Detecting Floating-Point Expression Errors Based Improved PSO Algorithm

Table 5

PSOED test results.

PSOED
No.	FPBench	Max relative error	Max ULP error	Max bits error
1	Bsplines3	2.77E-16	1.00E + 00	1.00
2	Exp1x	1.11E-14	2.00E + 00	5.67
3	Exp1x_log	2.94E-16	5.00E + 01	1.58
4	Intro_example	2.2E-16	1.00E + 00	1.00
5	Logexp	3.16E-16	1.00E + 00	1.00
6	NMSE example 3.1	2.24E-13	1.36E + 03	10.43
7	NMSE example 3.4	1.69E-3	1.68E + 09	30.98
8	NMSE example 3.5	2.21E-10	1.05E + 06	20.00
9	NMSE example 3.6	6.34E-13	3.58E + 03	11.79
10	NMSE example 3.7	1.10E-14	6.40E + 01	6.02
11	NMSE example 3.8	9.83E-09	3.66E + 07	26.04
12	NMSE example 3.9	1.35E-11	4.57E + 05	15.63
13	NMSE problem 331	2.16E-13	1.27E + 03	10.30
14	NMSE problem 333	2.12E-10	1.04E + 06	20.00
15	NMSE problem 336	8.83E-13	4.59E + 03	12.15
16	NMSE problem 337	1.62E-12	1.23E + 04	13.58
17	NMSE problem 341	5.12E-05	1.85E + 09	30.64
18	NMSE problem 344	8.22E-15	5.10E + 01	5.73
19	NMSE problem 345	7.47E-12	6.88E + 04	16.05
20	NMSE section 3.11	1.10E-14	7.70E + 01	6.29
21	predatorPrey	4.75E-16	3.00E + 00	1.58
22	Sine	2.03E-11	1.27E + 05	18.56
23	Sineorder3	8.40E-11	8.99E + 04	15.80
24	sqroot	5.15E-12	3.41E + 05	12.85
25	Sqrt_add	3.14E-16	2.00E + 00	1.58
26	Test05_nonlin1, r4	8.86E-10	4.43E + 06	21.65
27	Test05_nonlin1, test2	1.66E-16	1.00E + 00	1.00
28	verhulst	1.33E-12	1.60E + 04	13.90