Data update

Task/Nth-root/DuckDB/nth-root.duckdb

@@ -0,0 +1,20 @@
+# Newton's method, assuming a > 0 and n > 0
+create or replace function nth_root(a,n) as (
+  with recursive cte as (
+    select 0 as ix, a::DOUBLE as x, (a-1.0)::DOUBLE as xprime
+    union all
+    select ix+1 as ix,
+           ((n - 1) * x / n ) +  (a / (n * x ** (n-1))) as x,
+           x as xprime
+    from cte
+    where @(x - xprime) > 1e-15
+    and ix<10
+  )
+  select last(x order by ix)
+  from cte
+);
+
+select n,
+       5.0 ^ (1 / cast(n as double)) as builtin,
+       nth_root(5.0, n) as nth_root
+from unnest( [1,3,5,10,1000,10000] )  _(n);