. 1.01
time (sec) N/A 0.091 0.049 0.059 0. 0. 0. 1.298
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 31 30 0 0 0 66
normalized size 1 1. 1. 0.97 0. 0. 0. 2.13
time (sec) N/A 0.054 0.008 0.047 0. 0. 0. 1.283
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.022 0.401 0.047 0. 0. 0. 0.
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.025 0.485 0.055 0. 0. 0. 0.
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.026 0.5 0.052 0. 0. 0. 0.
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 47 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.316 3.607 0.155 0. 0. 0. 0.
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 184 184 95 154 0 0 0 108
normalized size 1 1. 0.52 0.84 0. 0. 0. 0.59
time (sec) N/A 0.374 0.218 0.052 0. 0. 0. 1.209
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 118 118 64 99 0 0 0 108
normalized size 1 1. 0.54 0.84 0. 0. 0. 0.92
time (sec) N/A 0.272 0.15 0.049 0. 0. 0. 1.177
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 71 71 49 60 0 0 0 108
normalized size 1 1. 0.69 0.85 0. 0. 0. 1.52
time (sec) N/A 0.207 0.105 0.049 0. 0. 0. 1.147
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 42 26 0 0 0 93
normalized size 1 1. 1.56 0.96 0. 0. 0. 3.44
time (sec) N/A 0.006 0.036 0.043 0. 0. 0. 1.134
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.021 0.612 0.056 0. 0. 0. 0.
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 47 47 40 49 0 0 0 201
normalized size 1 1. 0.85 1.04 0. 0. 0. 4.28
time (sec) N/A 0.222 0.08 0.057 0. 0. 0. 1.227
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 111 111 76 88 0 0 0 1010
normalized size 1 1. 0.68 0.79 0. 0. 0. 9.1
time (sec) N/A 0.327 0.399 0.056 0. 0. 0. 1.232
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.042 5.273 0.142 0. 0. 0. 0.
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 329 329 159 0 0 0 0 0
normalized size 1 1. 0.48 0. 0. 0. 0. 0.
time (sec) N/A 1.322 1.216 0.053 0. 0. 0. 0.
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 155 155 96 136 0 0 0 0
normalized size 1 1. 0.62 0.88 0. 0. 0. 0.
time (sec) N/A 0.338 0.327 0.061 0. 0. 0. 0.
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 48 48 41 43 0 0 0 0
normalized size 1 1. 0.85 0.9 0. 0. 0. 0.
time (sec) N/A 0.065 0.011 0.046 0. 0. 0. 0.
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.03 1.315 0.049 0. 0. 0. 0.
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.036 2.179 0.059 0. 0. 0. 0.
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.035 2.52 0.066 0. 0. 0. 0.
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 133 133 102 0 0 0 0 0
normalized size 1 1. 0.77 0. 0. 0. 0. 0.
time (sec) N/A 0.251 1.743 0.096 0. 0. 0. 0.
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 133 133 102 0 0 0 0 0
normalized size 1 1. 0.77 0. 0. 0. 0. 0.
time (sec) N/A 0.247 1.716 0.092 0. 0. 0. 0.
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 124 124 98 0 0 0 0 0
normalized size 1 1. 0.79 0. 0. 0. 0. 0.
time (sec) N/A 0.228 1.658 0.073 0. 0. 0. 0.
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 96 73 0 0 0 82
normalized size 1 1. 1.75 1.33 0. 0. 0. 1.49
time (sec) N/A 0.035 0.079 0.07 0. 0. 0. 1.336
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 127 127 102 0 0 0 0 0
normalized size 1 1. 0.8 0. 0. 0. 0. 0.
time (sec) N/A 0.247 1.701 0.096 0. 0. 0. 0.
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 135 135 105 0 0 0 0 0
normalized size 1 1. 0.78 0. 0. 0. 0. 0.
time (sec) N/A 0.239 1.713 0.097 0. 0. 0. 0.
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 172 172 124 0 0 0 0 0
normalized size 1 1. 0.72 0. 0. 0. 0. 0.
time (sec) N/A 0.295 3.042 0.082 0. 0. 0. 0.
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 102 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.251 1.466 0.056 0. 0. 0. 0.
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 44 44 44 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.103 0.01 0.059 0. 0. 0. 0.
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.027 2.051 0.057 0. 0. 0. 0.
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 35 35 37 34 0 0 0 46
normalized size 1 1. 1.06 0.97 0. 0. 0. 1.31
time (sec) N/A 0.061 0.013 0.052 0. 0. 0. 1.168
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 62 62 44 45 0 0 0 77
normalized size 1 1. 0.71 0.73 0. 0. 0. 1.24
time (sec) N/A 0.069 0.05 0.057 0. 0. 0. 1.178
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 111 111 72 107 0 0 0 89
normalized size 1 1. 0.65 0.96 0. 0. 0. 0.8
time (sec) N/A 0.128 0.086 0.062 0. 0. 0. 1.153
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 147 147 94 111 0 0 0 116
normalized size 1 1. 0.64 0.76 0. 0. 0. 0.79
time (sec) N/A 0.183 0.107 0.076 0. 0. 0. 1.237
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 97 97 97 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.199 0.014 0.082 0. 0. 0. 0.
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 50 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.093 0.444 0.057 0. 0. 0. 0.
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 10 10 10 9 0 0 7 11
normalized size 1 1. 1. 0.9 0. 0. 0.7 1.1
time (sec) N/A 0.02 0.003 0.046 0. 0. 1.068 1.243
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 25 25 25 22 0 0 0 54
normalized size 1 1. 1. 0.88 0. 0. 0. 2.16
time (sec) N/A 0.043 0.012 0.049 0. 0. 0. 1.255
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 42 57 0 0 0 59
normalized size 1 1. 0.7 0.95 0. 0. 0. 0.98
time (sec) N/A 0.08 0.046 0.059 0. 0. 0. 1.194
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 89 64 66 0 0 0 88
normalized size 1 1. 0.72 0.74 0. 0. 0. 0.99
time (sec) N/A 0.113 0.081 0.073 0. 0. 0. 1.2
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 142 142 93 136 0 0 0 103
normalized size 1 1. 0.65 0.96 0. 0. 0. 0.73
time (sec) N/A 0.19 0.105 0.065 0. 0. 0. 1.263
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 23 24 0 0 0 31
normalized size 1 1. 0.79 0.83 0. 0. 0. 1.07
time (sec) N/A 0.056 0.026 0.104 0. 0. 0. 1.218
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 27 24 0 0 0 31
normalized size 1 1. 0.93 0.83 0. 0. 0. 1.07
time (sec) N/A 0.053 0.024 0.095 0. 0. 0. 1.245
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 220 220 134 211 0 0 0 230
normalized size 1 1. 0.61 0.96 0. 0. 0. 1.05
time (sec) N/A 0.72 0.322 0.066 0. 0. 0. 1.319
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 109 109 76 106 0 0 0 150
normalized size 1 1. 0.7 0.97 0. 0. 0. 1.38
time (sec) N/A 0.229 0.182 0.062 0. 0. 0. 1.214
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 47 47 46 44 0 0 0 130
normalized size 1 1. 0.98 0.94 0. 0. 0. 2.77
time (sec) N/A 0.076 0.024 0.052 0. 0. 0. 1.191
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.131 6.969 0.085 0. 0. 0. 0.
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 185 185 123 168 0 0 0 221
normalized size 1 1. 0.66 0.91 0. 0. 0. 1.19
time (sec) N/A 0.586 0.301 0.083 0. 0. 0. 1.208
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 96 96 69 88 0 0 0 143
normalized size 1 1. 0.72 0.92 0. 0. 0. 1.49
time (sec) N/A 0.252 0.158 0.062 0. 0. 0. 1.178
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 33 33 32 30 0 0 0 76
normalized size 1 1. 0.97 0.91 0. 0. 0. 2.3
time (sec) N/A 0.056 0.019 0.053 0. 0. 0. 1.165
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.075 3.237 0.085 0. 0. 0. 0.
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 371 371 328 1208 0 0 0 0
normalized size 1 1. 0.88 3.26 0. 0. 0. 0.
time (sec) N/A 1.019 6.403 0.102 0. 0. 0. 0.
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 154 154 144 280 0 0 0 12438
normalized size 1 1. 0.94 1.82 0. 0. 0. 80.77
time (sec) N/A 0.222 1.387 0.078 0. 0. 0. 1.886
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.138 31.069 0.088 0. 0. 0. 0.
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 370 370 433 1212 0 0 0 0
normalized size 1 1. 1.17 3.28 0. 0. 0. 0.
time (sec) N/A 0.801 4.406 0.105 0. 0. 0. 0.
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 153 153 153 282 0 0 0 12879
normalized size 1 1. 1. 1.84 0. 0. 0. 84.18
time (sec) N/A 0.217 1.577 0.074 0. 0. 0. 1.94
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.092 18.706 0.089 0. 0. 0. 0.

2.3 Detailed conclusion table specific for Rubi results

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 [26] had the largest ratio of [ 1.583 ]

Table 2.1Rubi specific breakdown of results for each integral
# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac{\text{number of rules}}{\text{integrand leaf size}}\)
1 A 5 4 1. 8 0.5
2 A 6 4 1. 8 0.5
3 A 5 4 1. 8 0.5
4 A 4 4 1. 6 0.667
5 A 1 1 1. 4 0.25
6 A 1 1 1. 8 0.125
7 A 4 4 1. 8 0.5
8 A 5 4 1. 8 0.5
9 A 0 0 0. 0 0.
10 A 19 11 1. 10 1.1
11 A 15 10 1. 10 1.
12 A 10 8 1. 8 1.
13 A 6 5 1. 6 0.833
14 A 0 0 0. 0 0.
15 A 0 0 0. 0 0.
16 A 0 0 0. 0 0.
17 A 0 0 0. 0 0.
18 A 14 6 1. 10 0.6
19 A 10 6 1. 10 0.6
20 A 7 6 1. 8 0.75
21 A 1 1 1. 6 0.167
22 A 0 0 0. 0 0.
23 A 7 5 1. 10 0.5
24 A 11 6 1. 10 0.6
25 A 0 0 0. 0 0.
26 A 39 19 1. 12 1.583
27 A 17 14 1. 10 1.4
28 A 5 5 1. 8 0.625
29 A 0 0 0. 0 0.
30 A 0 0 0. 0 0.
31 A 0 0 0. 0 0.
32 A 7 5 1. 17 0.294
33 A 7 5 1. 15 0.333
34 A 7 5 1. 13 0.385
35 A 3 1 1. 17 0.059
36 A 7 5 1. 17 0.294
37 A 7 5 1. 17 0.294
38 A 7 5 1. 19 0.263
39 A 14 10 1. 12 0.833
40 A 0 0 0. 0 0.
41 A 1 1 1. 12 0.083
42 A 5 4 1. 9 0.444
43 A 9 7 1. 10 0.7
44 A 14 9 1. 12 0.75
45 A 18 10 1. 12 0.833
46 A 0 0 0. 0 0.
47 A 7 6 1. 12 0.5
48 A 0 0 0. 0 0.
49 A 5 4 1. 9 0.444
50 A 9 7 1. 10 0.7
51 A 13 9 1. 12 0.75
52 A 20 11 1. 12 0.917
53 A 6 4 1. 9 0.444
54 A 6 4 1. 9 0.444
55 A 21 16 1. 16 1.
56 A 11 9 1. 14 0.643
57 A 4 4 1. 13 0.308
58 A 0 0 0. 0 0.
59 A 21 14 1. 16 0.875
60 A 12 10 1. 14 0.714
61 A 4 3 1. 13 0.231
62 A 0 0 0. 0 0.
63 A 24 10 1. 14 0.714
64 A 9 5 1. 13 0.385
65 A 0 0 0. 0 0.
66 A 24 9 1. 14 0.643
67 A 9 5 1. 13 0.385
68 A 0 0 0. 0 0.
69 A 5 4 1. 8 0.5
70 A 6 4 1. 8 0.5
71 A 5 4 1. 8 0.5
72 A 4 4 1. 6 0.667
73 A 1 1 1. 4 0.25
74 A 1 1 1. 8 0.125
75 A 4 4 1. 8 0.5
76 A 5 4 1. 8 0.5
77 A 0 0 0. 0 0.
78 A 19 11 1. 10 1.1
79 A 15 10 1. 10 1.
80 A 10 8 1. 8 1.
81 A 6 5 1. 6 0.833
82 A 0 0 0. 0 0.
83 A 0 0 0. 0 0.
84 A 0 0 0. 0 0.
85 A 0 0 0. 0 0.
86 A 14 6 1. 10 0.6
87 A 10 6 1. 10 0.6
88 A 7 6 1. 8 0.75
89 A 1 1 1. 6 0.167
90 A 0 0 0. 0 0.
91 A 7 5 1. 10 0.5
92 A 11 6 1. 10 0.6
93 A 0 0 0. 0 0.
94 A 39 19 1. 12 1.583
95 A 17 14 1. 10 1.4
96 A 5 5 1. 8 0.625
97 A 0 0 0. 0 0.
98 A 0 0 0. 0 0.
99 A 0 0 0. 0 0.
100 A 7 5 1. 17 0.294
101 A 7 5 1. 15 0.333
102 A 7 5 1. 13 0.385
103 A 3 1 1. 17 0.059
104 A 7 5 1. 17 0.294
105 A 7 5 1. 17 0.294
106 A 7 5 1. 19 0.263
107 A 0 0 0. 0 0.
108 A 7 6 1. 12 0.5
109 A 0 0 0. 0 0.
110 A 5 4 1. 9 0.444
111 A 9 7 1. 10 0.7
112 A 13 9 1. 12 0.75
113 A 20 11 1. 12 0.917
114 A 14 10 1. 12 0.833
115 A 0 0 0. 0 0.
116 A 1 1 1. 12 0.083
117 A 5 4 1. 9 0.444
118 A 9 7 1. 10 0.7
119 A 14 9 1. 12 0.75
120 A 18 10 1. 12 0.833
121 A 6 4 1. 9 0.444
122 A 6 4 1. 9 0.444
123 A 21 14 1. 16 0.875
124 A 12 10 1. 14 0.714
125 A 4 3 1. 13 0.231
126 A 0 0 0. 0 0.
127 A 21 16 1. 16 1.
128 A 11 9 1. 14 0.643
129 A 4 4 1. 13 0.308
130 A 0 0 0. 0 0.
131 A 24 9 1. 14 0.643
132 A 9 5 1. 13 0.385
133 A 0 0 0. 0 0.
134 A 24 10 1. 14 0.714
135 A 9 5 1. 13 0.385
136 A 0 0 0. 0 0.

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