Construction of Optimal Derivative-Free Techniques without Memory

Table 2

The test functions considered in this study.

Test functions	Simple zeros	Initial guesses
𝑓1(𝑥)=3𝑥+sin(𝑥)−𝑒^𝑥	𝛼1≈0.360421702960324	𝑥0=0.2
𝑓2(𝑥)=sin(𝑥)−0.5	𝛼2≈0.523598775598299	𝑥0=0.3
𝑓3(𝑥)=𝑥^2−𝑒^𝑥−3𝑥+2	𝛼3≈0.257530285439861	𝑥0=0.4
𝑓4(𝑥)=𝑥^3+4𝑥^2−10	𝛼4≈1.365230013414097	𝑥0=1.37
𝑓5(𝑥)=𝑥𝑒^−𝑥−0.1	𝛼5≈0.111832559158963	𝑥0=0.2
𝑓6(𝑥)=𝑥^3−10	𝛼6≈2.15443490031884	𝑥0=2.16
𝑓7(𝑥)=10𝑥𝑒^−𝑥2−1	𝛼7≈1.679630610428450	𝑥0=1.4
𝑓8(𝑥)=cos(𝑥)−𝑥	𝛼8≈0.739085133215161	𝑥0=0.3