package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"strconv"
	"strings"
)

const NORMAL90CONFIDENCE = 1.6448536269514727

func boundsToLogParams(low float64, high float64) (float64, float64) {
	loglow := math.Log(low)
	loghigh := math.Log(high)
	logmean := (loghigh + loglow) / 2.0
	logstd := (loghigh - loglow) / (2.0 * NORMAL90CONFIDENCE)
	return logmean, logstd

}

func multiplyLognormals(logmean1 float64, logstd1 float64, logmean2 float64, logstd2 float64) (float64, float64) {
	return logmean1 + logmean2, math.Sqrt(logstd1*logstd1 + logstd2*logstd2)
}

func logParamsToBounds(logmean float64, logstd float64) (float64, float64) {
	h := logstd * NORMAL90CONFIDENCE
	loglow := logmean - h
	loghigh := logmean + h
	return math.Exp(loglow), math.Exp(loghigh)
}

func combineBounds(old_low, old_high, new_low, new_high float64) (float64, float64) {
	logmean_old, logstd_old := boundsToLogParams(old_low, old_high)
	logmean_new, logstd_new := boundsToLogParams(new_low, new_high)

	logmean_product, logstd_product := multiplyLognormals(logmean_old, logstd_old, logmean_new, logstd_new)

	return logParamsToBounds(logmean_product, logstd_product)
}

func main() {
	var old_low, old_high float64

	reader := bufio.NewReader(os.Stdin)
	input, _ := reader.ReadString('\n')
	input = strings.TrimSpace(input)
	tokens := strings.Split(input, " ")
	error_msg_start := "Please enter two floats separated by a space, like: 1 10"
	if len(tokens) != 2 {
		fmt.Println(error_msg_start)
		return
	}
	old_low, err1 := strconv.ParseFloat(tokens[0], 64)
	old_high, err2 := strconv.ParseFloat(tokens[1], 64)
	if err1 != nil || err2 != nil {
		fmt.Println(error_msg_start)
		return
	}

	fmt.Printf("=> %.1f %.1f\n", old_low, old_high)

	error_msg_cont := "Please enter two floats separated by a space, like: 1 10, or two floats preceded by a division, like: / 2 20. Or enter i to get the logmean and logstd"
EventForLoop:
	for {
		// fmt.Println("Enter another two floats separated by a space:")
		input, _ = reader.ReadString('\n')
		if strings.TrimSpace(input) == "" {
			continue EventForLoop
		}

		tokens := strings.Split(strings.TrimSpace(input), " ")
		var err1, err2 error

		var new_low, new_high float64
		switch len(tokens) {
		case 0:
			continue EventForLoop
		case 1:
			if tokens[0] == "i" {
				fmt.Printf("=> %.1f %.1f\n", old_low, old_high)
				logmean_old, logstd_old := boundsToLogParams(old_low, old_high)
				fmt.Printf("=> Lognormal, with logmean: %.1f, logstd: %.1f\n", logmean_old, logstd_old)
			}
			continue EventForLoop
		case 2:
			new_low, err1 = strconv.ParseFloat(tokens[0], 64)
			new_high, err2 = strconv.ParseFloat(tokens[1], 64)
			if err1 != nil || err2 != nil {
				fmt.Println(error_msg_cont)
				continue EventForLoop
			}
		case 3:
			switch tokens[0] {
			case "*":
				new_low, err1 = strconv.ParseFloat(tokens[1], 64)
				new_high, err2 = strconv.ParseFloat(tokens[2], 64)
				if err1 != nil || err2 != nil {
					fmt.Println(error_msg_cont)
					continue EventForLoop
				}
			case "/":
				new_low, err1 = strconv.ParseFloat(tokens[1], 64)
				new_high, err2 = strconv.ParseFloat(tokens[2], 64)
				if err1 != nil || err2 != nil {
					fmt.Println(error_msg_cont)
					continue EventForLoop
				}
				tmp_low := new_low
				new_low = 1.0 / new_high
				new_high = 1.0 / tmp_low
			default:
				fmt.Println(error_msg_cont)
				continue EventForLoop
			}
		default:
			fmt.Println(error_msg_cont)
			continue EventForLoop
		}
		// Use the abstracted function for combining floats
		old_low, old_high = combineBounds(old_low, old_high, new_low, new_high)
		fmt.Printf("=> %.1f %.1f\n", old_low, old_high)
	}
}