## Chapter 2detailed summary tables of results

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 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, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 400 }

#### 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, 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, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 276, 277, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 400 }

B grade: { 39, 40, 41, 42, 202, 203, 204, 239, 278 }

C grade: { 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 275, 366 }

F grade: { 136, 137, 138, 272, 273, 274}

#### 2.1.3 Maple

A grade: { 1, 2, 3, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 43, 44, 45, 46, 47, 52, 53, 58, 59, 60, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 88, 89, 90, 91, 100, 101, 102, 103, 104, 110, 111, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 128, 129, 130, 131, 132, 134, 135, 140, 141, 142, 143, 144, 145, 157, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 181, 182, 183, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 229, 240, 241, 242, 243, 244, 245, 246, 247, 248, 250, 251, 254, 256, 257, 258, 275, 276, 277, 279, 283, 284, 285, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 311, 312, 313, 314, 318, 319, 320, 321, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 363, 364, 374, 375, 376, 380, 381, 382, 386, 387, 388, 389, 392, 393, 394 }

B grade: { 4, 5, 6, 7, 15, 38, 39, 40, 41, 42, 48, 49, 50, 51, 54, 55, 56, 57, 61, 62, 63, 64, 82, 83, 84, 85, 86, 87, 92, 93, 94, 95, 96, 97, 98, 99, 105, 106, 107, 108, 109, 112, 113, 114, 127, 133, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 158, 159, 178, 179, 180, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 226, 227, 228, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 249, 252, 253, 255, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 278, 280, 281, 282, 286, 287, 288, 309, 310, 315, 316, 317, 322, 323, 358, 359, 360, 361, 362, 365, 366, 367, 368, 369, 372, 373, 377, 378, 379, 383, 384, 385, 390, 391, 395, 396, 397 }

F grade: { 136, 137, 138, 139, 272, 273, 274, 370, 371, 398, 399, 400 }

#### 2.1.4 Maxima

A grade: { 1, 2, 3, 11, 12, 13, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 69, 70, 71, 72, 73, 74, 75, 76, 77, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 132, 133, 134, 135, 140, 141, 142, 143, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 254, 255, 256, 257, 275, 276, 277, 279, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 318, 319, 320, 321, 322, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 361, 362, 363, 364, 374, 375, 376, 380, 381, 382, 386, 387, 388, 392, 393, 394

B grade: { 10, 39, 40, 41, 42, 131, 177, 252, 253, 278, 317, 323, 343, 358, 359, 360, 377, 383, 389, 395 }

F grade: { 4, 5, 6, 7, 8, 9, 14, 15, 16, 17, 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, 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, 136, 137, 138, 139, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 280, 281, 282, 283, 284, 285, 286, 287, 288, 365, 366, 367, 368, 369, 370, 371, 372, 373, 378, 379, 384, 385, 390, 391, 396, 397, 398, 399, 400 }

#### 2.1.5 FriCAS

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, 32, 33, 34, 35, 36, 37, 43, 44, 45, 46, 47, 52, 53, 59, 60, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 88, 89, 90, 91, 100, 101, 102, 103, 104, 108, 109, 110, 111, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 140, 141, 142, 143, 144, 148, 149, 150, 151, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 179, 180, 181, 186, 187, 188, 189, 199, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 254, 255, 256, 257, 275, 276, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 312, 313, 314, 320, 321, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 361, 362, 363, 364, 373, 374, 375, 376, 380, 381, 382, 386, 387, 388, 392, 393, 394 }

B grade: { 31, 38, 39, 40, 41, 42, 50, 51, 57, 58, 64, 65, 66, 67, 107, 112, 113, 114, 145, 146, 147, 155, 156, 157, 177, 178, 182, 183, 184, 196, 197, 198, 233, 234, 235, 236, 237, 253, 258, 277, 278, 310, 311, 315, 316, 317, 318, 319, 322, 323, 360, 367, 368, 369, 372, 377, 378, 379, 383, 384, 385, 389, 390, 391, 395, 396, 397 }

F grade: { 48, 49, 54, 55, 56, 61, 62, 63, 82, 83, 84, 85, 86, 87, 92, 93, 94, 95, 96, 97, 98, 99, 105, 106, 136, 137, 138, 139, 152, 153, 154, 158, 159, 185, 190, 191, 192, 193, 194, 195, 200, 201, 202, 203, 204, 205, 206, 207, 230, 231, 232, 238, 239, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 365, 366, 370, 371, 398, 399, 400 }

#### 2.1.6 Sympy

A grade: { 10, 11, 12, 13, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 53, 59, 60, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 88, 89, 90, 91, 100, 101, 102, 103, 104, 110, 111, 115, 118, 119, 120, 140, 141, 142, 143, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 276, 279, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 307, 314, 321 }

B grade: { 39, 40, 41, 42, 43, 44, 45, 46, 50, 51, 52, 58, 116, 117, 126, 132, 144, 145, 146, 147, 148, 149, 150, 151, 156, 157, 177, 275, 277, 278 }

C grade: { 1, 2, 3, 304, 305, 306, 308, 309, 311, 312, 313, 315, 316, 318, 319, 320 }

F grade: { 4, 5, 6, 7, 8, 9, 14, 15, 16, 17, 47, 48, 49, 54, 55, 56, 57, 61, 62, 63, 64, 65, 66, 82, 83, 84, 85, 86, 87, 92, 93, 94, 95, 96, 97, 98, 99, 105, 106, 107, 108, 109, 112, 113, 114, 121, 122, 123, 124, 125, 127, 128, 129, 130, 131, 133, 134, 135, 136, 137, 138, 139, 152, 153, 154, 155, 158, 159, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 280, 281, 282, 283, 284, 285, 286, 287, 288, 310, 317, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 400 }

#### 2.1.7 Giac

A grade: { 1, 2, 3, 10, 11, 12, 13, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 88, 89, 90, 91, 92, 100, 101, 102, 103, 104, 105, 108, 109, 110, 111, 115, 116, 117, 118, 119, 120, 124, 125, 126, 127, 130, 131, 132, 133, 135, 140, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 152, 153, 155, 156, 157, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 179, 180, 181, 182, 186, 187, 188, 189, 199, 208, 209, 210, 211, 214, 215, 216, 217, 220, 221, 222, 223, 226, 227, 228, 229, 235, 236, 240, 241, 242, 243, 246, 247, 248, 249, 252, 253, 254, 255, 279, 280, 281, 282, 284, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 334, 335, 336, 338, 344, 345, 346, 351, 352, 353, 354, 358, 359, 360, 361, 365, 366, 372, 373, 374, 375, 376, 380, 381, 382, 386, 387, 388, 392, 393, 394 }

B grade: { 39, 40, 41, 42, 61, 63, 64, 65, 84, 85, 86, 87, 94, 95, 97, 98, 99, 107, 112, 114, 121, 123, 129, 147, 154, 158, 159, 178, 183, 184, 185, 196, 197, 198, 203, 212, 218, 224, 232, 233, 234, 237, 239, 245, 251, 257, 275, 276, 277, 278, 285, 286, 287, 288, 327, 328, 329, 330, 331, 332, 333, 337, 339, 340, 341, 342, 343, 348, 349, 356, 357, 363, 364, 367, 368, 369 }

F grade: { 4, 5, 6, 7, 8, 9, 14, 15, 16, 17, 83, 93, 96, 106, 113, 122, 128, 134, 136, 137, 138, 139, 190, 191, 192, 193, 194, 195, 200, 201, 202, 204, 205, 206, 207, 213, 219, 225, 230, 231, 238, 244, 250, 256, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 283, 347, 350, 355, 362, 370, 371, 377, 378, 379, 383, 384, 385, 389, 390, 391, 395, 396, 397, 398, 399, 400 }

### 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 A A A C A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 236 236 226 371 505 464 1239 266 normalized size 1 1. 0.96 1.57 2.14 1.97 5.25 1.13 time (sec) N/A 0.47 0.518 0.087 1.515 2.398 21.467 1.15
 Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A C A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 186 186 190 304 304 375 675 216 normalized size 1 1. 1.02 1.63 1.63 2.02 3.63 1.16 time (sec) N/A 0.227 0.309 0.059 1.788 2.511 11.5 1.182
 Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A C A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 125 125 121 154 188 227 347 115 normalized size 1 1. 0.97 1.23 1.5 1.82 2.78 0.92 time (sec) N/A 0.069 0.144 0.051 1.53 2.036 6.477 1.141
 Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) A F F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 148 148 103 384 0 236 0 0 normalized size 1 1. 0.7 2.59 0. 1.59 0. 0. time (sec) N/A 0.176 0.226 0.058 0. 1.873 0. 0.
 Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) A F F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 170 170 109 439 0 409 0 0 normalized size 1 1. 0.64 2.58 0. 2.41 0. 0. time (sec) N/A 0.203 0.243 0.06 0. 1.881 0. 0.
 Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) A F F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 149 149 114 318 0 533 0 0 normalized size 1 1. 0.77 2.13 0. 3.58 0. 0. time (sec) N/A 0.189 0.236 0.062 0. 1.824 0. 0.
 Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) A F F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 196 196 112 453 0 637 0 0 normalized size 1 1. 0.57 2.31 0. 3.25 0. 0. time (sec) N/A 0.184 0.296 0.06 0. 1.916 0. 0.
 Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A F F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 180 180 109 116 0 678 0 0 normalized size 1 1. 0.61 0.64 0. 3.77 0. 0. time (sec) N/A 0.21 0.207 0.048 0. 1.968 0. 0.
 Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 234 234 144 152 0 852 0 0 normalized size 1 1. 0.62 0.65 0. 3.64 0. 0. time (sec) N/A 0.264 0.228 0.049 0. 2.55 0. 0.
 Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A B A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 236 236 174 374 575 406 1277 224 normalized size 1 1. 0.74 1.58 2.44 1.72 5.41 0.95 time (sec) N/A 0.657 0.454 0.066 1.505 2.353 20.234 1.233
 Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 191 191 139 301 390 319 898 177 normalized size 1 1. 0.73 1.58 2.04 1.67 4.7 0.93 time (sec) N/A 0.378 0.183 0.062 1.518 2.388 14.176 1.177
 Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 143 143 103 234 234 236 488 131 normalized size 1 1. 0.72 1.64 1.64 1.65 3.41 0.92 time (sec) N/A 0.199 0.116 0.056 1.552 1.761 7.577 1.191
 Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 87 87 67 108 126 153 264 70 normalized size 1 1. 0.77 1.24 1.45 1.76 3.03 0.8 time (sec) N/A 0.051 0.042 0.105 1.526 1.777 3.224 1.213
 Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A F F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 103 103 83 149 0 315 0 0 normalized size 1 1. 0.81 1.45 0. 3.06 0. 0. time (sec) N/A 0.121 0.161 0.057 0. 1.85 0. 0.
 Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) A F F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 163 163 95 355 0 451 0 0 normalized size 1 1. 0.58 2.18 0. 2.77 0. 0. time (sec) N/A 0.169 0.221 0.061 0. 1.828 0. 0.
 Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A F F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 180 180 103 116 0 510 0 0 normalized size 1 1. 0.57 0.64 0. 2.83 0. 0. time (sec) N/A 0.205 0.199 0.049 0. 1.781 0. 0.
 Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A F F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 234 234 139 152 0 689 0 0 normalized size 1 1. 0.59 0.65 0. 2.94 0. 0. time (sec) N/A 0.249 0.224 0.049 0. 2.056 0. 0.
 Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 175 173 208 217 273 595 257 327 normalized size 1 0.99 1.19 1.24 1.56 3.4 1.47 1.87 time (sec) N/A 0.313 0.09 0.044 1.022 1.534 0.092 1.145
 Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 175 173 150 148 190 423 173 231 normalized size 1 0.99 0.86 0.85 1.09 2.42 0.99 1.32 time (sec) N/A 0.216 0.059 0.046 1.064 1.474 0.083 1.173
 Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 86 86 86 79 108 250 97 135 normalized size 1 1. 1. 0.92 1.26 2.91 1.13 1.57 time (sec) N/A 0.106 0.029 0.043 0.981 1.469 0.071 1.163
 Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 46 46 46 39 51 104 42 54 normalized size 1 1. 1. 0.85 1.11 2.26 0.91 1.17 time (sec) N/A 0.029 0.012 0.047 0.995 1.489 0.062 1.149
 Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 145 143 136 210 215 344 143 230 normalized size 1 0.99 0.94 1.45 1.48 2.37 0.99 1.59 time (sec) N/A 0.245 0.078 0.049 1.001 1.689 0.766 1.124
 Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 153 151 142 234 228 545 184 324 normalized size 1 0.99 0.93 1.53 1.49 3.56 1.2 2.12 time (sec) N/A 0.205 0.158 0.056 0.999 1.583 1.567 1.148
 Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 156 154 176 257 239 585 204 225 normalized size 1 0.99 1.13 1.65 1.53 3.75 1.31 1.44 time (sec) N/A 0.199 0.103 0.056 0.996 1.686 5.848 1.139
 Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 304 301 335 385 486 992 445 571 normalized size 1 0.99 1.1 1.27 1.6 3.26 1.46 1.88 time (sec) N/A 0.535 0.135 0.046 1.026 1.442 0.119 1.149
 Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 217 216 241 268 347 709 311 408 normalized size 1 1. 1.11 1.24 1.6 3.27 1.43 1.88 time (sec) N/A 0.313 0.092 0.045 1.005 1.405 0.105 1.128
 Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 128 128 144 151 208 428 180 244 normalized size 1 1. 1.12 1.18 1.62 3.34 1.41 1.91 time (sec) N/A 0.159 0.051 0.047 0.989 1.574 0.091 1.168
 Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 67 67 69 75 100 185 83 103 normalized size 1 1. 1.03 1.12 1.49 2.76 1.24 1.54 time (sec) N/A 0.04 0.029 0.046 1.019 1.509 0.077 1.159
 Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 297 295 285 490 509 786 350 562 normalized size 1 0.99 0.96 1.65 1.71 2.65 1.18 1.89 time (sec) N/A 0.64 0.168 0.054 0.999 1.755 1.469 1.139
 Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 292 289 272 527 529 1185 411 671 normalized size 1 0.99 0.93 1.8 1.81 4.06 1.41 2.3 time (sec) N/A 0.525 0.291 0.058 1.019 1.74 3.764 1.178
 Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A B A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 295 292 274 563 543 1305 471 536 normalized size 1 0.99 0.93 1.91 1.84 4.42 1.6 1.82 time (sec) N/A 0.495 0.136 0.061 1.03 1.731 16.442 1.162
 Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 404 400 459 553 691 1413 646 818 normalized size 1 0.99 1.14 1.37 1.71 3.5 1.6 2.02 time (sec) N/A 0.691 0.205 0.046 1.011 1.431 0.137 1.142
 Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 289 288 329 388 495 996 447 583 normalized size 1 1. 1.14 1.34 1.71 3.45 1.55 2.02 time (sec) N/A 0.424 0.132 0.044 1.003 1.396 0.121 1.167
 Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 169 169 196 223 300 603 265 352 normalized size 1 1. 1.16 1.32 1.78 3.57 1.57 2.08 time (sec) N/A 0.187 0.075 0.044 1.321 1.457 0.102 1.14
 Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 87 87 100 111 146 261 122 150 normalized size 1 1. 1.15 1.28 1.68 3. 1.4 1.72 time (sec) N/A 0.058 0.032 0.044 1.227 1.507 0.08 1.144
 Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 490 487 498 880 907 1385 658 1031 normalized size 1 0.99 1.02 1.8 1.85 2.83 1.34 2.1 time (sec) N/A 1.098 0.505 0.054 1.065 1.723 2.321 1.148
 Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 486 483 641 928 933 1987 731 1131 normalized size 1 0.99 1.32 1.91 1.92 4.09 1.5 2.33 time (sec) N/A 0.98 0.358 0.059 0.999 1.861 5.691 1.21
 Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B A B A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 466 463 438 978 946 2198 799 981 normalized size 1 0.99 0.94 2.1 2.03 4.72 1.71 2.11 time (sec) N/A 0.967 0.235 0.061 1.086 1.828 36.916 1.151
 Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A B B B B B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 17 17 62 76 111 153 75 150 normalized size 1 1. 3.65 4.47 6.53 9. 4.41 8.82 time (sec) N/A 0.032 0.026 0.049 0.991 1.596 0.565 1.172
 Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A B B B B B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 17 17 62 76 111 153 75 150 normalized size 1 1. 3.65 4.47 6.53 9. 4.41 8.82 time (sec) N/A 0.019 0.013 0.047 0.959 1.672 0.546 1.169
 Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A B B B B B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 17 17 90 157 216 234 155 292 normalized size 1 1. 5.29 9.24 12.71 13.76 9.12 17.18 time (sec) N/A 0.046 0.039 0.05 1.004 1.687 0.778 1.162
 Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A B B B B B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 17 17 90 157 216 234 155 292 normalized size 1 1. 5.29 9.24 12.71 13.76 9.12 17.18 time (sec) N/A 0.025 0.021 0.05 0.959 1.606 0.761 1.174
 Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 240 237 223 399 0 1239 1000 377 normalized size 1 0.99 0.93 1.66 0. 5.16 4.17 1.57 time (sec) N/A 0.471 0.224 0.052 0. 1.882 6.769 1.144
 Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 168 166 155 256 0 855 638 238 normalized size 1 0.99 0.92 1.52 0. 5.09 3.8 1.42 time (sec) N/A 0.262 0.193 0.069 0. 1.853 4.463 1.137
 Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 93 93 86 133 0 468 335 123 normalized size 1 1. 0.92 1.43 0. 5.03 3.6 1.32 time (sec) N/A 0.117 0.11 0.05 0. 1.843 2.202 1.165
 Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 55 55 56 59 0 296 156 65 normalized size 1 1. 1.02 1.07 0. 5.38 2.84 1.18 time (sec) N/A 0.053 0.038 0.046 0. 1.739 0.674 1.166
 Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 133 133 120 247 0 575 0 169 normalized size 1 1. 0.9 1.86 0. 4.32 0. 1.27 time (sec) N/A 0.162 0.115 0.053 0. 47.1 0. 1.133
 Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 214 214 188 462 0 0 0 365 normalized size 1 1. 0.88 2.16 0. 0. 0. 1.71 time (sec) N/A 0.355 0.358 0.058 0. 0. 0. 1.154
 Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 305 305 277 754 0 0 0 660 normalized size 1 1. 0.91 2.47 0. 0. 0. 2.16 time (sec) N/A 0.651 0.348 0.061 0. 0. 0. 1.163
 Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) B B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 216 216 233 484 0 1881 949 390 normalized size 1 1. 1.08 2.24 0. 8.71 4.39 1.81 time (sec) N/A 0.505 0.214 0.056 0. 2.081 39.307 1.176
 Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) B B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 146 146 175 323 0 1276 593 248 normalized size 1 1. 1.2 2.21 0. 8.74 4.06 1.7 time (sec) N/A 0.245 0.151 0.051 0. 2.101 19.217 1.164
 Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 97 97 102 134 0 717 318 151 normalized size 1 1. 1.05 1.38 0. 7.39 3.28 1.56 time (sec) N/A 0.082 0.104 0.052 0. 1.769 6.495 1.151
 Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 69 69 68 76 0 412 116 81 normalized size 1 1. 0.99 1.1 0. 5.97 1.68 1.17 time (sec) N/A 0.043 0.053 0.049 0. 1.773 0.84 1.153
 Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 226 226 195 742 0 0 0 473 normalized size 1 1. 0.86 3.28 0. 0. 0. 2.09 time (sec) N/A 0.435 0.261 0.06 0. 0. 0. 1.204
 Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 374 371 320 1036 0 0 0 821 normalized size 1 0.99 0.86 2.77 0. 0. 0. 2.2 time (sec) N/A 0.95 0.467 0.067 0. 0. 0. 1.203
 Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 524 524 466 1588 0 0 0 1292 normalized size 1 1. 0.89 3.03 0. 0. 0. 2.47 time (sec) N/A 1.552 0.706 0.074 0. 0. 0. 1.189
 Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) B F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 209 209 281 402 0 2325 0 470 normalized size 1 1. 1.34 1.92 0. 11.12 0. 2.25 time (sec) N/A 0.304 0.324 0.056 0. 2.662 0. 1.165
 Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) B B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 156 175 211 283 0 1644 389 343 normalized size 1 1.12 1.35 1.81 0. 10.54 2.49 2.2 time (sec) N/A 0.231 0.154 0.053 0. 2.487 163.039 1.16
 Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 130 130 137 157 0 991 240 205 normalized size 1 1. 1.05 1.21 0. 7.62 1.85 1.58 time (sec) N/A 0.108 0.113 0.052 0. 2. 34.287 1.148
 Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 98 98 90 96 0 656 156 113 normalized size 1 1. 0.92 0.98 0. 6.69 1.59 1.15 time (sec) N/A 0.063 0.074 0.049 0. 1.764 1.567 1.153
 Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F(-1) B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 353 353 321 1598 0 0 0 965 normalized size 1 1. 0.91 4.53 0. 0. 0. 2.73 time (sec) N/A 0.734 0.486 0.069 0. 0. 0. 1.181
 Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 571 566 498 2159 0 0 0 1494 normalized size 1 0.99 0.87 3.78 0. 0. 0. 2.62 time (sec) N/A 1.925 0.818 0.076 0. 0. 0. 1.214
 Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F(-1) B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 753 753 672 2737 0 0 0 2068 normalized size 1 1. 0.89 3.63 0. 0. 0. 2.75 time (sec) N/A 3.143 1.226 0.081 0. 0. 0. 1.22
 Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) B F(-1) B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 234 234 437 647 0 3753 0 859 normalized size 1 1. 1.87 2.76 0. 16.04 0. 3.67 time (sec) N/A 0.291 0.305 0.056 0. 1.713 0. 1.167
 Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) B F(-1) B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 254 288 350 464 0 2807 0 641 normalized size 1 1.13 1.38 1.83 0. 11.05 0. 2.52 time (sec) N/A 0.542 0.322 0.053 0. 1.637 0. 1.188
 Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) B F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 225 225 266 333 0 2163 0 443 normalized size 1 1. 1.18 1.48 0. 9.61 0. 1.97 time (sec) N/A 0.398 0.169 0.053 0. 1.557 0. 1.154
 Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) B A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 165 165 171 182 0 1341 298 262 normalized size 1 1. 1.04 1.1 0. 8.13 1.81 1.59 time (sec) N/A 0.136 0.162 0.049 0. 1.455 127.102 1.159
 Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 126 126 112 113 0 900 196 147 normalized size 1 1. 0.89 0.9 0. 7.14 1.56 1.17 time (sec) N/A 0.078 0.089 0.05 0. 1.005 2.229 1.158
 Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 43 43 29 30 39 122 29 39 normalized size 1 1. 0.67 0.7 0.91 2.84 0.67 0.91 time (sec) N/A 0.05 0.018 0.046 1.477 0.975 0.119 1.155
 Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 30 30 27 24 31 111 20 31 normalized size 1 1. 0.9 0.8 1.03 3.7 0.67 1.03 time (sec) N/A 0.04 0.01 0.061 1.528 0.984 0.111 1.154
 Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 29 29 23 24 31 89 20 31 normalized size 1 1. 0.79 0.83 1.07 3.07 0.69 1.07 time (sec) N/A 0.025 0.008 0.046 1.467 0.989 0.114 1.152
 Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 14 14 14 13 16 58 10 16 normalized size 1 1. 1. 0.93 1.14 4.14 0.71 1.14 time (sec) N/A 0.011 0.007 0.045 1.484 0.98 0.105 1.162
 Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 31 31 28 26 34 117 24 35 normalized size 1 1. 0.9 0.84 1.1 3.77 0.77 1.13 time (sec) N/A 0.039 0.01 0.049 1.461 0.994 0.136 1.156
 Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 33 33 33 30 46 138 31 47 normalized size 1 1. 1. 0.91 1.39 4.18 0.94 1.42 time (sec) N/A 0.045 0.016 0.053 1.502 0.986 0.137 1.181
 Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 45 45 39 38 55 159 41 58 normalized size 1 1. 0.87 0.84 1.22 3.53 0.91 1.29 time (sec) N/A 0.063 0.016 0.051 1.474 1.037 0.159 1.155
 Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 12 22 12 13 16 50 8 16 normalized size 1 1.83 1. 1.08 1.33 4.17 0.67 1.33 time (sec) N/A 0.007 0.012 0.046 1.462 0.958 0.102 1.177
 Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 27 27 27 21 28 74 19 28 normalized size 1 1. 1. 0.78 1.04 2.74 0.7 1.04 time (sec) N/A 0.014 0.01 0.048 1.494 1.029 0.117 1.178
 Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 390 387 362 661 0 1889 1088 641 normalized size 1 0.99 0.93 1.69 0. 4.84 2.79 1.64 time (sec) N/A 0.83 0.471 0.058 0. 1.646 25.418 1.188
 Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 280 279 256 446 0 1319 738 433 normalized size 1 1. 0.91 1.59 0. 4.71 2.64 1.55 time (sec) N/A 0.498 0.697 0.054 0. 1.608 19.043 1.198
 Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 175 175 153 230 0 770 384 243 normalized size 1 1. 0.87 1.31 0. 4.4 2.19 1.39 time (sec) N/A 0.268 0.439 0.053 0. 1.426 10.094 1.192
 Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 106 106 98 111 0 448 170 117 normalized size 1 1. 0.92 1.05 0. 4.23 1.6 1.1 time (sec) N/A 0.064 0.2 0.05 0. 1.352 6.024 1.153
 Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 206 206 224 1265 0 0 0 375 normalized size 1 1. 1.09 6.14 0. 0. 0. 1.82 time (sec) N/A 0.392 0.477 0.301 0. 0. 0. 1.266
 Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F F(-1) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 308 303 264 2818 0 0 0 0 normalized size 1 0.98 0.86 9.15 0. 0. 0. 0. time (sec) N/A 0.509 0.284 0.234 0. 0. 0. 0.
 Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 296 295 318 4432 0 0 0 1246 normalized size 1 1. 1.07 14.97 0. 0. 0. 4.21 time (sec) N/A 0.546 0.653 0.239 0. 0. 0. 1.423
 Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 314 314 382 5565 0 0 0 2321 normalized size 1 1. 1.22 17.72 0. 0. 0. 7.39 time (sec) N/A 0.505 0.985 0.244 0. 0. 0. 1.478
 Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 313 312 439 7237 0 0 0 2869 normalized size 1 1. 1.4 23.12 0. 0. 0. 9.17 time (sec) N/A 0.429 1.316 0.25 0. 0. 0. 3.613
 Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F(-1) B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 433 432 583 8546 0 0 0 5686 normalized size 1 1. 1.35 19.74 0. 0. 0. 13.13 time (sec) N/A 0.743 1.528 0.25 0. 0. 0. 1.623
 Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 462 462 481 794 0 2634 1916 880 normalized size 1 1. 1.04 1.72 0. 5.7 4.15 1.9 time (sec) N/A 1.134 0.573 0.061 0. 2.58 67.618 1.229
 Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 346 345 346 552 0 1878 1304 610 normalized size 1 1. 1. 1.6 0. 5.43 3.77 1.76 time (sec) N/A 0.524 1.149 0.057 0. 2.116 50.033 1.189
 Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 213 212 209 287 0 1107 768 356 normalized size 1 1. 0.98 1.35 0. 5.2 3.61 1.67 time (sec) N/A 0.271 0.688 0.052 0. 1.473 25.584 1.171
 Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 137 137 125 146 0 618 348 174 normalized size 1 1. 0.91 1.07 0. 4.51 2.54 1.27 time (sec) N/A 0.083 0.269 0.049 0. 1.395 14.993 1.193
 Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 326 326 348 2420 0 0 0 744 normalized size 1 1. 1.07 7.42 0. 0. 0. 2.28 time (sec) N/A 0.766 1.426 0.228 0. 0. 0. 1.229
 Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F F(-1) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 432 428 392 5121 0 0 0 0 normalized size 1 0.99 0.91 11.85 0. 0. 0. 0. time (sec) N/A 0.901 0.582 0.226 0. 0. 0. 0.
 Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 488 480 435 7817 0 0 0 1399 normalized size 1 0.98 0.89 16.02 0. 0. 0. 2.87 time (sec) N/A 0.921 0.706 0.239 0. 0. 0. 1.47
 Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 475 469 517 9835 0 0 0 2565 normalized size 1 0.99 1.09 20.71 0. 0. 0. 5.4 time (sec) N/A 0.845 1.401 0.252 0. 0. 0. 1.684
 Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F F(-1) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 511 511 575 12481 0 0 0 0 normalized size 1 1. 1.13 24.42 0. 0. 0. 0. time (sec) N/A 1.092 2.522 0.254 0. 0. 0. 0.
 Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F(-1) B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 507 507 639 14169 0 0 0 5951 normalized size 1 1. 1.26 27.95 0. 0. 0. 11.74 time (sec) N/A 0.86 2.608 0.26 0. 0. 0. 2.139
 Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F(-1) B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 404 403 696 17026 0 0 0 8265 normalized size 1 1. 1.72 42.14 0. 0. 0. 20.46 time (sec) N/A 0.552 2.475 0.27 0. 0. 0. 2.112
 Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F(-1) B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 532 531 863 19093 0 0 0 10714 normalized size 1 1. 1.62 35.89 0. 0. 0. 20.14 time (sec) N/A 0.889 2.636 0.307 0. 0. 0. 2.142
 Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 168 168 150 181 0 809 510 227 normalized size 1 1. 0.89 1.08 0. 4.82 3.04 1.35 time (sec) N/A 0.102 0.334 0.05 0. 2.161 30.56 1.176
 Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 325 323 252 528 0 1284 796 424 normalized size 1 0.99 0.78 1.62 0. 3.95 2.45 1.3 time (sec) N/A 0.664 0.394 0.062 0. 2.084 19.693 1.173
 Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 223 222 164 339 0 871 518 278 normalized size 1 1. 0.74 1.52 0. 3.91 2.32 1.25 time (sec) N/A 0.372 0.25 0.061 0. 2.184 13.787 1.173
 Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 136 135 96 172 0 482 282 149 normalized size 1 0.99 0.71 1.26 0. 3.54 2.07 1.1 time (sec) N/A 0.179 0.113 0.055 0. 2.206 7.047 1.211
 Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 74 74 63 76 0 305 150 78 normalized size 1 1. 0.85 1.03 0. 4.12 2.03 1.05 time (sec) N/A 0.048 0.041 0.052 0. 2.003 3.071 1.173
 Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 130 130 125 453 0 0 0 186 normalized size 1 1. 0.96 3.48 0. 0. 0. 1.43 time (sec) N/A 0.174 0.231 0.236 0. 0. 0. 1.217
 Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 168 168 218 923 0 0 0 0 normalized size 1 1. 1.3 5.49 0. 0. 0. 0. time (sec) N/A 0.235 0.419 0.249 0. 0. 0. 0.
 Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) B F B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 225 224 254 1574 0 2209 0 1145 normalized size 1 1. 1.13 7. 0. 9.82 0. 5.09 time (sec) N/A 0.292 0.503 0.246 0. 62.253 0. 1.252
 Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) A F A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 229 228 246 516 0 1635 0 458 normalized size 1 1. 1.07 2.25 0. 7.14 0. 2. time (sec) N/A 0.325 0.503 0.06 0. 2.206 0. 1.201
 Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) A F A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 149 149 177 327 0 1142 0 296 normalized size 1 1. 1.19 2.19 0. 7.66 0. 1.99 time (sec) N/A 0.184 0.302 0.058 0. 2.052 0. 1.188
 Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 100 100 102 163 0 606 209 157 normalized size 1 1. 1.02 1.63 0. 6.06 2.09 1.57 time (sec) N/A 0.087 0.151 0.056 0. 1.9 12.768 1.169
 Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 61 61 74 69 0 396 87 85 normalized size 1 1. 1.21 1.13 0. 6.49 1.43 1.39 time (sec) N/A 0.036 0.063 0.052 0. 1.718 5.61 1.185
 Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) B F B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 138 138 137 862 0 1431 0 397 normalized size 1 1. 0.99 6.25 0. 10.37 0. 2.88 time (sec) N/A 0.141 0.203 0.256 0. 12.217 0. 1.185
 Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) B F(-1) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 239 239 285 1663 0 3160 0 0 normalized size 1 1. 1.19 6.96 0. 13.22 0. 0. time (sec) N/A 0.418 0.727 0.234 0. 21.091 0. 0.
 Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) B F(-1) B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 374 372 404 2584 0 5783 0 1944 normalized size 1 0.99 1.08 6.91 0. 15.46 0. 5.2 time (sec) N/A 1.028 1.272 0.258 0. 110.411 0. 1.39
 Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 67 67 50 47 112 139 194 65 normalized size 1 1. 0.75 0.7 1.67 2.07 2.9 0.97 time (sec) N/A 0.042 0.034 0.052 0.979 1.596 13.825 1.17
 Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 97 97 71 72 159 215 638 108