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() {
	reader := bufio.NewReader(os.Stdin)
	var old_low, old_high float64

	input, _ := reader.ReadString('\n')
	input = strings.TrimSpace(input)

	tokens := strings.Split(input, " ")
	if len(tokens) != 2 {
		fmt.Println("Please enter exactly two floats.")
		return
	}
	old_low, err1 := strconv.ParseFloat(tokens[0], 64)
	old_high, err2 := strconv.ParseFloat(tokens[1], 64)
	if err1 != nil || err2 != nil {
		fmt.Println("Invalid input. Please ensure you enter two floats.")
		return
	}

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

	for {
		// fmt.Println("Enter another two floats separated by a space:")
		input, _ = reader.ReadString('\n')
		if strings.TrimSpace(input) == "" {
			break // Exit if no input is given
		}

		tokens := strings.Split(strings.TrimSpace(input), " ")
		if len(tokens) != 2 {
			fmt.Println("Please enter exactly two floats.")
			continue
		}

		new_low, err1 := strconv.ParseFloat(tokens[0], 64)
		new_high, err2 := strconv.ParseFloat(tokens[1], 64)
		if err1 != nil || err2 != nil {
			fmt.Println("Invalid input. Please ensure you enter two floats.")
			continue
		}

		// 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)
	}
}