When I try to run your code, I get an incorrect answer for the root. I think the problem is in the exponent. The exponents are $root and ($root - 1), respectively.
When I run this code:
timethese( 100, {
'Root' => '$x = Root( 100, 3 )',
'Root2' => '$y = Root2( 100, 3 )',
});
print <<END;
Root: $x
-----
Root2: $y
END
I get this for output:
Benchmark: timing 100 iterations of Root, Root2...
Root: 29 wallclock secs (28.39 usr + 0.00 sys = 28.39 CPU) @ 3
+.52/s (n=1 00)
Root2: 20 wallclock secs (20.03 usr + 0.00 sys = 20.03 CPU) @ 4
+.99/s (n=1 00)
Root: 4.6415888336127788924100763542328778501807372125002714
-----
Root2: 0.6664902595019951166742874561807256134735
___________________
Kurt
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