test_that("saddlepoint MLE is opt-in and is limited to unknown-theta Beta", {
  normalize<-AccSamplingDesign:::.normalize_beta_theta_method
  expect_identical(normalize(NULL,"beta","unknown",TRUE),"delta_mle")
  expect_identical(normalize("saddlepoint_mle","beta","unknown"),"saddlepoint_mle")
  expect_error(manualPlan(distribution="normal",n=20,k=1,method="saddlepoint_mle"),"only applicable")
  expect_error(manualPlan(distribution="beta",n=20,k=1,theta=100,USL=.05,method="saddlepoint_mle"),"only applicable")
  for(n in c(1,2.5,NA_real_,Inf))expect_error(manualPlan(distribution="beta",theta_type="unknown",
    theta=500,USL=.05,n=n,k=2,method="saddlepoint_mle"),"integer sample size")
})

test_that("saddlepoint MLE construction and probability dispatch agree", {
  plan<-optPlan(.01,.03,distribution="beta",theta_type="unknown",theta=500,USL=.05,
                method="saddlepoint_mle")
  expect_identical(plan$method,"saddlepoint_mle")
  expect_equal(plan$n,plan$sample_size)
  expect_equal(plan$n,floor(plan$n))
  expect_lte(plan$PR,.05+1e-7);expect_lte(plan$CR,.10+1e-7)
  expect_equal(1-accProb(plan,.01),plan$PR,tolerance=1e-10)
  expect_equal(accProb(plan,.03),plan$CR,tolerance=1e-10)
  expect_true(plan$integration$experimental)
  expect_identical(plan$integration$search_initializer,"delta_mle")
  expect_null(plan$integration$initializer_fallback_reason)
  expect_gte(plan$integration$evaluated_sample_sizes,1)
  expect_equal(plan$integration$distribution_constructions,
               2L*plan$integration$evaluated_sample_sizes)
  expect_true(all(plan$integration$numerical_error_estimate<2e-5))
  expect_output(print(plan),"Saddlepoint MLE OC (experimental)",fixed=TRUE)
  expect_output(summary(plan),"Saddlepoint MLE OC (experimental)",fixed=TRUE)
  manual<-manualPlan(distribution="beta",theta_type="unknown",theta=500,USL=.05,
                     n=plan$n,k=plan$k,method="saddlepoint_mle")
  pd<-c(.01,.03)
  oc<-OCdata(manual,pd=pd)
  expect_equal(oc$paccept,vapply(pd,function(p)accProb(plan,p),0),tolerance=1e-10)
  expect_equal(accProb(manual,0),1);expect_equal(accProb(manual,1),0)
  expect_error(accProb(manual,-.01),"proportion")
  expect_error(OCdata(manual),"Supply pd")
  expect_silent(plot(plan,pd=pd))
  expect_silent(plot(plan,pd=pd,by="mean"))
})

test_that("saddlepoint MLE initializer validates Delta output and falls back", {
  initial<-AccSamplingDesign:::.beta_saddlepoint_initial(
    .01,.03,.05,.10,.05,NULL,500,
    delta_plan_function=function(...)list(sample_size=21,k=1.25))
  expect_identical(initial$source,"delta_mle")
  expect_identical(initial$n,21L)
  expect_equal(initial$k,1.25)
  expect_null(initial$fallback_reason)

  invalid<-AccSamplingDesign:::.beta_saddlepoint_initial(
    .01,.03,.05,.10,.05,NULL,500,
    delta_plan_function=function(...)list(sample_size=1,k=Inf))
  expect_identical(invalid$source,"normal")
  expect_match(invalid$fallback_reason,"invalid starting plan")
  expect_true(is.finite(invalid$n)&&invalid$n>=10)
  expect_identical(invalid$k,2)

  failed<-AccSamplingDesign:::.beta_saddlepoint_initial(
    .01,.03,.05,.10,.05,NULL,500,
    delta_plan_function=function(...)stop("forced Delta failure"))
  expect_identical(failed$source,"normal")
  expect_match(failed$fallback_reason,"forced Delta failure")
})