Actual timed Mathomatic output from the pie 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−> ; This is the famous Bailey-Borwein-Plouffe (BBP) formula.
1−> ; Sum this n = 0 to infinity to compute pi.
1−> ; This is especially useful for calculating pi in hexadecimal.
1−> ; One hexadecimal digit of pi is generated with each iteration.
1−> ((4/((8*n)+1))-(2/((8*n)+4))-(1/((8*n)+5))-(1/((8*n)+6)))/(16^n)
4 2 1 1
(––––––––––– − ––––––––––– − ––––––––––– − –––––––––––)
((8·n) + 1) ((8·n) + 4) ((8·n) + 5) ((8·n) + 6)
#1: –––––––––––––––––––––––––––––––––––––––––––––––––––––––
16^n
1−> simplify ; BBP simplifies to the ratio of two polynomials.
((120·n^2) + (151·n) + 47)
#1: ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––
(16^n·((512·n^4) + (1024·n^3) + (712·n^2) + (194·n) + 15))
1−> sum n=0 to 10 ; Numerically sum BBP from n = 0 to 10 in steps of 1.
#2: 3.1415926535898
1−> pi ; The digits should be the same.
answer = 3.1415926535898
3−> repeat echo *
*******************************************************************************
3−> x^n/n! ; Sum this n = 0 to infinity to compute (e^x).
x^n
#4: –––
n!
4−> replace x with 1 ; Sum this n = 0 to infinity to compute e:
1
#4: ––
n!
4−> sum n=0 to 20 ; Numerically sum from n = 0 to 20 in steps of 1.
#5: 2.718281828459
4−> e ; The digits should be the same.
answer = 2.718281828459
6−> repeat echo *
*******************************************************************************
6−> ; Euler's identity is made of these most important universal constants:
6−> e^(pi*i)+1=0
#7: (ê^(π·î)) + 1 = 0
7−> simplify ; An identity is when the LHS is identical to the RHS:
#7: 0 = 0
Finished reading file "pie.in".
7−>
End of input.
real 0.00 user 0.00 sys 0.00 seconds total execution time.
www.mathomatic.org