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Check Machin-like formulas: Difference between revisions
→{{header|J}}: add counterexample
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=={{header|J}}==
'''Solution''':<lang j> machin =: 1r4p1 = [: +/ ({. * _3 o. %/@:}.)"1@:x:</lang>
'''Example''' (''test cases from task description''):<lang j> R =: <@:(0&".);._2 ];._2 noun define
1 1 2
1 1 3
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machin&> R
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1</lang>
'''Example''' (''counterexample''):<lang j> counterExample=. 12944 (<_1;_1)} >{:R
'''Notes''': The function <tt>machin</tt> compares the results of each formula to π/4 (expressed as <tt>1r4p1</tt> in J's numeric notation). The last expression above shows the results of these comparisons for each formula (with 1 for true and 0 for false). In J, arctan is expressed as <tt>3 o. ''values''</tt> and the function <tt>x:</tt> coerces values to extended precision; J maintains this precision as far as possible.▼
counterExample NB. Same as final test case with 12943 incremented to 12944
88 1 172
51 1 239
32 1 682
44 1 5357
68 1 12944
machin counterExample
0</lang>
▲'''Notes''': The function <tt>machin</tt> compares the results of each formula to π/4 (expressed as <tt>1r4p1</tt> in J's numeric notation). The
=={{header|OCaml}}==
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