4. (50 points) The goal of this simulation study is to study the relative performance of uniform search, golden section search, and parabolic interpolation (algorithms 1-3 from class notes). Fix m =1000, and generate 21,..., m ~ Uniform(-0,0), with 1, 10, 102,..., 107. We want to find 771 *= arg min f(8), where f(8)=x -31. im1 For each value of 0, apply the three algorithms using a reasonable convergence criterion of your choice. Repeat this across 100 independent samples of size m, and report a single table with (a) the average runtime and (b) the average iterations until convergence for each algorithm. Interpret your results.