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$i+=1/(($_+=1e-7)**2+1)until$_>1;print$i/1e7*4
#23456789_123456789_123456789_123456789_123456
#        1         2         3         4

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$i+=($_&1?4:-4)/($_*2-1)for 1..1e6;print$i
#23456789_123456789_123456789_123456789_12
#        1         2         3         4