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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, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 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, 132, 133, 135, 136 }

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

C grade: { }

F grade: { }

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, 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, 65, 68, 70, 71, 72, 73, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 93, 95, 96, 97, 98, 99, 103, 108, 109, 110, 111, 112, 113, 114, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 133, 136 }

B grade: { }

C grade: { 1 }

F grade: { 23, 24, 26, 32, 33, 34, 36, 37, 38, 39, 47, 63, 64, 66, 67, 69, 74, 91, 92, 94, 100, 101, 102, 104, 105, 106, 107, 115, 131, 132, 134, 135 }

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, 108, 114, 116, 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, 107, 109, 110, 111, 112, 113, 115, 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, 108, 114, 116, 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, 107, 109, 110, 111, 112, 113, 115, 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, 108, 109, 114, 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, 107, 110, 111, 112, 113, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 127, 128, 129, 131, 132, 134, 135 }

2.1.7 Giac

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, 108, 114, 116, 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, 107, 109, 110, 111, 112, 113, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 127, 128, 129, 131, 132, 134, 135 }

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 76 76 56 37 0 0 44 0
normalized size 1 1. 0.74 0.49 0. 0. 0.58 0.
time (sec) N/A 0.074 0.089 0.104 0. 0. 1.036 0.
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 53 56 0 0 61 0
normalized size 1 1. 0.84 0.89 0. 0. 0.97 0.
time (sec) N/A 0.084 0.036 0.046 0. 0. 1.266 0.
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 44 44 0 0 46 0
normalized size 1 1. 0.9 0.9 0. 0. 0.94 0.
time (sec) N/A 0.056 0.025 0.046 0. 0. 1.48 0.
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 35 35 35 32 0 0 29 0
normalized size 1 1. 1. 0.91 0. 0. 0.83 0.
time (sec) N/A 0.026 0.007 0.046 0. 0. 0.775 0.
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 16 19 0 0 12 0
normalized size 1 1. 1. 1.19 0. 0. 0.75 0.
time (sec) N/A 0.004 0.001 0.049 0. 0. 0.843 0.
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 38 38 38 20 0 0 0 0
normalized size 1 1. 1. 0.53 0. 0. 0. 0.
time (sec) N/A 0.021 0.005 0.067 0. 0. 0. 0.
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 25 25 25 32 0 0 34 0
normalized size 1 1. 1. 1.28 0. 0. 1.36 0.
time (sec) N/A 0.049 0.01 0.049 0. 0. 1.247 0.
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 46 48 0 0 39 0
normalized size 1 1. 1. 1.04 0. 0. 0.85 0.
time (sec) N/A 0.071 0.013 0.048 0. 0. 0.893 0.
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 0.61 0.054 0. 0. 0. 0.
Problem 10 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 149 149 107 138 0 0 0 0
normalized size 1 1. 0.72 0.93 0. 0. 0. 0.
time (sec) N/A 0.232 0.123 0.06 0. 0. 0. 0.
Problem 11 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 112 112 78 84 0 0 0 0
normalized size 1 1. 0.7 0.75 0. 0. 0. 0.
time (sec) N/A 0.147 0.076 0.057 0. 0. 0. 0.
Problem 12 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 74 74 58 69 0 0 0 0
normalized size 1 1. 0.78 0.93 0. 0. 0. 0.
time (sec) N/A 0.095 0.051 0.054 0. 0. 0. 0.
Problem 13 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 31 31 31 30 0 0 0 0
normalized size 1 1. 1. 0.97 0. 0. 0. 0.
time (sec) N/A 0.058 0.007 0.046 0. 0. 0. 0.
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 0.153 0.052 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 0.025 0.169 0.05 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 0.199 0.055 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 0.28 10.295 0.059 0. 0. 0. 0.
Problem 18 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 184 184 94 156 0 0 0 0
normalized size 1 1. 0.51 0.85 0. 0. 0. 0.
time (sec) N/A 0.38 0.199 0.051 0. 0. 0. 0.
Problem 19 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 118 118 64 101 0 0 0 0
normalized size 1 1. 0.54 0.86 0. 0. 0. 0.
time (sec) N/A 0.283 0.185 0.047 0. 0. 0. 0.
Problem 20 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 71 71 47 60 0 0 0 0
normalized size 1 1. 0.66 0.85 0. 0. 0. 0.
time (sec) N/A 0.211 0.1 0.046 0. 0. 0. 0.
Problem 21 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 27 27 42 26 0 0 0 0
normalized size 1 1. 1.56 0.96 0. 0. 0. 0.
time (sec) N/A 0.006 0.035 0.044 0. 0. 0. 0.
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 0.023 0.354 0.056 0. 0. 0. 0.
Problem 23 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 46 46 39 0 0 0 0 0
normalized size 1 1. 0.85 0. 0. 0. 0. 0.
time (sec) N/A 0.228 0.106 0.057 0. 0. 0. 0.
Problem 24 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 111 111 86 0 0 0 0 0
normalized size 1 1. 0.77 0. 0. 0. 0. 0.
time (sec) N/A 0.353 0.273 0.055 0. 0. 0. 0.
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 0.043 5.265 0.056 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 328 328 158 0 0 0 0 0
normalized size 1 1. 0.48 0. 0. 0. 0. 0.
time (sec) N/A 1.49 1.395 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 0.327 0.284 0.056 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 48 48 41 43 0 0 0 0
normalized size 1 1. 0.85 0.9 0. 0. 0. 0.
time (sec) N/A 0.073 0.009 0.045 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 0.028 0.651 0.052 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 1.658 0.052 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 0.035 1.42 0.054 0. 0. 0. 0.
Problem 32 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 128 128 98 0 0 0 0 0
normalized size 1 1. 0.77 0. 0. 0. 0. 0.
time (sec) N/A 0.269 1.685 0.103 0. 0. 0. 0.
Problem 33 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 128 128 98 0 0 0 0 0
normalized size 1 1. 0.77 0. 0. 0. 0. 0.
time (sec) N/A 0.253 1.658 0.108 0. 0. 0. 0.
Problem 34 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 119 119 95 0 0 0 0 0
normalized size 1 1. 0.8 0. 0. 0. 0. 0.
time (sec) N/A 0.232 1.603 0.081 0. 0. 0. 0.
Problem 35 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 55 55 96 73 0 0 0 0
normalized size 1 1. 1.75 1.33 0. 0. 0. 0.
time (sec) N/A 0.033 0.077 0.072 0. 0. 0. 0.
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 122 122 146 0 0 0 0 0
normalized size 1 1. 1.2 0. 0. 0. 0. 0.
time (sec) N/A 0.25 1.821 0.103 0. 0. 0. 0.
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 130 130 148 0 0 0 0 0
normalized size 1 1. 1.14 0. 0. 0. 0. 0.
time (sec) N/A 0.247 1.902 0.106 0. 0. 0. 0.
Problem 38 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 167 167 120 0 0 0 0 0
normalized size 1 1. 0.72 0. 0. 0. 0. 0.
time (sec) N/A 0.304 2.919 0.086 0. 0. 0. 0.
Problem 39 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 96 96 96 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.22 0.017 0.053 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 0.151 0.252 0.053 0. 0. 0. 0.
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 10 10 10 9 0 0 7 0
normalized size 1 1. 1. 0.9 0. 0. 0.7 0.
time (sec) N/A 0.021 0.004 0.042 0. 0. 1.024 0.
Problem 42 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 25 25 25 22 0 0 0 0
normalized size 1 1. 1. 0.88 0. 0. 0. 0.
time (sec) N/A 0.049 0.01 0.045 0. 0. 0. 0.
Problem 43 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 61 61 44 58 0 0 0 0
normalized size 1 1. 0.72 0.95 0. 0. 0. 0.
time (sec) N/A 0.09 0.083 0.053 0. 0. 0. 0.
Problem 44 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 90 90 64 68 0 0 0 0
normalized size 1 1. 0.71 0.76 0. 0. 0. 0.
time (sec) N/A 0.128 0.076 0.053 0. 0. 0. 0.
Problem 45 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 125 125 93 126 0 0 0 0
normalized size 1 1. 0.74 1.01 0. 0. 0. 0.
time (sec) N/A 0.204 0.163 0.056 0. 0. 0. 0.
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 101 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.197 0.446 0.056 0. 0. 0. 0.
Problem 47 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 0.098 0.009 0.054 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 0.028 0.261 0.056 0. 0. 0. 0.
Problem 49 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 34 34 36 33 0 0 0 0
normalized size 1 1. 1.06 0.97 0. 0. 0. 0.
time (sec) N/A 0.06 0.013 0.052 0. 0. 0. 0.
Problem 50 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 62 62 46 46 0 0 0 0
normalized size 1 1. 0.74 0.74 0. 0. 0. 0.
time (sec) N/A 0.072 0.051 0.056 0. 0. 0. 0.
Problem 51 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 98 98 72 95 0 0 0 0
normalized size 1 1. 0.73 0.97 0. 0. 0. 0.
time (sec) N/A 0.132 0.094 0.058 0. 0. 0. 0.
Problem 52 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 128 128 94 104 0 0 0 0
normalized size 1 1. 0.73 0.81 0. 0. 0. 0.
time (sec) N/A 0.189 0.102 0.059 0. 0. 0. 0.
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 25 24 0 0 0 0
normalized size 1 1. 0.86 0.83 0. 0. 0. 0.
time (sec) N/A 0.056 0.028 0.203 0. 0. 0. 0.
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 25 24 0 0 0 0
normalized size 1 1. 0.86 0.83 0. 0. 0. 0.
time (sec) N/A 0.057 0.028 0.207 0. 0. 0. 0.
Problem 55 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 186 186 123 170 0 0 0 0
normalized size 1 1. 0.66 0.91 0. 0. 0. 0.
time (sec) N/A 0.584 0.307 0.061 0. 0. 0. 0.
Problem 56 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 97 97 73 89 0 0 0 0
normalized size 1 1. 0.75 0.92 0. 0. 0. 0.
time (sec) N/A 0.252 0.174 0.056 0. 0. 0. 0.
Problem 57 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 33 33 32 30 0 0 0 0
normalized size 1 1. 0.97 0.91 0. 0. 0. 0.
time (sec) N/A 0.062 0.016 0.047 0. 0. 0. 0.
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 0.128 0.659 0.057 0. 0. 0. 0.
Problem 59 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 219 219 134 198 0 0 0 0
normalized size 1 1. 0.61 0.9 0. 0. 0. 0.
time (sec) N/A 0.697 0.334 0.063 0. 0. 0. 0.
Problem 60 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 109 109 78 106 0 0 0 0
normalized size 1 1. 0.72 0.97 0. 0. 0. 0.
time (sec) N/A 0.214 0.192 0.059 0. 0. 0. 0.
Problem 61 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 46 46 45 43 0 0 0 0
normalized size 1 1. 0.98 0.93 0. 0. 0. 0.
time (sec) N/A 0.075 0.025 0.051 0. 0. 0. 0.
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 0.114 0.959 0.058 0. 0. 0. 0.
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 371 371 887 0 0 0 0 0
normalized size 1 1. 2.39 0. 0. 0. 0. 0.
time (sec) N/A 0.964 17.368 0.302 0. 0. 0. 0.
Problem 64 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 153 153 209 0 0 0 0 0
normalized size 1 1. 1.37 0. 0. 0. 0. 0.
time (sec) N/A 0.252 2.278 0.132 0. 0. 0. 0.
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 0.131 10.429 0.063 0. 0. 0. 0.
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 371 371 887 0 0 0 0 0
normalized size 1 1. 2.39 0. 0. 0. 0. 0.
time (sec) N/A 1.317 8.202 0.303 0. 0. 0. 0.
Problem 67 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 153 153 209 0 0 0 0 0
normalized size 1 1. 1.37 0. 0. 0. 0. 0.
time (sec) N/A 0.242 0.581 0.154 0. 0. 0. 0.
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 0.103 10.445 0.066 0. 0. 0. 0.
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 76 76 74 0 0 0 649 0
normalized size 1 1. 0.97 0. 0. 0. 8.54 0.
time (sec) N/A 0.077 0.057 0.069 0. 0. 2.347 0.
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 53 56 0 0 85 0
normalized size 1 1. 0.84 0.89 0. 0. 1.35 0.
time (sec) N/A 0.081 0.041 0.044 0. 0. 2.895 0.
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 44 44 0 0 70 0
normalized size 1 1. 0.9 0.9 0. 0. 1.43 0.
time (sec) N/A 0.055 0.027 0.043 0. 0. 2.438 0.
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 35 35 35 32 0 0 53 0
normalized size 1 1. 1. 0.91 0. 0. 1.51 0.
time (sec) N/A 0.027 0.007 0.045 0. 0. 1.792 0.
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 16 19 0 0 31 0
normalized size 1 1. 1. 1.19 0. 0. 1.94 0.
time (sec) N/A 0.004 0.002 0.043 0. 0. 1.743 0.
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 52 52 52 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.022 0.005 0.083 0. 0. 0. 0.
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 25 25 25 32 0 0 39 0
normalized size 1 1. 1. 1.28 0. 0. 1.56 0.
time (sec) N/A 0.051 0.012 0.046 0. 0. 1.425 0.
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 46 48 0 0 87 0
normalized size 1 1. 1. 1.04 0. 0. 1.89 0.
time (sec) N/A 0.073 0.013 0.045 0. 0. 3.101 0.
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 0.032 0.605 0.054 0. 0. 0. 0.
Problem 78 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 164 164 107 138 0 0 0 0
normalized size 1 1. 0.65 0.84 0. 0. 0. 0.
time (sec) N/A 0.235 0.1 0.06 0. 0. 0. 0.
Problem 79 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 112 112 78 84 0 0 0 0
normalized size 1 1. 0.7 0.75 0. 0. 0. 0.
time (sec) N/A 0.147 0.073 0.056 0. 0. 0. 0.
Problem 80 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 74 74 57 69 0 0 0 0
normalized size 1 1. 0.77 0.93 0. 0. 0. 0.
time (sec) N/A 0.092 0.043 0.059 0. 0. 0. 0.
Problem 81 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 31 31 31 30 0 0 0 0
normalized size 1 1. 1. 0.97 0. 0. 0. 0.
time (sec) N/A 0.053 0.008 0.046 0. 0. 0. 0.
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 0.142 0.05 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 0.026 0.168 0.052 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 0.195 0.053 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 0.258 9.799 0.055 0. 0. 0. 0.
Problem 86 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 184 184 94 156 0 0 0 0
normalized size 1 1. 0.51 0.85 0. 0. 0. 0.
time (sec) N/A 0.388 0.198 0.056 0. 0. 0. 0.
Problem 87 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 118 118 64 101 0 0 0 0
normalized size 1 1. 0.54 0.86 0. 0. 0. 0.
time (sec) N/A 0.28 0.177 0.048 0. 0. 0. 0.
Problem 88 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 71 71 47 60 0 0 0 0
normalized size 1 1. 0.66 0.85 0. 0. 0. 0.
time (sec) N/A 0.21 0.098 0.047 0. 0. 0. 0.
Problem 89 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 27 27 42 26 0 0 0 0
normalized size 1 1. 1.56 0.96 0. 0. 0. 0.
time (sec) N/A 0.006 0.035 0.045 0. 0. 0. 0.
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 0.02 0.264 0.054 0. 0. 0. 0.
Problem 91 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 46 46 39 0 0 0 0 0
normalized size 1 1. 0.85 0. 0. 0. 0. 0.
time (sec) N/A 0.216 0.103 0.057 0. 0. 0. 0.
Problem 92 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 111 111 80 0 0 0 0 0
normalized size 1 1. 0.72 0. 0. 0. 0. 0.
time (sec) N/A 0.331 0.306 0.056 0. 0. 0. 0.
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 0.043 3.775 0.053 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 327 327 158 0 0 0 0 0
normalized size 1 1. 0.48 0. 0. 0. 0. 0.
time (sec) N/A 1.306 1.117 0.051 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 154 154 95 135 0 0 0 0
normalized size 1 1. 0.62 0.88 0. 0. 0. 0.
time (sec) N/A 0.327 0.23 0.059 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 0.072 0.009 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 0.536 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 0.035 1.126 0.056 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 1.438 0.055 0. 0. 0. 0.
Problem 100 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 128 128 97 0 0 0 0 0
normalized size 1 1. 0.76 0. 0. 0. 0. 0.
time (sec) N/A 0.248 0.952 0.112 0. 0. 0. 0.
Problem 101 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 128 128 97 0 0 0 0 0
normalized size 1 1. 0.76 0. 0. 0. 0. 0.
time (sec) N/A 0.225 1.664 0.111 0. 0. 0. 0.
Problem 102 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 119 119 93 0 0 0 0 0
normalized size 1 1. 0.78 0. 0. 0. 0. 0.
time (sec) N/A 0.217 0.877 0.086 0. 0. 0. 0.
Problem 103 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 55 55 96 73 0 0 0 0
normalized size 1 1. 1.75 1.33 0. 0. 0. 0.
time (sec) N/A 0.033 0.078 0.079 0. 0. 0. 0.
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 122 122 144 0 0 0 0 0
normalized size 1 1. 1.18 0. 0. 0. 0. 0.
time (sec) N/A 0.239 1.139 0.114 0. 0. 0. 0.
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 130 130 146 0 0 0 0 0
normalized size 1 1. 1.12 0. 0. 0. 0. 0.
time (sec) N/A 0.236 1.199 0.115 0. 0. 0. 0.
Problem 106 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 167 167 119 0 0 0 0 0
normalized size 1 1. 0.71 0. 0. 0. 0. 0.
time (sec) N/A 0.285 2.981 0.083 0. 0. 0. 0.
Problem 107 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 96 96 96 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.213 0.016 0.054 0. 0. 0. 0.
Problem 108 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 0.148 0.208 0.055 0. 0. 0. 0.
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 10 10 10 9 0 0 7 0
normalized size 1 1. 1. 0.9 0. 0. 0.7 0.
time (sec) N/A 0.02 0.003 0.043 0. 0. 1.027 0.
Problem 110 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 25 25 25 22 0 0 0 0
normalized size 1 1. 1. 0.88 0. 0. 0. 0.
time (sec) N/A 0.049 0.011 0.046 0. 0. 0. 0.
Problem 111 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 61 61 46 58 0 0 0 0
normalized size 1 1. 0.75 0.95 0. 0. 0. 0.
time (sec) N/A 0.086 0.051 0.059 0. 0. 0. 0.
Problem 112 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 90 90 64 68 0 0 0 0
normalized size 1 1. 0.71 0.76 0. 0. 0. 0.
time (sec) N/A 0.122 0.078 0.06 0. 0. 0. 0.
Problem 113 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 142 142 94 125 0 0 0 0
normalized size 1 1. 0.66 0.88 0. 0. 0. 0.
time (sec) N/A 0.213 0.102 0.062 0. 0. 0. 0.
Problem 114 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 101 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.206 0.428 0.056 0. 0. 0. 0.
Problem 115 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 0.099 0.007 0.056 0. 0. 0. 0.
Problem 116 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 0.257 0.056 0. 0. 0. 0.
Problem 117 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 34 34 36 33 0 0 0 0
normalized size 1 1. 1.06 0.97 0. 0. 0. 0.
time (sec) N/A 0.059 0.011 0.056 0. 0. 0. 0.
Problem 118 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 62 62 44 46 0 0 0 0
normalized size 1 1. 0.71 0.74 0. 0. 0. 0.
time (sec) N/A 0.072 0.074 0.057 0. 0. 0. 0.
Problem 119 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 109 109 72 96 0 0 0 0
normalized size 1 1. 0.66 0.88 0. 0. 0. 0.
time (sec) N/A 0.127 0.109 0.062 0. 0. 0. 0.
Problem 120 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 146 146 94 104 0 0 0 0
normalized size 1 1. 0.64 0.71 0. 0. 0. 0.
time (sec) N/A 0.189 0.102 0.062 0. 0. 0. 0.
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 27 24 0 0 0 0
normalized size 1 1. 0.93 0.83 0. 0. 0. 0.
time (sec) N/A 0.056 0.027 0.128 0. 0. 0. 0.
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 27 24 0 0 0 0
normalized size 1 1. 0.93 0.83 0. 0. 0. 0.
time (sec) N/A 0.054 0.024 0.11 0. 0. 0. 0.
Problem 123 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 220 220 134 199 0 0 0 0
normalized size 1 1. 0.61 0.9 0. 0. 0. 0.
time (sec) N/A 0.697 0.37 0.066 0. 0. 0. 0.
Problem 124 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 109 109 78 106 0 0 0 0
normalized size 1 1. 0.72 0.97 0. 0. 0. 0.
time (sec) N/A 0.224 0.185 0.062 0. 0. 0. 0.
Problem 125 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 46 46 45 43 0 0 0 0
normalized size 1 1. 0.98 0.93 0. 0. 0. 0.
time (sec) N/A 0.076 0.025 0.05 0. 0. 0. 0.
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 0.134 0.88 0.062 0. 0. 0. 0.
Problem 127 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 186 186 123 171 0 0 0 0
normalized size 1 1. 0.66 0.92 0. 0. 0. 0.
time (sec) N/A 0.572 0.279 0.067 0. 0. 0. 0.
Problem 128 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 97 97 73 89 0 0 0 0
normalized size 1 1. 0.75 0.92 0. 0. 0. 0.
time (sec) N/A 0.251 0.16 0.067 0. 0. 0. 0.
Problem 129 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 33 33 32 30 0 0 0 0
normalized size 1 1. 0.97 0.91 0. 0. 0. 0.
time (sec) N/A 0.061 0.016 0.047 0. 0. 0. 0.
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 0.077 0.548 0.056 0. 0. 0. 0.
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 371 371 916 0 0 0 0 0
normalized size 1 1. 2.47 0. 0. 0. 0. 0.
time (sec) N/A 0.989 9.773 0.298 0. 0. 0. 0.
Problem 132 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 153 153 209 0 0 0 0 0
normalized size 1 1. 1.37 0. 0. 0. 0. 0.
time (sec) N/A 0.239 0.619 0.14 0. 0. 0. 0.
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 0.132 9.976 0.061 0. 0. 0. 0.
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 371 371 916 0 0 0 0 0
normalized size 1 1. 2.47 0. 0. 0. 0. 0.
time (sec) N/A 0.857 2.461 0.297 0. 0. 0. 0.
Problem 135 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 153 153 209 0 0 0 0 0
normalized size 1 1. 1.37 0. 0. 0. 0. 0.
time (sec) N/A 0.253 0.604 0.135 0. 0. 0. 0.
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 0.087 9.172 0.065 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 14 10 1. 12 0.833
108 A 0 0 0. 0 0.
109 A 1 1 1. 12 0.083
110 A 5 4 1. 9 0.444
111 A 9 7 1. 10 0.7
112 A 14 9 1. 12 0.75
113 A 18 10 1. 12 0.833
114 A 0 0 0. 0 0.
115 A 7 6 1. 12 0.5
116 A 0 0 0. 0 0.
117 A 5 4 1. 9 0.444
118 A 9 7 1. 10 0.7
119 A 13 9 1. 12 0.75
120 A 20 11 1. 12 0.917
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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