N.seq <- as.integer(10^seq(2,log10(max(diff.list$subtrain$example)),l=10))
  N.seq <- as.integer(10^seq(log10(100),log10(1600),l=10))
  atime.list <- atime::atime(
    N=N.seq,
    setup={
      maxIterations <- N*(N-1)/2
      X.subtrain <- X.keep[index.list$subtrain,]
      X.sub <- X.subtrain[1:N,]
      diff.sub <- diff.list$subtrain[example %in% seq(0,N-1)]
    },
    result=TRUE,
    seconds.limit=1,
    times=1,
    aum_line_search={
      nb.weight.search <- aum::aum_line_search(
        diff.sub,
        maxIterations=maxIterations,
        feature.mat=X.sub,
        weight.vec=weight.vec)
      list(
        total.iterations=nrow(nb.weight.search$line_search_result),
        iterations.to.min=nb.weight.search$line_search_result[,which.min(aum)])
    })
  atime.list$measurements[, total.iterations := sapply(
    result, function(L)L$total.iterations)]
  atime.list$measurements[, iterations.to.min := sapply(
    result, function(L)L$iterations.to.min)]

  best.list <- atime::references_best(atime.list, unit.col.vec=c("total.iterations","iterations.to.min"))
best.ref <- best.list$ref[each.sign.rank==1]
  library(ggplot2)
  gg <- ggplot()+
    theme_bw()+
    facet_grid(unit ~ ., scales="free")+
    geom_line(aes(
      N, empirical, color=expr.name),
      data=best.list$meas)+
    scale_x_log10()+
    scale_y_log10("median line, min/max band")
  gg.show <- gg+
     directlabels::geom_dl(aes(
       N, empirical, color=expr.name, label=expr.name),
       method="right.polygons",
       data=best.list$meas)+
     theme(legend.position="none")+
     coord_cartesian(xlim=c(min(N.seq),max(best.list$meas$N)*5))
  gg.ref <- gg.show+
    geom_line(aes(
      N, reference, group=paste(fun.name, expr.name)),
      color="grey",
      data=best.ref)
    gg.ref+
      directlabels::geom_dl(aes(
        N, reference,
        label.group=paste(fun.name, expr.name),
        label=fun.name),
        data=best.ref,
        color="grey",
        method="left.polygons")