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Table 1 Numerical results for test functions

From: Three-point iterative algorithm in the absence of the derivative for solving nonlinear equations and their basins of attraction

Function \({\varvec{x_{0}}}\) \(|g_i(x_m)|,i=1,2,3,4,5, m=3,\) for 8th BM
\(\theta =1\) \(\theta =-1\) \(\theta =0.5\) \(\theta =-0.5\) COC
\(g_{1}(x_3)\) \(-\)1.5 \(5.75\times 10^{-41}\) \(5.75\times 10^{-41}\) \(4.36\times 10^{-65}\) \(4.36\times 10^{-65}\) 8.11
\(g_{2}(x_3)\) \(-\)0.2 \(1.00\times 10^{-100}\) \(1.00\times 10^{-100}\) \(1.45\times 10^{-488}\) \(1.45\times 10^{-488}\) 7.99
\(g_{3}(x_3)\) 1.5 \(3.00\times 10^{-500}\) \(3.00\times 10^{-500}\) \(3.00\times 10^{-500}\) \(3.00\times 10^{-500}\) 8.00
\(g_{4}(x_3)\) \(-\)1.7 \(3.00\times 10^{-499}\) \(3.00\times 10^{-499}\) \(3.00\times 10^{-499}\) \(3.00\times 10^{-499}\) 8.00
\(g_{5}(x_3)\) 0.7 \(1.32\times 10^{-395}\) \(1.32\times 10^{-395}\) \(31.75\times 10^{-433}\) \(31.75\times 10^{-433}\) 8.00