... Nowadays, numerous effective numerical methods are used to solve nonlinear equations, yet one of the standard and widely used solvers for these problems is the Newton-Raphson method (NRM) [5]. In addition to NRM, several other iterative methods, including Broyden and Campbell, typically yield various solvers for nonlinear systems of equations [6,7] and Jacobian matrices via automatic differentiation [8][9][10][11]. Lately, many researchers such as Jaffari and Gejji, Abbasbandy, Sharma and Vahidi, have given a myriad of up-to-date deterministic methods that reliably and efficiently solve the nonlinear system of equations [12][13][14][15][16][17][18] However, all these solvers belong to well-established deterministic approaches. Besides deterministic approaches, systems of nonlinear equations have been solved by stochastic numerical solvers as well such as memetic computing [19], genetic algorithms [20], an improved cuckoo optimization algorithm [21] (Abdollahi et al 2016), a weighted bi-objective transformation technique [22], evolutionary multi-objective optimization [23], repulsion-based adaptive differential evolution [24,25], nature-inspired computational intelligence [26], Chebyshev-Halley's methods [27], Davidenko's method [28], A decomposition-based differential evolution [29], modified firefly algorithm [30], two-phase evolutionary algorithm [31], decomposition technique [32,33], monarch butterfly optimization [34][35][36], hybrid harmony search-based multi-start method [35], spiral optimization algorithm with clustering [36,37], conjugate direction de algorithm [38], memetic nichingbased evolutionary algorithms [39], an improved differential evolution algorithm [40] and the design of stochastic solvers [41]. ...