-------------------------------- Start Of Program -------------------------------- The value which was entered for x is 8. -------------------------------- Computing the approximate cube root of x: C = 8. // real number to take the cube root of B = 0. // variable for storing the approximate cube root of x A = 0. // number to add to C before dividing the sum of A and C by 2 for each while loop iteration, i epsilon = 0. // variable for storing the difference between the input value and B raised to the power of 3 i := 0. C := 8. A := 0. B := (A + C) / 2 = 4. epsilon = difference(x , B) = 56. i := 1. C := 4. A := 0. B := (A + C) / 2 = 2. epsilon = difference(x , B) = 0. -------------------------------- S = approximate_cube_root(8) = 2. -------------------------------- The value which was entered for x is 125. -------------------------------- Computing the approximate cube root of x: C = 125. // real number to take the cube root of B = 0. // variable for storing the approximate cube root of x A = 0. // number to add to C before dividing the sum of A and C by 2 for each while loop iteration, i epsilon = 0. // variable for storing the difference between the input value and B raised to the power of 3 i := 0. C := 125. A := 0. B := (A + C) / 2 = 62.5. epsilon = difference(x , B) = 244015.625. i := 1. C := 62.5. A := 0. B := (A + C) / 2 = 31.25. epsilon = difference(x , B) = 30392.578125. i := 2. C := 31.25. A := 0. B := (A + C) / 2 = 15.625. epsilon = difference(x , B) = 3689.697265625. i := 3. C := 15.625. A := 0. B := (A + C) / 2 = 7.8125. epsilon = difference(x , B) = 351.837158203125. i := 4. C := 7.8125. A := 0. B := (A + C) / 2 = 3.90625. epsilon = difference(x , B) = 65.395355224609375. i := 5. C := 7.8125. A := 3.90625. B := (A + C) / 2 = 5.859375. epsilon = difference(x , B) = 76.165676116943359375. i := 6. C := 5.859375. A := 3.90625. B := (A + C) / 2 = 4.8828125. epsilon = difference(x , B) = 8.584678173065185546875. i := 7. C := 5.859375. A := 4.8828125. B := (A + C) / 2 = 5.37109375. epsilon = difference(x , B) = 29.948793351650238037109375. i := 8. C := 5.37109375. A := 4.8828125. B := (A + C) / 2 = 5.126953125. epsilon = difference(x , B) = 9.765286929905414581298828125. i := 9. C := 5.126953125. A := 4.8828125. B := (A + C) / 2 = 5.0048828125. epsilon = difference(x , B) = 0.366568681783974170684814453125. i := 10. C := 5.0048828125. A := 4.8828125. B := (A + C) / 2 = 4.94384765625. epsilon = difference(x , B) = 4.164306548773311078548431396484375. i := 11. C := 5.0048828125. A := 4.94384765625. B := (A + C) / 2 = 4.974365234375. epsilon = difference(x , B) = 1.912767149406136013567447662353515625. i := 12. C := 5.0048828125. A := 4.974365234375. B := (A + C) / 2 = 4.9896240234375. epsilon = difference(x , B) = 0.776584445929984212853014469146728515625. i := 13. C := 5.0048828125. A := 4.9896240234375. B := (A + C) / 2 = 4.99725341796875. epsilon = difference(x , B) = 0.205880517370360394124872982501983642578125. i := 14. C := 5.0048828125. A := 4.99725341796875. B := (A + C) / 2 = 5.001068115234375. epsilon = difference(x , B) = 0.080125756849014351246296428143978118896484375. i := 15. C := 5.001068115234375. A := 4.99725341796875. B := (A + C) / 2 = 4.9991607666015625. epsilon = difference(x , B) = 0.062931940783439443976021721027791500091552734375. i := 16. C := 5.001068115234375. A := 4.9991607666015625. B := (A + C) / 2 = 5.00011444091796875. epsilon = difference(x , B) = 0.008583265300010634035743350978009402751922607421875. i := 17. C := 5.00011444091796875. A := 4.9991607666015625. B := (A + C) / 2 = 4.999637603759765625. epsilon = difference(x , B) = 0.027177748099647958124336355467676185071468353271484375. i := 18. C := 5.00011444091796875. A := 4.999637603759765625. B := (A + C) / 2 = 4.9998760223388671875. epsilon = difference(x , B) = 0.009298094029959631801052211130809155292809009552001953125. i := 19. C := 5.00011444091796875. A := 4.9998760223388671875. B := (A + C) / 2 = 4.99999523162841796875. epsilon = difference(x , B) = 0.00035762752759194160745437329751439392566680908203125. i := 20. C := 5.00011444091796875. A := 4.99999523162841796875. B := (A + C) / 2 = 5.000054836273193359375. epsilon = difference(x , B) = 0.0041127655949197150508922504741349257528781890869140625. i := 21. C := 5.000054836273193359375. A := 4.99999523162841796875. B := (A + C) / 2 = 5.0000250339508056640625. epsilon = difference(x , B) = 0.001877555710920887632742193318335921503603458404541015625. i := 22. C := 5.0000250339508056640625. A := 4.99999523162841796875. B := (A + C) / 2 = 5.00001013278961181640625. epsilon = difference(x , B) = 0.00075996076098865106285273895991849713027477264404296875. i := 23. C := 5.00001013278961181640625. A := 4.99999523162841796875. B := (A + C) / 2 = 5.000002682209014892578125. epsilon = difference(x , B) = 0.000201165784030642169621927450862131081521511077880859375. i := 24. C := 5.000002682209014892578125. A := 4.99999523162841796875. B := (A + C) / 2 = 4.9999989569187164306640625. epsilon = difference(x , B) = 7.823107994742173332269885577261447906494140625e-05. i := 25. C := 5.000002682209014892578125. A := 4.9999989569187164306640625. B := (A + C) / 2 = 5.00000081956386566162109375. epsilon = difference(x , B) = 6.14672999998955305045456043444573879241943359375e-05. i := 26. C := 5.00000081956386566162109375. A := 4.9999989569187164306640625. B := (A + C) / 2 = 4.999999888241291046142578125. epsilon = difference(x , B) = 8.381902984189171235129833803512156009674072265625e-06. i := 27. C := 5.00000081956386566162109375. A := 4.999999888241291046142578125. B := (A + C) / 2 = 5.0000003539025783538818359375. epsilon = difference(x , B) = 2.654269525524666217819458324811421334743499755859375e-05. i := 28. C := 5.0000003539025783538818359375. A := 4.999999888241291046142578125. B := (A + C) / 2 = 5.00000012107193470001220703125. epsilon = difference(x , B) = 9.080395322380585554356002830900251865386962890625e-06. i := 29. C := 5.00000012107193470001220703125. A := 4.999999888241291046142578125. B := (A + C) / 2 = 5.000000004656612873077392578125. epsilon = difference(x , B) = 3.4924596579999356293910750537179410457611083984375e-07. i := 30. C := 5.000000004656612873077392578125. A := 4.999999888241291046142578125. B := (A + C) / 2 = 4.9999999464489519596099853515625. epsilon = difference(x , B) = 4.016328560015047788311903786961920559406280517578125e-06. i := 31. C := 5.000000004656612873077392578125. A := 4.9999999464489519596099853515625. B := (A + C) / 2 = 4.99999997555278241634368896484375. epsilon = difference(x , B) = 1.833541309802233509884672457701526582241058349609375e-06. i := 32. C := 5.000000004656612873077392578125. A := 4.99999997555278241634368896484375. B := (A + C) / 2 = 4.999999990104697644710540771484375. epsilon = difference(x , B) = 7.42147675182602828414246687316335737705230712890625e-07. i := 33. C := 5.000000004656612873077392578125. A := 4.999999990104697644710540771484375. B := (A + C) / 2 = 4.9999999973806552588939666748046875. epsilon = difference(x , B) = 1.96450855478869090831040011835284531116485595703125e-07. i := 34. C := 5.000000004656612873077392578125. A := 4.9999999973806552588939666748046875. B := (A + C) / 2 = 5.00000000101863406598567962646484375. epsilon = difference(x , B) = 7.6397554969742653696584966382943093776702880859375e-08. i := 35. C := 5.00000000101863406598567962646484375. A := 4.9999999973806552588939666748046875. B := (A + C) / 2 = 4.999999999199644662439823150634765625. epsilon = difference(x , B) = 6.0026650310074369798485349747352302074432373046875e-08. i := 36. C := 5.00000000101863406598567962646484375. A := 4.999999999199644662439823150634765625. B := (A + C) / 2 = 5.0000000001091393642127513885498046875. epsilon = difference(x , B) = 8.1854523159563541412353515625e-09. -------------------------------- S = approximate_cube_root(125) = 5.0000000001091393642127513885498046875. -------------------------------- The value which was entered for x is -8. -------------------------------- Computing the approximate cube root of x: C = 8. // real number to take the cube root of B = 0. // variable for storing the approximate cube root of x A = 0. // number to add to C before dividing the sum of A and C by 2 for each while loop iteration, i epsilon = 0. // variable for storing the difference between the input value and B raised to the power of 3 i := 0. C := 8. A := 0. B := (A + C) / 2 = 4. epsilon = difference(x , B) = 56. i := 1. C := 4. A := 0. B := (A + C) / 2 = 2. epsilon = difference(x , B) = 0. -------------------------------- S = approximate_cube_root(-8) = -2. -------------------------------- The value which was entered for x is 1000. -------------------------------- Computing the approximate cube root of x: C = 1000. // real number to take the cube root of B = 0. // variable for storing the approximate cube root of x A = 0. // number to add to C before dividing the sum of A and C by 2 for each while loop iteration, i epsilon = 0. // variable for storing the difference between the input value and B raised to the power of 3 i := 0. C := 1000. A := 0. B := (A + C) / 2 = 500. epsilon = difference(x , B) = 124999000. i := 1. C := 500. A := 0. B := (A + C) / 2 = 250. epsilon = difference(x , B) = 15624000. i := 2. C := 250. A := 0. B := (A + C) / 2 = 125. epsilon = difference(x , B) = 1952125. i := 3. C := 125. A := 0. B := (A + C) / 2 = 62.5. epsilon = difference(x , B) = 243140.625. i := 4. C := 62.5. A := 0. B := (A + C) / 2 = 31.25. epsilon = difference(x , B) = 29517.578125. i := 5. C := 31.25. A := 0. B := (A + C) / 2 = 15.625. epsilon = difference(x , B) = 2814.697265625. i := 6. C := 15.625. A := 0. B := (A + C) / 2 = 7.8125. epsilon = difference(x , B) = 523.162841796875. i := 7. C := 15.625. A := 7.8125. B := (A + C) / 2 = 11.71875. epsilon = difference(x , B) = 609.325408935546875. i := 8. C := 11.71875. A := 7.8125. B := (A + C) / 2 = 9.765625. epsilon = difference(x , B) = 68.677425384521484375. i := 9. C := 11.71875. A := 9.765625. B := (A + C) / 2 = 10.7421875. epsilon = difference(x , B) = 239.590346813201904296875. i := 10. C := 10.7421875. A := 9.765625. B := (A + C) / 2 = 10.25390625. epsilon = difference(x , B) = 78.122295439243316650390625. i := 11. C := 10.25390625. A := 9.765625. B := (A + C) / 2 = 10.009765625. epsilon = difference(x , B) = 2.932549454271793365478515625. i := 12. C := 10.009765625. A := 9.765625. B := (A + C) / 2 = 9.8876953125. epsilon = difference(x , B) = 33.314452390186488628387451171875. i := 13. C := 10.009765625. A := 9.8876953125. B := (A + C) / 2 = 9.94873046875. epsilon = difference(x , B) = 15.302137195249088108539581298828125. i := 14. C := 10.009765625. A := 9.94873046875. B := (A + C) / 2 = 9.979248046875. epsilon = difference(x , B) = 6.212675567439873702824115753173828125. i := 15. C := 10.009765625. A := 9.979248046875. B := (A + C) / 2 = 9.9945068359375. epsilon = difference(x , B) = 1.647044138962883152998983860015869140625. i := 16. C := 10.009765625. A := 9.9945068359375. B := (A + C) / 2 = 10.00213623046875. epsilon = difference(x , B) = 0.641006054792114809970371425151824951171875. i := 17. C := 10.00213623046875. A := 9.9945068359375. B := (A + C) / 2 = 9.998321533203125. epsilon = difference(x , B) = 0.503455526267515551808173768222332000732421875. i := 18. C := 10.00213623046875. A := 9.998321533203125. B := (A + C) / 2 = 10.0002288818359375. epsilon = difference(x , B) = 0.068666122400085072285946807824075222015380859375. i := 19. C := 10.0002288818359375. A := 9.998321533203125. B := (A + C) / 2 = 9.99927520751953125. epsilon = difference(x , B) = 0.217421984797183664994690843741409480571746826171875. i := 20. C := 10.0002288818359375. A := 9.99927520751953125. B := (A + C) / 2 = 9.999752044677734375. epsilon = difference(x , B) = 0.074384752239677054408417689046473242342472076416015625. i := 21. C := 10.0002288818359375. A := 9.999752044677734375. B := (A + C) / 2 = 9.9999904632568359375. epsilon = difference(x , B) = 0.00286102022073553285963498638011515140533447265625. i := 22. C := 10.0002288818359375. A := 9.9999904632568359375. B := (A + C) / 2 = 10.00010967254638671875. epsilon = difference(x , B) = 0.0329021247593577204071380037930794060230255126953125. i := 23. C := 10.00010967254638671875. A := 9.9999904632568359375. B := (A + C) / 2 = 10.000050067901611328125. epsilon = difference(x , B) = 0.015020445687367101061937546546687372028827667236328125. i := 24. C := 10.000050067901611328125. A := 9.9999904632568359375. B := (A + C) / 2 = 10.0000202655792236328125. epsilon = difference(x , B) = 0.00607968608790920850282191167934797704219818115234375. i := 25. C := 10.0000202655792236328125. A := 9.9999904632568359375. B := (A + C) / 2 = 10.00000536441802978515625. epsilon = difference(x , B) = 0.001609326272245137356975419606897048652172088623046875. i := 26. C := 10.00000536441802978515625. A := 9.9999904632568359375. B := (A + C) / 2 = 9.999997913837432861328125. epsilon = difference(x , B) = 0.00062584863957937386658159084618091583251953125. i := 27. C := 10.00000536441802978515625. A := 9.999997913837432861328125. B := (A + C) / 2 = 10.0000016391277313232421875. epsilon = difference(x , B) = 0.0004917383999991642440363648347556591033935546875. i := 28. C := 10.0000016391277313232421875. A := 9.999997913837432861328125. B := (A + C) / 2 = 9.99999977648258209228515625. epsilon = difference(x , B) = 6.7055223873513369881038670428097248077392578125e-05. i := 29. C := 10.0000016391277313232421875. A := 9.99999977648258209228515625. B := (A + C) / 2 = 10.000000707805156707763671875. epsilon = difference(x , B) = 0.00021234156204197329742555666598491370677947998046875. i := 30. C := 10.000000707805156707763671875. A := 9.99999977648258209228515625. B := (A + C) / 2 = 10.0000002421438694000244140625. epsilon = difference(x , B) = 7.2643162579044684434848022647202014923095703125e-05. i := 31. C := 10.0000002421438694000244140625. A := 9.99999977648258209228515625. B := (A + C) / 2 = 10.00000000931322574615478515625. epsilon = difference(x , B) = 2.79396772639994850351286004297435283660888671875e-06. i := 32. C := 10.00000000931322574615478515625. A := 9.99999977648258209228515625. B := (A + C) / 2 = 9.999999892897903919219970703125. epsilon = difference(x , B) = 3.2130628480120382306495230295695364475250244140625e-05. i := 33. C := 10.00000000931322574615478515625. A := 9.999999892897903919219970703125. B := (A + C) / 2 = 9.9999999511055648326873779296875. epsilon = difference(x , B) = 1.4668330478417868079077379661612212657928466796875e-05. i := 34. C := 10.00000000931322574615478515625. A := 9.9999999511055648326873779296875. B := (A + C) / 2 = 9.99999998020939528942108154296875. epsilon = difference(x , B) = 5.937181401460822627313973498530685901641845703125e-06. i := 35. C := 10.00000000931322574615478515625. A := 9.99999998020939528942108154296875. B := (A + C) / 2 = 9.999999994761310517787933349609375. epsilon = difference(x , B) = 1.571606843830952726648320094682276248931884765625e-06. i := 36. C := 10.00000000931322574615478515625. A := 9.999999994761310517787933349609375. B := (A + C) / 2 = 10.0000000020372681319713592529296875. epsilon = difference(x , B) = 6.11180439757941229572679731063544750213623046875e-07. i := 37. C := 10.0000000020372681319713592529296875. A := 9.999999994761310517787933349609375. B := (A + C) / 2 = 9.99999999839928932487964630126953125. epsilon = difference(x , B) = 4.80213202480594958387882797978818416595458984375e-07. i := 38. C := 10.0000000020372681319713592529296875. A := 9.99999999839928932487964630126953125. B := (A + C) / 2 = 10.000000000218278728425502777099609375. epsilon = difference(x , B) = 6.54836185276508331298828125e-08. i := 39. C := 10.000000000218278728425502777099609375. A := 9.99999999839928932487964630126953125. B := (A + C) / 2 = 9.9999999993087840266525745391845703125. epsilon = difference(x , B) = 2.0736479200422763824462890625e-07. i := 40. C := 10.000000000218278728425502777099609375. A := 9.9999999993087840266525745391845703125. B := (A + C) / 2 = 9.99999999976353137753903865814208984375. epsilon = difference(x , B) = 7.0940586738288402557373046875e-08. i := 41. C := 10.000000000218278728425502777099609375. A := 9.99999999976353137753903865814208984375. B := (A + C) / 2 = 9.999999999990905052982270717620849609375. epsilon = difference(x , B) = 2.7284841053187847137451171875e-09. -------------------------------- S = approximate_cube_root(1000) = 9.999999999990905052982270717620849609375. -------------------------------- The value which was entered for x is 3.1400001049041748046875. -------------------------------- Computing the approximate cube root of x: C = 3.1400001049041748046875. // real number to take the cube root of B = 0. // variable for storing the approximate cube root of x A = 0. // number to add to C before dividing the sum of A and C by 2 for each while loop iteration, i epsilon = 0. // variable for storing the difference between the input value and B raised to the power of 3 i := 0. C := 3.1400001049041748046875. A := 0. B := (A + C) / 2 = 1.57000005245208740234375. epsilon = difference(x , B) = 0.72989328296328886773979005564427779972902499139308929443359375. i := 1. C := 1.57000005245208740234375. A := 0. B := (A + C) / 2 = 0.785000026226043701171875. epsilon = difference(x , B) = 2.65626343142074184560698368873232766418368555605411529541015625. i := 2. C := 1.57000005245208740234375. A := 0.785000026226043701171875. B := (A + C) / 2 = 1.1775000393390655517578125. epsilon = difference(x , B) = 1.5073888318975885679262827210322939208708703517913818359375. i := 3. C := 1.57000005245208740234375. A := 1.1775000393390655517578125. B := (A + C) / 2 = 1.37375004589557647705078125. epsilon = difference(x , B) = 0.5474738704539012898626915148980742742423899471759796142578125. i := 4. C := 1.57000005245208740234375. A := 1.37375004589557647705078125. B := (A + C) / 2 = 1.471875049173831939697265625. epsilon = difference(x , B) = 0.04869378768681393893254238935952571409870870411396026611328125. i := 5. C := 1.471875049173831939697265625. A := 1.37375004589557647705078125. B := (A + C) / 2 = 1.4228125475347042083740234375. epsilon = difference(x , B) = 0.25966472170411463902227333644390228073461912572383880615234375. i := 6. C := 1.471875049173831939697265625. A := 1.4228125475347042083740234375. B := (A + C) / 2 = 1.44734379835426807403564453125. epsilon = difference(x , B) = 0.10809842450396796591401138432075867967796511948108673095703125. i := 7. C := 1.471875049173831939697265625. A := 1.44734379835426807403564453125. B := (A + C) / 2 = 1.459609423764050006866455078125. epsilon = difference(x , B) = 0.0303610937093032767254696668857150143594481050968170166015625. i := 8. C := 1.471875049173831939697265625. A := 1.459609423764050006866455078125. B := (A + C) / 2 = 1.4657422364689409732818603515625. epsilon = difference(x , B) = 0.0090009611727116579406315910460989471175707876682281494140625. i := 9. C := 1.4657422364689409732818603515625. A := 1.459609423764050006866455078125. B := (A + C) / 2 = 1.46267583011649549007415771484375. epsilon = difference(x , B) = 0.0107213262234489643993928797982562173274345695972442626953125. i := 10. C := 1.4657422364689409732818603515625. A := 1.46267583011649549007415771484375. B := (A + C) / 2 = 1.464209033292718231678009033203125. epsilon = difference(x , B) = 0.0008705083265141623678762261562269486603327095508575439453125. i := 11. C := 1.4657422364689409732818603515625. A := 1.464209033292718231678009033203125. B := (A + C) / 2 = 1.4649756348808296024799346923828125. epsilon = difference(x , B) = 0.0040626436212677177230168101829121951595880091190338134765625. i := 12. C := 1.4649756348808296024799346923828125. A := 1.464209033292718231678009033203125. B := (A + C) / 2 = 1.46459233408677391707897186279296875. epsilon = difference(x , B) = 0.00159542211586210179972977751816642921767197549343109130859375. i := 13. C := 1.46459233408677391707897186279296875. A := 1.464209033292718231678009033203125. B := (A + C) / 2 = 1.464400683689746074378490447998046875. epsilon = difference(x , B) = 0.00036229553291318612739946303236138192005455493927001953125. i := 14. C := 1.464400683689746074378490447998046875. A := 1.464209033292718231678009033203125. B := (A + C) / 2 = 1.4643048584912321530282497406005859375. epsilon = difference(x , B) = 0.00025414673460094866323799589480358918081037700176239013671875. i := 15. C := 1.464400683689746074378490447998046875. A := 1.4643048584912321530282497406005859375. B := (A + C) / 2 = 1.46435277109048911370337009429931640625. epsilon = difference(x , B) = 5.406431437603685663528807481270632706582546234130859375e-05. i := 16. C := 1.46435277109048911370337009429931640625. A := 1.4643048584912321530282497406005859375. B := (A + C) / 2 = 1.464328814790860633365809917449951171875. epsilon = difference(x , B) = 0.00010004373126623069233109841746909296489320695400238037109375. i := 17. C := 1.46435277109048911370337009429931640625. A := 1.464328814790860633365809917449951171875. B := (A + C) / 2 = 1.4643407929406748735345900058746337890625. epsilon = difference(x , B) = 2.2990338738696457221433178119696094654500484466552734375e-05. i := 18. C := 1.46435277109048911370337009429931640625. A := 1.4643407929406748735345900058746337890625. B := (A + C) / 2 = 1.46434678201558199361898005008697509765625. epsilon = difference(x , B) = 1.55368302446261090377088720515530440025031566619873046875e-05. i := 19. C := 1.46434678201558199361898005008697509765625. A := 1.4643407929406748735345900058746337890625. B := (A + C) / 2 = 1.464343787478128433576785027980804443359375. epsilon = difference(x , B) = 3.72679364046553211753387557791938888840377330780029296875e-06. i := 20. C := 1.46434678201558199361898005008697509765625. A := 1.464343787478128433576785027980804443359375. B := (A + C) / 2 = 1.4643452847468552135978825390338897705078125. epsilon = difference(x , B) = 5.90500845371239903303095530873179086484014987945556640625e-06. i := 21. C := 1.4643452847468552135978825390338897705078125. A := 1.464343787478128433576785027980804443359375. B := (A + C) / 2 = 1.46434453611249182358733378350734710693359375. epsilon = difference(x , B) = 1.08910494453257240821120177542979945428669452667236328125e-06. i := 22. C := 1.46434453611249182358733378350734710693359375. A := 1.464343787478128433576785027980804443359375. B := (A + C) / 2 = 1.464344161795310128582059405744075775146484375. epsilon = difference(x , B) = 1.318844963489086696828422873295494355261325836181640625e-06. i := 23. C := 1.46434453611249182358733378350734710693359375. A := 1.464344161795310128582059405744075775146484375. B := (A + C) / 2 = 1.4643443489539009760846965946257114410400390625. epsilon = difference(x , B) = 1.1487016335874622452450921628042124211788177490234375e-07. i := 24. C := 1.46434453611249182358733378350734710693359375. A := 1.4643443489539009760846965946257114410400390625. B := (A + C) / 2 = 1.46434444253319639983601518906652927398681640625. epsilon = difference(x , B) = 4.8711735211692634706093230079204658977687358856201171875e-07. i := 25. C := 1.46434444253319639983601518906652927398681640625. A := 1.4643443489539009760846965946257114410400390625. B := (A + C) / 2 = 1.464344395743548687960355891846120357513427734375. epsilon = difference(x , B) = 1.8612358476167469023554446039270260371267795562744140625e-07. i := 26. C := 1.464344395743548687960355891846120357513427734375. A := 1.4643443489539009760846965946257114410400390625. B := (A + C) / 2 = 1.4643443723487248320225262432359158992767333984375. epsilon = difference(x , B) = 3.562670829702907493441443875781260430812835693359375e-08. i := 27. C := 1.4643443723487248320225262432359158992767333984375. A := 1.4643443489539009760846965946257114410400390625. B := (A + C) / 2 = 1.46434436065131290405361141893081367015838623046875. epsilon = difference(x , B) = 3.9621728131940259221011046975036151707172393798828125e-08. i := 28. C := 1.4643443723487248320225262432359158992767333984375. A := 1.46434436065131290405361141893081367015838623046875. B := (A + C) / 2 = 1.464344366500018868038068831083364784717559814453125. epsilon = difference(x , B) = 1.997510067942853684286319548846222460269927978515625e-09. -------------------------------- S = approximate_cube_root(3.1400001049041748046875) = 1.464344366500018868038068831083364784717559814453125. -------------------------------- The value which was entered for x is 2. -------------------------------- Computing the approximate cube root of x: C = 2. // real number to take the cube root of B = 0. // variable for storing the approximate cube root of x A = 0. // number to add to C before dividing the sum of A and C by 2 for each while loop iteration, i epsilon = 0. // variable for storing the difference between the input value and B raised to the power of 3 i := 0. C := 2. A := 0. B := (A + C) / 2 = 1. epsilon = difference(x , B) = 1. i := 1. C := 2. A := 1. B := (A + C) / 2 = 1.5. epsilon = difference(x , B) = 1.375. i := 2. C := 1.5. A := 1. B := (A + C) / 2 = 1.25. epsilon = difference(x , B) = 0.046875. i := 3. C := 1.5. A := 1.25. B := (A + C) / 2 = 1.375. epsilon = difference(x , B) = 0.599609375. i := 4. C := 1.375. A := 1.25. B := (A + C) / 2 = 1.3125. epsilon = difference(x , B) = 0.260986328125. i := 5. C := 1.3125. A := 1.25. B := (A + C) / 2 = 1.28125. epsilon = difference(x , B) = 0.103302001953125. i := 6. C := 1.28125. A := 1.25. B := (A + C) / 2 = 1.265625. epsilon = difference(x , B) = 0.027286529541015625. i := 7. C := 1.265625. A := 1.25. B := (A + C) / 2 = 1.2578125. epsilon = difference(x , B) = 0.010024547576904296875. i := 8. C := 1.265625. A := 1.2578125. B := (A + C) / 2 = 1.26171875. epsilon = difference(x , B) = 0.008573234081268310546875. i := 9. C := 1.26171875. A := 1.2578125. B := (A + C) / 2 = 1.259765625. epsilon = difference(x , B) = 0.000740073621273040771484375. i := 10. C := 1.26171875. A := 1.259765625. B := (A + C) / 2 = 1.2607421875. epsilon = difference(x , B) = 0.003912973217666149139404296875. i := 11. C := 1.2607421875. A := 1.259765625. B := (A + C) / 2 = 1.26025390625. epsilon = difference(x , B) = 0.001585548394359648227691650390625. i := 12. C := 1.26025390625. A := 1.259765625. B := (A + C) / 2 = 1.260009765625. epsilon = difference(x , B) = 0.000422512079239822924137115478515625. i := 13. C := 1.260009765625. A := 1.259765625. B := (A + C) / 2 = 1.2598876953125. epsilon = difference(x , B) = 0.000158837092385510914027690887451171875. i := 14. C := 1.260009765625. A := 1.2598876953125. B := (A + C) / 2 = 1.25994873046875. epsilon = difference(x , B) = 0.000131823412402809481136500835418701171875. i := 15. C := 1.25994873046875. A := 1.2598876953125. B := (A + C) / 2 = 1.259918212890625. epsilon = difference(x , B) = 1.3510360162172219133935868740081787109375e-05. i := 16. C := 1.25994873046875. A := 1.259918212890625. B := (A + C) / 2 = 1.2599334716796875. epsilon = difference(x , B) = 5.9155646066955114292795769870281219482421875e-05. i := 17. C := 1.2599334716796875. A := 1.259918212890625. B := (A + C) / 2 = 1.25992584228515625. epsilon = difference(x , B) = 2.2822422940382836031858460046350955963134765625e-05. i := 18. C := 1.25992584228515625. A := 1.259918212890625. B := (A + C) / 2 = 1.259922027587890625. epsilon = difference(x , B) = 4.655976386269689015762196504510939121246337890625e-06. i := 19. C := 1.259922027587890625. A := 1.259918212890625. B := (A + C) / 2 = 1.2599201202392578125. epsilon = difference(x , B) = 4.427205638639353235674889219808392226696014404296875e-06. i := 20. C := 1.259922027587890625. A := 1.2599201202392578125. B := (A + C) / 2 = 1.25992107391357421875. epsilon = difference(x , B) = 1.14381936140543760682675156203913502395153045654296875e-07. i := 21. C := 1.25992107391357421875. A := 1.2599201202392578125. B := (A + C) / 2 = 1.259920597076416015625. epsilon = difference(x , B) = 2.156412710667735509184606002008877112530171871185302734375e-06. i := 22. C := 1.25992107391357421875. A := 1.259920597076416015625. B := (A + C) / 2 = 1.2599208354949951171875. epsilon = difference(x , B) = 1.02101560211825988233602657828669180162250995635986328125e-06. i := 23. C := 1.25992107391357421875. A := 1.2599208354949951171875. B := (A + C) / 2 = 1.25992095470428466796875. epsilon = difference(x , B) = 4.5331688670251051032078493108201655559241771697998046875e-07. i := 24. C := 1.25992107391357421875. A := 1.25992095470428466796875. B := (A + C) / 2 = 1.259921014308929443359375. epsilon = difference(x , B) = 1.6946748870936938213827005483835819177329540252685546875e-07. i := 25. C := 1.25992107391357421875. A := 1.259921014308929443359375. B := (A + C) / 2 = 1.2599210441112518310546875. epsilon = difference(x , B) = 2.7542779641536417611913378777899197302758693695068359375e-08. i := 26. C := 1.25992107391357421875. A := 1.2599210441112518310546875. B := (A + C) / 2 = 1.25992105901241302490234375. epsilon = difference(x , B) = 4.341957741027697992297618156953831203281879425048828125e-08. i := 27. C := 1.25992105901241302490234375. A := 1.2599210441112518310546875. B := (A + C) / 2 = 1.259921051561832427978515625. epsilon = difference(x , B) = 7.93839867452295067096201819367706775665283203125e-09. -------------------------------- S = approximate_cube_root(2) = 1.259921051561832427978515625. -------------------------------- The value which was entered for x is -10. -------------------------------- Computing the approximate cube root of x: C = 10. // real number to take the cube root of B = 0. // variable for storing the approximate cube root of x A = 0. // number to add to C before dividing the sum of A and C by 2 for each while loop iteration, i epsilon = 0. // variable for storing the difference between the input value and B raised to the power of 3 i := 0. C := 10. A := 0. B := (A + C) / 2 = 5. epsilon = difference(x , B) = 115. i := 1. C := 5. A := 0. B := (A + C) / 2 = 2.5. epsilon = difference(x , B) = 5.625. i := 2. C := 2.5. A := 0. B := (A + C) / 2 = 1.25. epsilon = difference(x , B) = 8.046875. i := 3. C := 2.5. A := 1.25. B := (A + C) / 2 = 1.875. epsilon = difference(x , B) = 3.408203125. i := 4. C := 2.5. A := 1.875. B := (A + C) / 2 = 2.1875. epsilon = difference(x , B) = 0.467529296875. i := 5. C := 2.1875. A := 1.875. B := (A + C) / 2 = 2.03125. epsilon = difference(x , B) = 1.619110107421875. i := 6. C := 2.1875. A := 2.03125. B := (A + C) / 2 = 2.109375. epsilon = difference(x , B) = 0.614414215087890625. i := 7. C := 2.1875. A := 2.109375. B := (A + C) / 2 = 2.1484375. epsilon = difference(x , B) = 0.083277225494384765625. i := 8. C := 2.1875. A := 2.1484375. B := (A + C) / 2 = 2.16796875. epsilon = difference(x , B) = 0.189644992351531982421875. i := 9. C := 2.16796875. A := 2.1484375. B := (A + C) / 2 = 2.158203125. epsilon = difference(x , B) = 0.052566416561603546142578125. i := 10. C := 2.158203125. A := 2.1484375. B := (A + C) / 2 = 2.1533203125. epsilon = difference(x , B) = 0.015509421937167644500732421875. i := 11. C := 2.158203125. A := 2.1533203125. B := (A + C) / 2 = 2.15576171875. epsilon = difference(x , B) = 0.018489949288778007030487060546875. i := 12. C := 2.15576171875. A := 2.1533203125. B := (A + C) / 2 = 2.154541015625. epsilon = difference(x , B) = 0.001480632126913405954837799072265625. i := 13. C := 2.154541015625. A := 2.1533203125. B := (A + C) / 2 = 2.1539306640625. epsilon = difference(x , B) = 0.007016802110229036770761013031005859375. i := 14. C := 2.154541015625. A := 2.1539306640625. B := (A + C) / 2 = 2.15423583984375. epsilon = difference(x , B) = 0.002768686878198423073627054691314697265625. i := 15. C := 2.154541015625. A := 2.15423583984375. B := (A + C) / 2 = 2.154388427734375. epsilon = difference(x , B) = 0.000644177857935801512212492525577545166015625. i := 16. C := 2.154541015625. A := 2.154388427734375. B := (A + C) / 2 = 2.1544647216796875. epsilon = difference(x , B) = 0.000418189512583211353557999245822429656982421875. i := 17. C := 2.1544647216796875. A := 2.154388427734375. B := (A + C) / 2 = 2.15442657470703125. epsilon = difference(x , B) = 0.000113003577986159342572136665694415569305419921875. i := 18. C := 2.1544647216796875. A := 2.15442657470703125. B := (A + C) / 2 = 2.154445648193359375. epsilon = difference(x , B) = 0.000152590615950243257969987098476849496364593505859375. i := 19. C := 2.154445648193359375. A := 2.15442657470703125. B := (A + C) / 2 = 2.1544361114501953125. epsilon = difference(x , B) = 1.9792931147573356032154379136045463383197784423828125e-05. i := 20. C := 2.1544361114501953125. A := 2.15442657470703125. B := (A + C) / 2 = 2.15443134307861328125. epsilon = difference(x , B) = 4.6605470377584883034938201262775692157447338104248046875e-05. i := 21. C := 2.1544361114501953125. A := 2.15443134307861328125. B := (A + C) / 2 = 2.154433727264404296875. epsilon = difference(x , B) = 1.34063063546192851038796334250946529209613800048828125e-05. i := 22. C := 2.1544361114501953125. A := 2.154433727264404296875. B := (A + C) / 2 = 2.1544349193572998046875. epsilon = difference(x , B) = 3.193303211568125632435766192429582588374614715576171875e-06. i := 23. C := 2.1544349193572998046875. A := 2.154433727264404296875. B := (A + C) / 2 = 2.15443432331085205078125. epsilon = difference(x , B) = 5.106503867751722991474849777659983374178409576416015625e-06. i := 24. C := 2.1544349193572998046875. A := 2.15443432331085205078125. B := (A + C) / 2 = 2.154434621334075927734375. epsilon = difference(x , B) = 9.56600902148226073240522282503661699593067169189453125e-07. i := 25. C := 2.1544349193572998046875. A := 2.154434621334075927734375. B := (A + C) / 2 = 2.1544347703456878662109375. epsilon = difference(x , B) = 1.118351011196276612036371034264448098838329315185546875e-06. i := 26. C := 2.1544347703456878662109375. A := 2.154434621334075927734375. B := (A + C) / 2 = 2.15443469583988189697265625. epsilon = difference(x , B) = 8.0875018644739615769623242158559150993824005126953125e-08. i := 27. C := 2.15443469583988189697265625. A := 2.154434621334075927734375. B := (A + C) / 2 = 2.154434658586978912353515625. epsilon = difference(x , B) = 4.37862950721130961273530601829406805336475372314453125e-07. i := 28. C := 2.15443469583988189697265625. A := 2.154434658586978912353515625. B := (A + C) / 2 = 2.1544346772134304046630859375. epsilon = difference(x , B) = 1.78493968280325765451976849362836219370365142822265625e-07. i := 29. C := 2.15443469583988189697265625. A := 2.1544346772134304046630859375. B := (A + C) / 2 = 2.15443468652665615081787109375. epsilon = difference(x , B) = 4.88094753781087575816854950971901416778564453125e-08. i := 30. C := 2.15443469583988189697265625. A := 2.15443468652665615081787109375. B := (A + C) / 2 = 2.154434691183269023895263671875. epsilon = difference(x , B) = 1.6032771493236508408841700656921602785587310791015625e-08. i := 31. C := 2.154434691183269023895263671875. A := 2.15443468652665615081787109375. B := (A + C) / 2 = 2.1544346888549625873565673828125. epsilon = difference(x , B) = 1.63883519775642749749522408819757401943206787109375e-08. i := 32. C := 2.154434691183269023895263671875. A := 2.1544346888549625873565673828125. B := (A + C) / 2 = 2.15443469001911580562591552734375. epsilon = difference(x , B) = 1.777902512711815319335073581896722316741943359375e-10. -------------------------------- S = approximate_cube_root(-10) = -2.15443469001911580562591552734375. -------------------------------- The value which was entered for x is -1. -------------------------------- Computing the approximate cube root of x: C = 1. // real number to take the cube root of B = 0. // variable for storing the approximate cube root of x A = 0. // number to add to C before dividing the sum of A and C by 2 for each while loop iteration, i epsilon = 0. // variable for storing the difference between the input value and B raised to the power of 3 i := 0. C := 1. A := 0. B := (A + C) / 2 = 0.5. epsilon = difference(x , B) = 0.875. i := 1. C := 1. A := 0.5. B := (A + C) / 2 = 0.75. epsilon = difference(x , B) = 0.578125. i := 2. C := 1. A := 0.75. B := (A + C) / 2 = 0.875. epsilon = difference(x , B) = 0.330078125. i := 3. C := 1. A := 0.875. B := (A + C) / 2 = 0.9375. epsilon = difference(x , B) = 0.176025390625. i := 4. C := 1. A := 0.9375. B := (A + C) / 2 = 0.96875. epsilon = difference(x , B) = 0.090850830078125. i := 5. C := 1. A := 0.96875. B := (A + C) / 2 = 0.984375. epsilon = difference(x , B) = 0.046146392822265625. i := 6. C := 1. A := 0.984375. B := (A + C) / 2 = 0.9921875. epsilon = difference(x , B) = 0.023254871368408203125. i := 7. C := 1. A := 0.9921875. B := (A + C) / 2 = 0.99609375. epsilon = difference(x , B) = 0.011673033237457275390625. i := 8. C := 1. A := 0.99609375. B := (A + C) / 2 = 0.998046875. epsilon = difference(x , B) = 0.005847938358783721923828125. i := 9. C := 1. A := 0.998046875. B := (A + C) / 2 = 0.9990234375. epsilon = difference(x , B) = 0.002926827408373355865478515625. i := 10. C := 1. A := 0.9990234375. B := (A + C) / 2 = 0.99951171875. epsilon = difference(x , B) = 0.001464128610678017139434814453125. i := 11. C := 1. A := 0.99951171875. B := (A + C) / 2 = 0.999755859375. epsilon = difference(x , B) = 0.000732243075617589056491851806640625. i := 12. C := 1. A := 0.999755859375. B := (A + C) / 2 = 0.9998779296875. epsilon = difference(x , B) = 0.000366166235835407860577106475830078125. i := 13. C := 1. A := 0.9998779296875. B := (A + C) / 2 = 0.99993896484375. epsilon = difference(x , B) = 0.000183094293106478289701044559478759765625. i := 14. C := 1. A := 0.99993896484375. B := (A + C) / 2 = 0.999969482421875. epsilon = difference(x , B) = 9.1549940435697862994857132434844970703125e-05. i := 15. C := 1. A := 0.999969482421875. B := (A + C) / 2 = 0.9999847412109375. epsilon = difference(x , B) = 4.5775668699121752069913782179355621337890625e-05. i := 16. C := 1. A := 0.9999847412109375. B := (A + C) / 2 = 0.99999237060546875. epsilon = difference(x , B) = 2.2888008971211348807628382928669452667236328125e-05. i := 17. C := 1. A := 0.99999237060546875. B := (A + C) / 2 = 0.999996185302734375. epsilon = difference(x , B) = 1.1444048141184826050675837905146181583404541015625e-05. i := 18. C := 1. A := 0.999996185302734375. B := (A + C) / 2 = 0.9999980926513671875. epsilon = difference(x , B) = 5.722034984508017618765052247908897697925567626953125e-06. i := 19. C := 1. A := 0.9999980926513671875. B := (A + C) / 2 = 0.99999904632568359375. epsilon = difference(x , B) = 2.861020220735512042953274658430018462240695953369140625e-06. i := 20. C := 1. A := 0.99999904632568359375. B := (A + C) / 2 = 0.999999523162841796875. epsilon = difference(x , B) = 1.430510792488457090521070114164103870280086994171142578125e-06. i := 21. C := 1. A := 0.999999523162841796875. B := (A + C) / 2 = 0.9999997615814208984375. epsilon = difference(x , B) = 7.1525556677443091757595539093017578125e-07. i := 22. C := 1. A := 0.9999997615814208984375. B := (A + C) / 2 = 0.99999988079071044921875. epsilon = difference(x , B) = 3.576278260197796043939888477325439453125e-07. i := 23. C := 1. A := 0.99999988079071044921875. B := (A + C) / 2 = 0.999999940395355224609375. epsilon = difference(x , B) = 1.78813923668030838598497211933135986328125e-07. i := 24. C := 1. A := 0.999999940395355224609375. B := (A + C) / 2 = 0.9999999701976776123046875. epsilon = difference(x , B) = 8.940696449855067839962430298328399658203125e-08. i := 25. C := 1. A := 0.9999999701976776123046875. B := (A + C) / 2 = 0.99999998509883880615234375. epsilon = difference(x , B) = 4.47034829154091539749060757458209991455078125e-08. i := 26. C := 1. A := 0.99999998509883880615234375. B := (A + C) / 2 = 0.999999992549419403076171875. epsilon = difference(x , B) = 2.2351741624238030681226518936455249786376953125e-08. i := 27. C := 1. A := 0.999999992549419403076171875. B := (A + C) / 2 = 0.9999999962747097015380859375. epsilon = difference(x , B) = 1.117587085375237876405662973411381244659423828125e-08. i := 28. C := 1. A := 0.9999999962747097015380859375. B := (A + C) / 2 = 0.99999999813735485076904296875. epsilon = difference(x , B) = 5.5879354372845302378891574335284531116485595703125e-09. -------------------------------- S = approximate_cube_root(-1) = -0.99999999813735485076904296875. -------------------------------- The value which was entered for x is 0. -------------------------------- Computing the approximate cube root of x: C = 0. // real number to take the cube root of B = 0. // variable for storing the approximate cube root of x A = 0. // number to add to C before dividing the sum of A and C by 2 for each while loop iteration, i epsilon = 0. // variable for storing the difference between the input value and B raised to the power of 3 i := 0. C := 0. A := 0. B := (A + C) / 2 = 0. epsilon = difference(x , B) = 0. -------------------------------- S = approximate_cube_root(0) = 0. -------------------------------- The value which was entered for x is 0.5. -------------------------------- Computing the approximate cube root of x: C = 0. // real number to take the cube root of B = 0. // variable for storing the approximate cube root of x A = 0. // number to add to C before dividing the sum of A and C by 2 for each while loop iteration, i epsilon = 0. // variable for storing the difference between the input value and B raised to the power of 3 i := 0. C := 0. A := 0. B := (A + C) / 2 = 0. epsilon = difference(x , B) = 0. -------------------------------- S = approximate_cube_root(0.5) = 0. -------------------------------- The value which was entered for x is -81. -------------------------------- Computing the approximate cube root of x: C = 81. // real number to take the cube root of B = 0. // variable for storing the approximate cube root of x A = 0. // number to add to C before dividing the sum of A and C by 2 for each while loop iteration, i epsilon = 0. // variable for storing the difference between the input value and B raised to the power of 3 i := 0. C := 81. A := 0. B := (A + C) / 2 = 40.5. epsilon = difference(x , B) = 66349.125. i := 1. C := 40.5. A := 0. B := (A + C) / 2 = 20.25. epsilon = difference(x , B) = 8222.765625. i := 2. C := 20.25. A := 0. B := (A + C) / 2 = 10.125. epsilon = difference(x , B) = 956.970703125. i := 3. C := 10.125. A := 0. B := (A + C) / 2 = 5.0625. epsilon = difference(x , B) = 48.746337890625. i := 4. C := 5.0625. A := 0. B := (A + C) / 2 = 2.53125. epsilon = difference(x , B) = 64.781707763671875. i := 5. C := 5.0625. A := 2.53125. B := (A + C) / 2 = 3.796875. epsilon = difference(x , B) = 26.263263702392578125. i := 6. C := 5.0625. A := 3.796875. B := (A + C) / 2 = 4.4296875. epsilon = difference(x , B) = 5.919909954071044921875. i := 7. C := 4.4296875. A := 3.796875. B := (A + C) / 2 = 4.11328125. epsilon = difference(x , B) = 11.407054603099822998046875. i := 8. C := 4.4296875. A := 4.11328125. B := (A + C) / 2 = 4.271484375. epsilon = difference(x , B) = 3.064295388758182525634765625. i := 9. C := 4.4296875. A := 4.271484375. B := (A + C) / 2 = 4.3505859375. epsilon = difference(x , B) = 1.346141687594354152679443359375. i := 10. C := 4.3505859375. A := 4.271484375. B := (A + C) / 2 = 4.31103515625. epsilon = difference(x , B) = 0.879307645722292363643646240234375. i := 11. C := 4.3505859375. A := 4.31103515625. B := (A + C) / 2 = 4.330810546875. epsilon = difference(x , B) = 0.228336121697793714702129364013671875. i := 12. C := 4.330810546875. A := 4.31103515625. B := (A + C) / 2 = 4.3209228515625. epsilon = difference(x , B) = 0.326753086765165789984166622161865234375. i := 13. C := 4.330810546875. A := 4.3209228515625. B := (A + C) / 2 = 4.32586669921875. epsilon = difference(x , B) = 0.049525676228995507699437439441680908203125. i := 14. C := 4.330810546875. A := 4.32586669921875. B := (A + C) / 2 = 4.328338623046875. epsilon = difference(x , B) = 0.089325878997186691776732914149761199951171875. i := 15. C := 4.328338623046875. A := 4.32586669921875. B := (A + C) / 2 = 4.3271026611328125. epsilon = difference(x , B) = 0.019880271113965619633745518513023853302001953125. i := 16. C := 4.3271026611328125. A := 4.32586669921875. B := (A + C) / 2 = 4.32648468017578125. epsilon = difference(x , B) = 0.014827659417025795818290134775452315807342529296875. i := 17. C := 4.3271026611328125. A := 4.32648468017578125. B := (A + C) / 2 = 4.326793670654296875. epsilon = difference(x , B) = 0.002525066545089493796893975741113536059856414794921875. i := 18. C := 4.326793670654296875. A := 4.32648468017578125. B := (A + C) / 2 = 4.3266391754150390625. epsilon = difference(x , B) = 0.006151606250750417392847424480351037345826625823974609375. i := 19. C := 4.326793670654296875. A := 4.3266391754150390625. B := (A + C) / 2 = 4.32671642303466796875. epsilon = difference(x , B) = 0.001813347307908885763794160084216855466365814208984375. i := 20. C := 4.326793670654296875. A := 4.32671642303466796875. B := (A + C) / 2 = 4.326755046844482421875. epsilon = difference(x , B) = 0.00035584025464784063697010196847259066998958587646484375. i := 21. C := 4.326755046844482421875. A := 4.32671642303466796875. B := (A + C) / 2 = 4.3267357349395751953125. epsilon = difference(x , B) = 0.000728758367594527223243261460083886049687862396240234375. i := 22. C := 4.326755046844482421875. A := 4.3267357349395751953125. B := (A + C) / 2 = 4.32674539089202880859375. epsilon = difference(x , B) = 0.000186460266717043687823007758197491057217121124267578125. i := 23. C := 4.326755046844482421875. A := 4.32674539089202880859375. B := (A + C) / 2 = 4.326750218868255615234375. epsilon = difference(x , B) = 8.4689691404134237462386636252631433308124542236328125e-05. i := 24. C := 4.326750218868255615234375. A := 4.32674539089202880859375. B := (A + C) / 2 = 4.3267478048801422119140625. epsilon = difference(x , B) = 5.0885363296726549009463269612751901149749755859375e-05. i := 25. C := 4.326750218868255615234375. A := 4.3267478048801422119140625. B := (A + C) / 2 = 4.32674901187419891357421875. epsilon = difference(x , B) = 1.69021451436324188222215525456704199314117431640625e-05. i := 26. C := 4.32674901187419891357421875. A := 4.3267478048801422119140625. B := (A + C) / 2 = 4.326748408377170562744140625. epsilon = difference(x , B) = 1.6991613804064054082942902823560871183872222900390625e-05. i := 27. C := 4.32674901187419891357421875. A := 4.326748408377170562744140625. B := (A + C) / 2 = 4.3267487101256847381591796875. epsilon = difference(x , B) = 4.47355121002690481191166327334940433502197265625e-08. i := 28. C := 4.32674901187419891357421875. A := 4.3267487101256847381591796875. B := (A + C) / 2 = 4.32674886099994182586669921875. epsilon = difference(x , B) = 8.42870452029409467087361917947418987751007080078125e-06. i := 29. C := 4.32674886099994182586669921875. A := 4.3267487101256847381591796875. B := (A + C) / 2 = 4.326748785562813282012939453125. epsilon = difference(x , B) = 4.191984430225448310380897964932955801486968994140625e-06. i := 30. C := 4.326748785562813282012939453125. A := 4.3267487101256847381591796875. B := (A + C) / 2 = 4.3267487478442490100860595703125. epsilon = difference(x , B) = 2.073624440601662399785709567368030548095703125e-06. i := 31. C := 4.3267487478442490100860595703125. A := 4.3267487101256847381591796875. B := (A + C) / 2 = 4.32674872898496687412261962890625. epsilon = difference(x , B) = 1.014444459636332229734989596181549131870269775390625e-06. i := 32. C := 4.32674872898496687412261962890625. A := 4.3267487101256847381591796875. B := (A + C) / 2 = 4.326748719555325806140899658203125. epsilon = difference(x , B) = 4.8485447261270575580738295684568583965301513671875e-07. i := 33. C := 4.326748719555325806140899658203125. A := 4.3267487101256847381591796875. B := (A + C) / 2 = 4.3267487148405052721500396728515625. epsilon = difference(x , B) = 2.20059479971723703783936798572540283203125e-07. i := 34. C := 4.3267487148405052721500396728515625. A := 4.3267487101256847381591796875. B := (A + C) / 2 = 4.32674871248309500515460968017578125. epsilon = difference(x , B) = 8.76619838663383887933377991430461406707763671875e-08. i := 35. C := 4.32674871248309500515460968017578125. A := 4.3267487101256847381591796875. B := (A + C) / 2 = 4.326748711304389871656894683837890625. epsilon = difference(x , B) = 2.1463235862217988625388898071832954883575439453125e-08. i := 36. C := 4.326748711304389871656894683837890625. A := 4.3267487101256847381591796875. B := (A + C) / 2 = 4.3267487107150373049080371856689453125. epsilon = difference(x , B) = 1.1636138115556082794910253142006695270538330078125e-08. i := 37. C := 4.326748711304389871656894683837890625. A := 4.3267487107150373049080371856689453125. B := (A + C) / 2 = 4.32674871100971358828246593475341796875. epsilon = difference(x , B) = 4.9135488733309529152393224649131298065185546875e-09. -------------------------------- S = approximate_cube_root(-81) = -4.32674871100971358828246593475341796875. -------------------------------- The value which was entered for x is 27. -------------------------------- Computing the approximate cube root of x: C = 27. // real number to take the cube root of B = 0. // variable for storing the approximate cube root of x A = 0. // number to add to C before dividing the sum of A and C by 2 for each while loop iteration, i epsilon = 0. // variable for storing the difference between the input value and B raised to the power of 3 i := 0. C := 27. A := 0. B := (A + C) / 2 = 13.5. epsilon = difference(x , B) = 2433.375. i := 1. C := 13.5. A := 0. B := (A + C) / 2 = 6.75. epsilon = difference(x , B) = 280.546875. i := 2. C := 6.75. A := 0. B := (A + C) / 2 = 3.375. epsilon = difference(x , B) = 11.443359375. i := 3. C := 3.375. A := 0. B := (A + C) / 2 = 1.6875. epsilon = difference(x , B) = 22.194580078125. i := 4. C := 3.375. A := 1.6875. B := (A + C) / 2 = 2.53125. epsilon = difference(x , B) = 10.781707763671875. i := 5. C := 3.375. A := 2.53125. B := (A + C) / 2 = 2.953125. epsilon = difference(x , B) = 1.245952606201171875. i := 6. C := 3.375. A := 2.953125. B := (A + C) / 2 = 3.1640625. epsilon = difference(x , B) = 4.676352024078369140625. i := 7. C := 3.1640625. A := 2.953125. B := (A + C) / 2 = 3.05859375. epsilon = difference(x , B) = 1.613131463527679443359375. i := 8. C := 3.05859375. A := 2.953125. B := (A + C) / 2 = 3.005859375. epsilon = difference(x , B) = 0.158512316644191741943359375. i := 9. C := 3.005859375. A := 2.953125. B := (A + C) / 2 = 2.9794921875. epsilon = difference(x , B) = 0.549934429116547107696533203125. i := 10. C := 3.005859375. A := 2.9794921875. B := (A + C) / 2 = 2.99267578125. epsilon = difference(x , B) = 0.197271501529030501842498779296875. i := 11. C := 3.005859375. A := 2.99267578125. B := (A + C) / 2 = 2.999267578125. epsilon = difference(x , B) = 0.019770563041674904525279998779296875. i := 12. C := 3.005859375. A := 2.999267578125. B := (A + C) / 2 = 3.0025634765625. epsilon = difference(x , B) = 0.069273026741939247585833072662353515625. i := 13. C := 3.0025634765625. A := 2.999267578125. B := (A + C) / 2 = 3.00091552734375. epsilon = difference(x , B) = 0.024726782761490539996884763240814208984375. i := 14. C := 3.00091552734375. A := 2.999267578125. B := (A + C) / 2 = 3.000091552734375. epsilon = difference(x , B) = 0.002471999266020930008380673825740814208984375. i := 15. C := 3.000091552734375. A := 2.999267578125. B := (A + C) / 2 = 2.9996795654296875. epsilon = difference(x , B) = 0.008650809326514519170814310200512409210205078125. i := 16. C := 3.000091552734375. A := 2.9996795654296875. B := (A + C) / 2 = 2.99988555908203125. epsilon = difference(x , B) = 0.003089786916141701311744327540509402751922607421875. i := 17. C := 3.000091552734375. A := 2.99988555908203125. B := (A + C) / 2 = 2.999988555908203125. epsilon = difference(x , B) = 0.000308989299811990303368247623438946902751922607421875. i := 18. C := 3.000091552734375. A := 2.999988555908203125. B := (A + C) / 2 = 3.0000400543212890625. epsilon = difference(x , B) = 0.001081481114006833943452789981165551580488681793212890625. i := 19. C := 3.0000400543212890625. A := 2.999988555908203125. B := (A + C) / 2 = 3.00001430511474609375. epsilon = difference(x , B) = 0.00038623993987423055340713062832946889102458953857421875. i := 20. C := 3.00001430511474609375. A := 2.999988555908203125. B := (A + C) / 2 = 3.000001430511474609375. epsilon = difference(x , B) = 3.86238282317243053487487713937298394739627838134765625e-05. i := 21. C := 3.000001430511474609375. A := 2.999988555908203125. B := (A + C) / 2 = 2.9999949932098388671875. epsilon = difference(x , B) = 0.00013518310873918137904325931231142021715641021728515625. i := 22. C := 3.000001430511474609375. A := 2.9999949932098388671875. B := (A + C) / 2 = 2.99999821186065673828125. epsilon = difference(x , B) = 4.827973349109081213637040264075039885938167572021484375e-05. i := 23. C := 3.000001430511474609375. A := 2.99999821186065673828125. B := (A + C) / 2 = 2.999999821186065673828125. epsilon = difference(x , B) = 4.827975939036832642159424722194671630859375e-06. i := 24. C := 3.000001430511474609375. A := 2.999999821186065673828125. B := (A + C) / 2 = 3.0000006258487701416015625. epsilon = difference(x , B) = 1.689792031900338997729704715311527252197265625e-05. i := 25. C := 3.0000006258487701416015625. A := 2.999999821186065673828125. B := (A + C) / 2 = 3.00000022351741790771484375. epsilon = difference(x , B) = 6.0349707331486257544383988715708255767822265625e-06. i := 26. C := 3.00000022351741790771484375. A := 2.999999821186065673828125. B := (A + C) / 2 = 3.000000022351741790771484375. epsilon = difference(x , B) = 6.03497032847233327856883988715708255767822265625e-07. i := 27. C := 3.000000022351741790771484375. A := 2.999999821186065673828125. B := (A + C) / 2 = 2.9999999217689037322998046875. epsilon = difference(x , B) = 2.11223954414696546422192113823257386684417724609375e-06. i := 28. C := 3.000000022351741790771484375. A := 2.9999999217689037322998046875. B := (A + C) / 2 = 2.99999997206032276153564453125. epsilon = difference(x , B) = 7.543712784129075199501812676317058503627777099609375e-07. i := 29. C := 3.000000022351741790771484375. A := 2.99999997206032276153564453125. B := (A + C) / 2 = 2.999999997206032276153564453125. epsilon = difference(x , B) = 7.543712847446482072655271622352302074432373046875e-08. i := 30. C := 3.000000022351741790771484375. A := 2.999999997206032276153564453125. B := (A + C) / 2 = 3.0000000097788870334625244140625. epsilon = difference(x , B) = 2.640299507639110032641838188283145427703857421875e-07. i := 31. C := 3.0000000097788870334625244140625. A := 2.999999997206032276153564453125. B := (A + C) / 2 = 3.00000000349245965480804443359375. epsilon = difference(x , B) = 9.429641078910477869357009694795124232769012451171875e-08. i := 32. C := 3.00000000349245965480804443359375. A := 2.999999997206032276153564453125. B := (A + C) / 2 = 3.000000000349245965480804443359375. epsilon = difference(x , B) = 9.429641067981719970703125e-09. -------------------------------- S = approximate_cube_root(27) = 3.000000000349245965480804443359375. -------------------------------- End Of Program --------------------------------