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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
  2.1.8 Mupad
 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 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 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 }

B grade: { 3, 24, 53 }

C grade: { 101, 102 }

F grade: { 37 }

2.1.3 Maple

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, 27, 28, 29, 30, 31, 32, 33, 34, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 56, 57, 61, 67, 72, 74, 75, 77, 79, 83, 84, 85, 86, 87, 91, 92, 95, 100 }

B grade: { 35, 36, 93, 94, 98, 99 }

C grade: { 26, 39, 55, 58, 59, 60, 62, 63, 82, 88, 89, 90 }

F grade: { 24, 25, 37, 38, 53, 54, 64, 65, 66, 68, 69, 70, 71, 73, 76, 78, 80, 81, 96, 97, 101, 102 }

2.1.4 Maxima

A grade: { 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 23, 27, 28, 29, 30, 31, 32, 33, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 77, 79, 83, 84, 85, 86, 87, 91, 92, 93, 94, 98, 99, 100 }

B grade: { 1, 2, 4, 17, 22, 88, 89, 90, 95 }

C grade: { 34, 35, 36, 50, 52 }

F grade: { 24, 25, 26, 37, 38, 39, 53, 54, 55, 76, 78, 80, 81, 82, 96, 97, 101, 102 }

2.1.5 FriCAS

A grade: { 1, 3, 4, 5, 7, 8, 10, 11, 12, 14, 15, 17, 18, 19, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 40, 42, 44, 46, 47, 48, 50, 52, 56, 57, 67, 72, 74, 75, 77, 79, 83, 87, 88, 90, 91, 92, 93, 94, 95, 98, 99, 100 }

B grade: { 2, 6, 9, 13, 16, 20, 22, 41, 43, 45, 49, 51, 61, 84, 85, 86, 89, 96, 97, 101, 102 }

C grade: { }

F grade: { 37, 38, 39, 53, 54, 55, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69, 70, 71, 73, 76, 78, 80, 81, 82 }

2.1.6 Sympy

A grade: { 1, 3, 8, 10, 15, 17, 22, 23, 27, 28, 32, 33, 34, 35, 36, 40, 48, 50, 52, 56, 57, 74, 75, 77, 83, 91, 92, 93, 94, 95, 100 }

B grade: { }

C grade: { }

F grade: { 2, 4, 5, 6, 7, 9, 11, 12, 13, 14, 16, 18, 19, 20, 21, 24, 25, 26, 29, 30, 31, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 51, 53, 54, 55, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 76, 78, 79, 80, 81, 82, 84, 85, 86, 87, 88, 89, 90, 96, 97, 98, 99, 101, 102 }

2.1.7 Giac

A grade: { 1, 2, 3, 4, 5, 9, 11, 12, 16, 17, 18, 19, 22, 23, 27, 28, 40, 50, 56, 57, 74, 75, 77, 79, 83, 87, 91, 92, 95, 100 }

B grade: { 7, 8, 10, 14, 15, 21, 29, 30, 31, 32, 33, 34, 35, 36, 42, 44, 48, 93, 94, 98, 99 }

C grade: { 88, 89, 90 }

F grade: { 6, 13, 20, 24, 25, 26, 37, 38, 39, 41, 43, 45, 46, 47, 49, 51, 52, 53, 54, 55, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 76, 78, 80, 81, 82, 84, 85, 86, 96, 97, 101, 102 }

2.1.8 Mupad

A grade: { 23, 27, 40, 56, 74, 75, 77, 79, 83, 91, 92 }

B grade: { 1, 3, 8, 10, 15, 17, 22, 28, 33, 34, 35, 36, 48, 50, 52, 57, 95, 100 }

C grade: { }

F grade: { 2, 4, 5, 6, 7, 9, 11, 12, 13, 14, 16, 18, 19, 20, 21, 24, 25, 26, 29, 30, 31, 32, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 51, 53, 54, 55, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 76, 78, 80, 81, 82, 84, 85, 86, 87, 88, 89, 90, 93, 94, 96, 97, 98, 99, 101, 102 }

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 Mupad
grade A A A A B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 31 45 81 29 36 47 28
normalized size 1 1.00 0.91 1.32 2.38 0.85 1.06 1.38 0.82
time (sec) N/A 0.036 0.034 0.017 0.307 0.504 0.804 0.258 0.088
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 69 69 67 74 110 190 0 75 -1
normalized size 1 1.00 0.97 1.07 1.59 2.75 0.00 1.09 -0.01
time (sec) N/A 0.041 0.068 0.075 0.305 0.516 0.000 0.358 0.000
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 31 14 13 13 19 25 13
normalized size 1 1.00 2.07 0.93 0.87 0.87 1.27 1.67 0.87
time (sec) N/A 0.016 0.010 0.004 0.300 0.722 0.214 0.389 0.374
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 45 40 86 48 0 41 -1
normalized size 1 1.00 0.85 0.75 1.62 0.91 0.00 0.77 -0.02
time (sec) N/A 0.018 0.036 0.030 0.302 0.462 0.000 0.302 0.000
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 23 27 24 39 0 24 -1
normalized size 1 1.00 0.92 1.08 0.96 1.56 0.00 0.96 -0.04
time (sec) N/A 0.035 0.014 0.020 0.373 0.484 0.000 0.311 0.000
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 70 70 54 184 0 0 -1
normalized size 1 1.00 1.06 1.06 0.82 2.79 0.00 0.00 -0.02
time (sec) N/A 0.035 0.062 0.032 0.319 0.480 0.000 0.000 0.000
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 38 58 39 71 0 109 -1
normalized size 1 1.00 0.90 1.38 0.93 1.69 0.00 2.60 -0.02
time (sec) N/A 0.092 0.042 0.022 0.427 0.459 0.000 0.643 0.000
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 42 55 59 56 78 117 42
normalized size 1 1.00 0.82 1.08 1.16 1.10 1.53 2.29 0.82
time (sec) N/A 0.050 0.104 0.055 0.329 0.480 1.550 0.545 0.103
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 99 99 101 90 95 427 0 97 -1
normalized size 1 1.00 1.02 0.91 0.96 4.31 0.00 0.98 -0.01
time (sec) N/A 0.096 0.216 0.089 0.430 0.444 0.000 0.909 0.000
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 27 34 38 29 60 56 22
normalized size 1 1.00 0.87 1.10 1.23 0.94 1.94 1.81 0.71
time (sec) N/A 0.027 0.023 0.013 0.333 0.522 0.438 0.791 0.379
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 78 78 86 51 56 73 0 58 -1
normalized size 1 1.00 1.10 0.65 0.72 0.94 0.00 0.74 -0.01
time (sec) N/A 0.046 0.070 0.052 0.429 0.445 0.000 0.563 0.000
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 33 34 31 49 0 35 -1
normalized size 1 1.00 0.89 0.92 0.84 1.32 0.00 0.95 -0.03
time (sec) N/A 0.059 0.020 0.055 0.412 0.412 0.000 0.344 0.000
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 88 88 94 86 61 396 0 0 -1
normalized size 1 1.00 1.07 0.98 0.69 4.50 0.00 0.00 -0.01
time (sec) N/A 0.068 0.223 0.069 0.381 0.500 0.000 0.000 0.000
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 57 57 46 69 36 90 0 126 -1
normalized size 1 1.00 0.81 1.21 0.63 1.58 0.00 2.21 -0.02
time (sec) N/A 0.121 0.090 0.057 0.378 0.458 0.000 0.160 0.000
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 58 93 100 94 92 183 70
normalized size 1 1.00 0.73 1.18 1.27 1.19 1.16 2.32 0.89
time (sec) N/A 0.083 0.127 0.091 0.353 0.464 2.772 0.209 0.126
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 160 160 184 157 162 904 0 166 -1
normalized size 1 1.00 1.15 0.98 1.01 5.65 0.00 1.04 -0.01
time (sec) N/A 0.138 0.302 0.122 0.433 0.432 0.000 0.197 0.000
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 33 33 33 28 62 46 44 56 28
normalized size 1 1.00 1.00 0.85 1.88 1.39 1.33 1.70 0.85
time (sec) N/A 0.033 0.013 0.015 0.324 0.519 0.783 0.238 0.060
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 125 125 136 86 91 112 0 95 -1
normalized size 1 1.00 1.09 0.69 0.73 0.90 0.00 0.76 -0.01
time (sec) N/A 0.072 0.129 0.059 0.397 0.443 0.000 0.308 0.000
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 49 55 50 83 0 50 -1
normalized size 1 1.00 0.89 1.00 0.91 1.51 0.00 0.91 -0.02
time (sec) N/A 0.094 0.034 0.077 0.426 0.439 0.000 0.244 0.000
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 136 136 204 149 102 892 0 0 -1
normalized size 1 1.00 1.50 1.10 0.75 6.56 0.00 0.00 -0.01
time (sec) N/A 0.110 0.315 0.097 0.442 0.507 0.000 0.000 0.000
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 91 91 90 120 58 160 0 223 -1
normalized size 1 1.00 0.99 1.32 0.64 1.76 0.00 2.45 -0.01
time (sec) N/A 0.214 0.118 0.084 0.428 0.498 0.000 0.189 0.000
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 67 52 126 154 94 108 52
normalized size 1 1.00 1.00 0.78 1.88 2.30 1.40 1.61 0.78
time (sec) N/A 0.047 0.025 0.119 0.424 0.415 7.686 0.230 0.474
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 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 0.020 2.506 0.052 0.000 0.431 0.000 0.000 0.000
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 214 214 735 0 0 252 0 0 -1
normalized size 1 1.00 3.43 0.00 0.00 1.18 0.00 0.00 -0.00
time (sec) N/A 0.201 12.547 0.239 0.000 0.594 0.000 0.000 0.000
Problem 25 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 135 135 152 0 0 174 0 0 -1
normalized size 1 1.00 1.13 0.00 0.00 1.29 0.00 0.00 -0.01
time (sec) N/A 0.148 0.579 0.163 0.000 0.753 0.000 0.000 0.000
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 95 95 98 77 0 124 0 0 -1
normalized size 1 1.00 1.03 0.81 0.00 1.31 0.00 0.00 -0.01
time (sec) N/A 0.068 0.153 0.100 0.000 0.452 0.000 0.000 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 26 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 -0.04
time (sec) N/A 0.025 2.965 0.071 0.000 0.499 0.000 0.000 0.000
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 15 14 13 13 19 25 13
normalized size 1 1.00 1.00 0.93 0.87 0.87 1.27 1.67 0.87
time (sec) N/A 0.020 0.008 0.005 0.301 0.420 0.771 0.216 0.382
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 78 78 70 130 47 93 0 534 -1
normalized size 1 1.00 0.90 1.67 0.60 1.19 0.00 6.85 -0.01
time (sec) N/A 0.143 0.067 0.056 0.367 0.417 0.000 0.394 0.000
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 54 93 44 83 0 313 -1
normalized size 1 1.00 0.90 1.55 0.73 1.38 0.00 5.22 -0.02
time (sec) N/A 0.107 0.046 0.048 0.349 0.419 0.000 0.218 0.000
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 33 33 33 56 36 58 0 173 -1
normalized size 1 1.00 1.00 1.70 1.09 1.76 0.00 5.24 -0.03
time (sec) N/A 0.076 0.020 0.046 0.359 0.441 0.000 0.138 0.000
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 21 21 21 27 24 39 17 44 -1
normalized size 1 1.00 1.00 1.29 1.14 1.86 0.81 2.10 -0.05
time (sec) N/A 0.032 0.010 0.043 0.394 0.396 1.029 0.408 0.000
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 14 13 15 15 27 13
normalized size 1 1.00 1.00 1.08 1.00 1.15 1.15 2.08 1.00
time (sec) N/A 0.017 0.004 0.004 0.375 0.417 0.982 0.423 0.367
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 29 44 48 34 29 95 29
normalized size 1 1.00 1.00 1.52 1.66 1.17 1.00 3.28 1.00
time (sec) N/A 0.030 0.028 0.019 0.407 0.510 1.769 0.241 0.380
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B C A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 39 94 47 43 46 214 67
normalized size 1 1.00 0.85 2.04 1.02 0.93 1.00 4.65 1.46
time (sec) N/A 0.054 0.048 0.016 0.353 0.382 2.963 0.201 0.427
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B C A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 62 62 48 165 48 53 61 386 85
normalized size 1 1.00 0.77 2.66 0.77 0.85 0.98 6.23 1.37
time (sec) N/A 0.080 0.065 0.017 0.388 0.385 4.899 0.188 0.442
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F(-1) F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 146 146 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.251 180.001 0.200 0.000 0.473 0.000 0.000 0.000
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 90 90 88 0 0 0 0 0 -1
normalized size 1 1.00 0.98 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.158 0.256 0.184 0.000 0.425 0.000 0.000 0.000
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 63 70 0 0 0 0 -1
normalized size 1 1.00 0.94 1.04 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.088 0.087 0.109 0.000 0.422 0.000 0.000 0.000
Problem 40 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 26 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 -0.04
time (sec) N/A 0.024 3.418 0.086 0.000 0.449 0.000 0.000 0.000
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 104 104 102 138 62 323 0 0 -1
normalized size 1 1.00 0.98 1.33 0.60 3.11 0.00 0.00 -0.01
time (sec) N/A 0.090 0.112 0.079 1.339 0.435 0.000 0.000 0.000
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 62 62 56 93 44 89 0 353 -1
normalized size 1 1.00 0.90 1.50 0.71 1.44 0.00 5.69 -0.02
time (sec) N/A 0.113 0.044 0.042 0.507 0.428 0.000 0.200 0.000
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 86 86 84 103 58 267 0 0 -1
normalized size 1 1.00 0.98 1.20 0.67 3.10 0.00 0.00 -0.01
time (sec) N/A 0.066 0.088 0.048 0.386 0.426 0.000 0.000 0.000
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 39 58 39 63 0 193 -1
normalized size 1 1.00 0.93 1.38 0.93 1.50 0.00 4.60 -0.02
time (sec) N/A 0.082 0.026 0.025 0.390 0.470 0.000 0.184 0.000
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 70 70 71 228 0 0 -1
normalized size 1 1.00 1.04 1.04 1.06 3.40 0.00 0.00 -0.01
time (sec) N/A 0.044 0.067 0.048 0.360 0.560 0.000 0.000 0.000
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 25 27 24 39 0 0 -1
normalized size 1 1.00 1.00 1.08 0.96 1.56 0.00 0.00 -0.04
time (sec) N/A 0.033 0.015 0.029 0.397 0.431 0.000 0.000 0.000
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 57 57 50 44 62 52 0 0 -1
normalized size 1 1.00 0.88 0.77 1.09 0.91 0.00 0.00 -0.02
time (sec) N/A 0.031 0.034 0.039 0.458 0.545 0.000 0.000 0.000
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 15 14 13 17 22 27 13
normalized size 1 1.00 1.00 0.93 0.87 1.13 1.47 1.80 0.87
time (sec) N/A 0.019 0.005 0.005 0.320 0.470 2.738 0.165 0.375
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 75 75 74 82 62 251 0 0 -1
normalized size 1 1.00 0.99 1.09 0.83 3.35 0.00 0.00 -0.01
time (sec) N/A 0.048 0.073 0.050 0.388 0.512 0.000 0.000 0.000
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 34 55 48 40 37 43 58
normalized size 1 1.00 1.00 1.62 1.41 1.18 1.09 1.26 1.71
time (sec) N/A 0.034 0.030 0.031 0.475 0.536 7.672 0.192 0.406
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 93 93 97 117 62 313 0 0 -1
normalized size 1 1.00 1.04 1.26 0.67 3.37 0.00 0.00 -0.01
time (sec) N/A 0.068 0.123 0.058 0.775 0.454 0.000 0.000 0.000
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 47 47 44 73 47 50 51 0 74
normalized size 1 1.00 0.94 1.55 1.00 1.06 1.09 0.00 1.57
time (sec) N/A 0.059 0.050 0.048 0.375 0.472 19.216 0.000 0.436
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 194 194 1039 0 0 0 0 0 -1
normalized size 1 1.00 5.36 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.221 24.294 0.197 0.000 0.537 0.000 0.000 0.000
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 117 117 122 0 0 0 0 0 -1
normalized size 1 1.00 1.04 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.166 0.829 0.183 0.000 0.557 0.000 0.000 0.000
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 87 87 84 77 0 0 0 0 -1
normalized size 1 1.00 0.97 0.89 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.087 0.144 0.103 0.000 0.572 0.000 0.000 0.000
Problem 56 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 26 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 -0.04
time (sec) N/A 0.024 3.397 0.079 0.000 0.515 0.000 0.000 0.000
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 8 8 8 7 6 6 7 11 6
normalized size 1 1.00 1.00 0.88 0.75 0.75 0.88 1.38 0.75
time (sec) N/A 0.012 0.003 0.009 0.442 0.561 0.263 0.172 0.400
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 75 75 88 77 73 0 0 0 -1
normalized size 1 1.00 1.17 1.03 0.97 0.00 0.00 0.00 -0.01
time (sec) N/A 0.074 0.098 0.126 0.563 0.523 0.000 0.000 0.000
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 75 75 88 69 73 0 0 0 -1
normalized size 1 1.00 1.17 0.92 0.97 0.00 0.00 0.00 -0.01
time (sec) N/A 0.041 0.085 0.089 0.508 0.414 0.000 0.000 0.000
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 79 74 61 0 0 0 -1
normalized size 1 1.00 1.18 1.10 0.91 0.00 0.00 0.00 -0.01
time (sec) N/A 0.017 0.082 0.072 0.524 0.743 0.000 0.000 0.000
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 23 33 30 55 0 0 -1
normalized size 1 1.00 0.92 1.32 1.20 2.20 0.00 0.00 -0.04
time (sec) N/A 0.037 0.027 0.022 0.610 0.578 0.000 0.000 0.000
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 68 77 65 0 0 0 -1
normalized size 1 1.00 0.96 1.08 0.92 0.00 0.00 0.00 -0.01
time (sec) N/A 0.063 0.071 0.112 0.692 0.524 0.000 0.000 0.000
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 75 75 72 77 69 0 0 0 -1
normalized size 1 1.00 0.96 1.03 0.92 0.00 0.00 0.00 -0.01
time (sec) N/A 0.062 0.076 0.053 0.668 0.439 0.000 0.000 0.000
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 99 99 89 0 82 0 0 0 -1
normalized size 1 1.00 0.90 0.00 0.83 0.00 0.00 0.00 -0.01
time (sec) N/A 0.137 1.509 0.131 0.443 0.479 0.000 0.000 0.000
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 99 99 85 0 82 0 0 0 -1
normalized size 1 1.00 0.86 0.00 0.83 0.00 0.00 0.00 -0.01
time (sec) N/A 0.107 1.308 0.145 0.421 0.506 0.000 0.000 0.000
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 89 89 81 0 68 0 0 0 -1
normalized size 1 1.00 0.91 0.00 0.76 0.00 0.00 0.00 -0.01
time (sec) N/A 0.065 1.113 0.095 0.418 0.485 0.000 0.000 0.000
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 39 40 37 69 0 0 -1
normalized size 1 1.00 0.91 0.93 0.86 1.60 0.00 0.00 -0.02
time (sec) N/A 0.064 0.035 0.140 0.401 0.535 0.000 0.000 0.000
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 91 91 79 0 74 0 0 0 -1
normalized size 1 1.00 0.87 0.00 0.81 0.00 0.00 0.00 -0.01
time (sec) N/A 0.128 1.428 0.099 0.429 0.457 0.000 0.000 0.000
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 166 166 161 0 149 0 0 0 -1
normalized size 1 1.00 0.97 0.00 0.90 0.00 0.00 0.00 -0.01
time (sec) N/A 0.195 1.538 0.164 0.499 0.446 0.000 0.000 0.000
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 166 166 161 0 149 0 0 0 -1
normalized size 1 1.00 0.97 0.00 0.90 0.00 0.00 0.00 -0.01
time (sec) N/A 0.133 1.599 0.135 0.502 0.654 0.000 0.000 0.000
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 150 150 140 0 125 0 0 0 -1
normalized size 1 1.00 0.93 0.00 0.83 0.00 0.00 0.00 -0.01
time (sec) N/A 0.076 1.211 0.125 0.495 0.489 0.000 0.000 0.000
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 52 67 62 115 0 0 -1
normalized size 1 1.00 0.78 1.00 0.93 1.72 0.00 0.00 -0.01
time (sec) N/A 0.100 0.062 0.191 0.433 0.604 0.000 0.000 0.000
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 154 154 126 0 133 0 0 0 -1
normalized size 1 1.00 0.82 0.00 0.86 0.00 0.00 0.00 -0.01
time (sec) N/A 0.182 1.408 0.137 0.464 0.485 0.000 0.000 0.000
Problem 74 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 21 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 0.021 5.406 0.881 0.000 0.727 0.000 0.000 0.000
Problem 75 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 23 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 -0.04
time (sec) N/A 0.025 8.076 0.743 0.000 0.651 0.000 0.000 0.000
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 94 94 93 0 0 0 0 0 -1
normalized size 1 1.00 0.99 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.104 0.135 0.960 0.000 0.519 0.000 0.000 0.000
Problem 77 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 39 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 0.051 5.895 0.880 0.000 0.587 0.000 0.000 0.000
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 150 150 167 0 0 0 0 0 -1
normalized size 1 1.00 1.11 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.199 0.411 0.846 0.000 0.512 0.000 0.000 0.000
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 41 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 0.060 8.447 0.790 0.000 0.521 0.000 0.000 0.000
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 220 220 185 0 0 0 0 0 -1
normalized size 1 1.00 0.84 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.234 2.151 0.324 0.000 0.555 0.000 0.000 0.000
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 143 143 117 0 0 0 0 0 -1
normalized size 1 1.00 0.82 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.174 1.998 0.260 0.000 0.496 0.000 0.000 0.000
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 99 99 102 115 0 0 0 0 -1
normalized size 1 1.00 1.03 1.16 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.071 0.182 0.270 0.000 0.570 0.000 0.000 0.000
Problem 83 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 28 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 -0.04
time (sec) N/A 0.038 24.337 0.175 0.000 0.539 0.000 0.000 0.000
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 46 74 34 139 0 0 -1
normalized size 1 1.00 1.02 1.64 0.76 3.09 0.00 0.00 -0.02
time (sec) N/A 0.093 0.067 0.047 0.406 0.456 0.000 0.000 0.000
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 54 90 47 182 0 0 -1
normalized size 1 1.00 0.81 1.34 0.70 2.72 0.00 0.00 -0.01
time (sec) N/A 0.123 0.138 0.123 0.428 0.626 0.000 0.000 0.000
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 113 113 95 152 70 303 0 0 -1
normalized size 1 1.00 0.84 1.35 0.62 2.68 0.00 0.00 -0.01
time (sec) N/A 0.217 0.219 0.169 0.482 0.538 0.000 0.000 0.000
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 60 54 69 97 0 53 -1
normalized size 1 1.00 0.85 0.76 0.97 1.37 0.00 0.75 -0.01
time (sec) N/A 0.045 1.577 0.076 0.395 0.725 0.000 0.146 0.000
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B A F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 113 113 63 136 817 165 0 137 -1
normalized size 1 1.00 0.56 1.20 7.23 1.46 0.00 1.21 -0.01
time (sec) N/A 0.096 0.138 0.070 0.743 0.532 0.000 0.150 0.000
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B B F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 44 66 649 134 0 99 -1
normalized size 1 1.00 0.81 1.22 12.02 2.48 0.00 1.83 -0.02
time (sec) N/A 0.053 0.028 0.043 0.675 0.552 0.000 0.148 0.000
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B A F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 27 36 477 55 0 39 -1
normalized size 1 1.00 0.73 0.97 12.89 1.49 0.00 1.05 -0.03
time (sec) N/A 0.017 0.005 0.042 0.585 0.586 0.000 0.129 0.000
Problem 91 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 20 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 0.036 9.983 0.063 0.000 0.531 0.000 0.000 0.000
Problem 92 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 15 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 -0.07
time (sec) N/A 0.039 13.406 0.067 0.000 0.658 0.000 0.000 0.000
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 346 346 104 831 486 104 269 914 -1
normalized size 1 1.00 0.30 2.40 1.40 0.30 0.78 2.64 -0.00
time (sec) N/A 0.418 1.302 0.022 0.363 0.535 1.743 0.164 0.000
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 167 167 72 303 293 68 151 299 -1
normalized size 1 1.00 0.43 1.81 1.75 0.41 0.90 1.79 -0.01
time (sec) N/A 0.186 0.207 0.019 0.325 0.643 0.615 0.136 0.000
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 50 63 111 44 65 64 43
normalized size 1 1.00 0.93 1.17 2.06 0.81 1.20 1.19 0.80
time (sec) N/A 0.046 0.063 0.008 0.320 0.591 0.475 0.136 0.441
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 124 124 130 0 0 217 0 0 -1
normalized size 1 1.00 1.05 0.00 0.00 1.75 0.00 0.00 -0.01
time (sec) N/A 0.287 0.989 0.032 0.000 0.582 0.000 0.000 0.000
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 182 182 199 0 0 315 0 0 -1
normalized size 1 1.00 1.09 0.00 0.00 1.73 0.00 0.00 -0.01
time (sec) N/A 0.361 3.092 0.030 0.000 0.487 0.000 0.000 0.000
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 537 537 378 1815 642 180 0 2162 -1
normalized size 1 1.00 0.70 3.38 1.20 0.34 0.00 4.03 -0.00
time (sec) N/A 0.697 2.902 0.020 0.331 0.489 0.000 0.207 0.000
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 261 261 118 659 371 109 0 706 -1
normalized size 1 1.00 0.45 2.52 1.42 0.42 0.00 2.70 -0.00
time (sec) N/A 0.315 0.348 0.020 0.323 0.520 0.000 0.147 0.000
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 65 133 137 58 94 128 75
normalized size 1 1.00 0.76 1.56 1.61 0.68 1.11 1.51 0.88
time (sec) N/A 0.079 0.086 0.017 0.318 0.564 1.216 0.132 0.467
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 232 232 233 0 0 503 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 2.17 0.00 0.00 -0.00
time (sec) N/A 0.519 0.070 0.040 0.000 0.673 0.000 0.000 0.000
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 329 329 210 0 0 704 0 0 -1
normalized size 1 1.00 0.64 0.00 0.00 2.14 0.00 0.00 -0.00
time (sec) N/A 0.724 1.849 0.035 0.000 0.644 0.000 0.000 0.000

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 [88] had the largest ratio of [.7500]

Table 2.1:Rubi 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 3 3 1.00 12 0.250
2 A 4 4 1.00 12 0.333
3 A 2 2 1.00 10 0.200
4 A 3 3 1.00 8 0.375
5 A 3 3 1.00 12 0.250
6 A 4 4 1.00 12 0.333
7 A 5 5 1.00 12 0.417
8 A 3 3 1.00 14 0.214
9 A 6 5 1.00 14 0.357
10 A 3 3 1.00 12 0.250
11 A 5 4 1.00 10 0.400
12 A 5 4 1.00 14 0.286
13 A 6 6 1.00 14 0.429
14 A 7 6 1.00 14 0.429
15 A 4 4 1.00 14 0.286
16 A 10 5 1.00 14 0.357
17 A 3 2 1.00 12 0.167
18 A 8 4 1.00 10 0.400
19 A 8 4 1.00 14 0.286
20 A 9 5 1.00 14 0.357
21 A 12 6 1.00 14 0.429
22 A 3 2 1.00 12 0.167
23 A 0 0 0.00 0 0.000
24 A 8 3 1.00 16 0.188
25 A 5 3 1.00 16 0.188
26 A 3 2 1.00 14 0.143
27 A 0 0 0.00 0 0.000
28 A 2 2 1.00 12 0.167
29 A 7 5 1.00 12 0.417
30 A 6 5 1.00 10 0.500
31 A 5 5 1.00 8 0.625
32 A 3 3 1.00 12 0.250
33 A 2 2 1.00 12 0.167
34 A 3 3 1.00 12 0.250
35 A 4 3 1.00 12 0.250
36 A 5 3 1.00 12 0.250
37 A 9 4 1.00 16 0.250
38 A 6 4 1.00 16 0.250
39 A 4 3 1.00 14 0.214
40 A 0 0 0.00 0 0.000
41 A 7 6 1.00 12 0.500
42 A 6 5 1.00 12 0.417
43 A 6 6 1.00 12 0.500
44 A 5 5 1.00 10 0.500
45 A 5 5 1.00 8 0.625
46 A 3 3 1.00 12 0.250
47 A 4 4 1.00 12 0.333
48 A 2 2 1.00 12 0.167
49 A 5 5 1.00 12 0.417
50 A 3 3 1.00 12 0.250
51 A 6 6 1.00 12 0.500
52 A 4 3 1.00 12 0.250
53 A 9 4 1.00 16 0.250
54 A 6 4 1.00 16 0.250
55 A 4 3 1.00 14 0.214
56 A 0 0 0.00 0 0.000
57 A 2 2 1.00 12 0.167
58 A 3 2 1.00 12 0.167
59 A 3 2 1.00 10 0.200
60 A 3 2 1.00 8 0.250
61 A 3 3 1.00 12 0.250
62 A 3 2 1.00 12 0.167
63 A 3 2 1.00 12 0.167
64 A 5 3 1.00 14 0.214
65 A 5 3 1.00 12 0.250
66 A 5 3 1.00 10 0.300
67 A 5 4 1.00 14 0.286
68 A 5 3 1.00 14 0.214
69 A 8 3 1.00 14 0.214
70 A 8 3 1.00 12 0.250
71 A 8 3 1.00 10 0.300
72 A 8 4 1.00 14 0.286
73 A 8 3 1.00 14 0.214
74 A 0 0 0.00 0 0.000
75 A 0 0 0.00 0 0.000
76 A 3 3 1.00 20 0.150
77 A 0 0 0.00 0 0.000
78 A 5 5 1.00 22 0.227
79 A 0 0 0.00 0 0.000
80 A 8 3 1.00 16 0.188
81 A 5 3 1.00 16 0.188
82 A 3 2 1.00 14 0.143
83 A 0 0 0.00 0 0.000
84 A 5 5 1.00 16 0.312
85 A 7 6 1.00 18 0.333
86 A 12 6 1.00 18 0.333
87 A 4 4 1.00 18 0.222
88 A 12 9 1.00 12 0.750
89 A 8 7 1.00 10 0.700
90 A 4 4 1.00 8 0.500
91 A 0 0 0.00 0 0.000
92 A 0 0 0.00 0 0.000
93 A 16 4 1.00 18 0.222
94 A 10 4 1.00 16 0.250
95 A 4 4 1.00 14 0.286
96 A 10 5 1.00 18 0.278
97 A 11 6 1.00 18 0.333
98 A 23 6 1.00 18 0.333
99 A 13 5 1.00 16 0.312
100 A 5 4 1.00 14 0.286
101 A 13 5 1.00 18 0.278
102 A 14 6 1.00 18 0.333

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