Actual timed Mathomatic output from the simplify script
Mathomatic version 15.7.2
Copyright (C) 1987-2012 George Gesslein II.
200 equation spaces available in memory,
1920 kilobytes per equation space.
HTML color mode enabled; manage by typing "help color".
1−>
1−> ; Some complete simplifications Mathomatic has always been able to do.
1−> ; The result is the smallest expression that gives exactly the same results.
1−>
1−> 2*(x^2-y^2)^16-(x^2-y^2)^15*(2x^2-3)
#1: (2·((x^2 − y^2)^16)) − (((x^2 − y^2)^15)·((2·x^2) − 3))
1−> simplify ; Simplify the previously entered expression above.
#1: ((x^2 − y^2)^15)·(3 − (2·y^2))
1−> repeat echo *
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1−> a^3/((a-b)*(a-c))+b^3/((b-c)*(b-a))+c^3/((c-a)*(c-b))
a^3 b^3 c^3
#2: ––––––––––––––––– + ––––––––––––––––– + –––––––––––––––––
((a − b)·(a − c)) ((b − c)·(b − a)) ((c − a)·(c − b))
2−> simplify ; Simplify algebraic fractions.
#2: a + b + c
2−> repeat echo *
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2−> (x^6+a^6)*(x+1)/((x^6+a^6)*(x^2-a^2)+a^2*x^2*(x^4-a^4))+a^2*x^2*(x+1)/(x^6-a^6-a^2*x^2*(x^2-a^2))
(x^6 + a^6)·(x + 1) a^2·x^2·(x + 1)
#3: ––––––––––––––––––––––––––––––––––––––––––––––––––– + –––––––––––––––––––––––––––––––––––
(((x^6 + a^6)·(x^2 − a^2)) + (a^2·x^2·(x^4 − a^4))) (x^6 − a^6 − (a^2·x^2·(x^2 − a^2)))
3−> simplify
(x + 1)
#3: –––––––––––
(x^2 − a^2)
3−> repeat echo *
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3−> (1-(1-(y+1)/(x+y+1))/(1-x/(x+y+1)))/((y+1)^2-x/(1+x/(y-x+1))*(x*(y+1)/(y-x+1)-x))
(y + 1)
(1 − –––––––––––)
(x + y + 1)
(1 − –––––––––––––––––)
x
(1 − –––––––––––)
(x + y + 1)
#4: –––––––––––––––––––––––––––––––––––
x·(y + 1)
x·(––––––––––– − x)
(y − x + 1)
(((y + 1)^2) − –––––––––––––––––––)
x
(1 + –––––––––––)
(y − x + 1)
4−> simplify fraction ; Any complex fraction can be reduced to a simple fraction with this command.
1
#4: –––––––––––––––––––––––––––––––––––––
(1 + y^2 + (2·y) + (x·(y + 1)) + x^2)
4−> repeat echo *
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4−> ((2*((x*(x+(((x^2)-1)^(1/2))))-1))+1)/((2*x*((x^2)-1))+((((x^2)-1)^(1/2))*((2*(x^2))-1)))
1
((2·((x·(x + ((x^2 − 1)^–))) − 1)) + 1)
2
#5: –––––––––––––––––––––––––––––––––––––––––––––––––
1
((2·x·(x^2 − 1)) + (((x^2 − 1)^–)·((2·x^2) − 1)))
2
5−> simplify ; Simplify an expression containing radicals (roots).
1
#5: –––––––––––––
1
((x^2 − 1)^–)
2
5−> ; Rationalizing the denominator was required to simplify the above expression.
5−> repeat echo *
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5−> ((x - 2*y)^4/(x^2 - 4*y^2)^2 + 1)*(y + a)*(2*y + x) / (4*y^2 + x^2)
((x − (2·y))^4)
(––––––––––––––––––– + 1)·(y + a)·((2·y) + x)
((x^2 − (4·y^2))^2)
#6: –––––––––––––––––––––––––––––––––––––––––––––
((4·y^2) + x^2)
6−> repeat simplify
2·(y + a)
#6: –––––––––––
((2·y) + x)
Finished reading file "simplify.in".
6−>
End of input.
real 0.01 user 0.00 sys 0.01 seconds total execution time.
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