human
Solve the following python programming problem given the following code:
def backgroundProfileFormula(cntlr, profileReportFile, maxRunTime, excludeCompileTime) : 
    from arelle import Locale, XPathParser, ValidateXbrlDimensions, ValidateFormula 
    XPathParser.initializeParser (cntlr.modelManager) 
    ValidateXbrlDimensions.loadDimensionDefaults (cntlr.modelManager) 
    import cProfile, pstats, sys, time 
    class Validate () : 
        def __init__(self, modelXbrl, maxRunTime) : 
            self.modelXbrl = modelXbrl 
            self.parameters = None 
            self.validateSBRNL = False 
            self.maxFormulaRunTime = maxRunTime 
def close(self) : 
            self.__dict__.clear () 
val = Validate (cntlr.modelManager.modelXbrl, maxRunTime) 
    formulaOptions = val.modelXbrl.modelManager.formulaOptions 
    if excludeCompileTime : 
        startedAt = time.time () 
        cntlr.addToLog (_ ('pre-compiling formulas before profiling')) 
        val.validateFormulaCompileOnly = True 
        ValidateFormula.validate (val) 
        del val.validateFormulaCompileOnly 
        cntlr.addToLog (Locale.format_string (val.modelManager.locale, _ ('formula pre-compiling completed in %.2f secs'), (time.time () - startedAt))) 
        cntlr.addToLog (_ ('executing formulas for profiling')) 
else : 
        cntlr.addToLog (_ ('compiling and executing formulas for profiling')) 
startedAt = time.time () 
    statsFile = (profileReportFile + '.bin') 
    cProfile.runctx ('ValidateFormula.validate(val)', globals (), locals (), statsFile) 
    cntlr.addToLog (Locale.format_string (cntlr.modelManager.locale, _ ('formula profiling completed in %.2f secs'), (time.time () - startedAt))) 
    val.close () 
    priorStdOut = sys.stdout 
    sys.stdout = open (profileReportFile, 'w') 
    statObj = pstats.Stats (statsFile) 
    statObj.strip_dirs () 
    statObj.sort_stats ('time') 
    statObj.print_stats () 
    statObj.print_callees () 
    statObj.print_callers () 
    sys.stdout.flush () 
    sys.stdout.close () 
    del statObj 
    sys.stdout = priorStdOut 
    os.remove (statsFile) 

    
    

    Fix the buggy line: cntlr.addToLog (Locale.format_string (val.modelManager.locale, _ ('formula pre-compiling completed in %.2f secs'), (time.time () - startedAt)))
assistant
#Here is Python program to fix the buggy line: cntlr.

cntlr.addToLog (Locale.format_string (cntlr.modelManager.locale, _ ('formula pre-compiling completed in %.2f secs'), (time.time () - startedAt)))