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cube_root_approximation_output.txt
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--------------------------------
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.
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S = approximate_cube_root(2) = 1.259921051561832427978515625.
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The value which was entered for x is -10.
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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.