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Check Machin-like formulas: Difference between revisions
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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 first example 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; thereafter J will maintain extended precision throughout its calculations, as long as it can.
=={{header|Mathematica}}==
<lang>Tan[ArcTan[1/2] + ArcTan[1/3]] == 1
Tan[2 ArcTan[1/3] + ArcTan[1/7]] == 1
Tan[4 ArcTan[1/5] - ArcTan[1/239]] == 1
Tan[5 ArcTan[1/7] + 2 ArcTan[3/79]] == 1
Tan[5 ArcTan[29/278] + 7 ArcTan[3/79]] == 1
Tan[ArcTan[1/2] + ArcTan[1/5] + ArcTan[1/8]] == 1
Tan[4 ArcTan[1/5] - ArcTan[1/70] + ArcTan[1/99]] == 1
Tan[5 ArcTan[1/7] + 4 ArcTan[1/53] + 2 ArcTan[1/4443]] == 1
Tan[6 ArcTan[1/8] + 2 ArcTan[1/57] + ArcTan[1/239]] == 1
Tan[8 ArcTan[1/10] - ArcTan[1/239] - 4 ArcTan[1/515]] == 1
Tan[12 ArcTan[1/18] + 8 ArcTan[1/57] - 5 ArcTan[1/239]] == 1
Tan[16 ArcTan[1/21] + 3 ArcTan[1/239] + 4 ArcTan[3/1042]] == 1
Tan[22 ArcTan[1/28] + 2 ArcTan[1/443] - 5 ArcTan[1/1393] -
10 ArcTan[1/11018]] == 1
Tan[22 ArcTan[1/38] + 17 ArcTan[7/601] + 10 ArcTan[7/8149]] == 1
Tan[44 ArcTan[1/57] + 7 ArcTan[1/239] - 12 ArcTan[1/682] +
24 ArcTan[1/12943]] == 1
Tan[88 ArcTan[1/172] + 51 ArcTan[1/239] + 32 ArcTan[1/682] +
44 ArcTan[1/5357] + 68 ArcTan[1/12943]] == 1
Tan[88 ArcTan[1/172] + 51 ArcTan[1/239] + 32 ArcTan[1/682] +
44 ArcTan[1/5357] + 68 ArcTan[1/12944]] == 1</lang>
{{Out}}
<pre>True
True
True
True
True
True
True
True
True
True
True
True
True
True
True
True
False</pre>
=={{header|Maxima}}==
<lang maxima>trigexpand:true$
is(tan(atan(1/2)+atan(1/3))=1);
is(tan(2*atan(1/3)+atan(1/7))=1);
is(tan(4*atan(1/5)-atan(1/239))=1);
is(tan(5*atan(1/7)+2*atan(3/79))=1);
is(tan(5*atan(29/278)+7*atan(3/79))=1);
is(tan(atan(1/2)+atan(1/5)+atan(1/8))=1);
is(tan(4*atan(1/5)-atan(1/70)+atan(1/99))=1);
is(tan(5*atan(1/7)+4*atan(1/53)+2*atan(1/4443))=1);
is(tan(6*atan(1/8)+2*atan(1/57)+atan(1/239))=1);
is(tan(8*atan(1/10)-atan(1/239)-4*atan(1/515))=1);
is(tan(12*atan(1/18)+8*atan(1/57)-5*atan(1/239))=1);
is(tan(16*atan(1/21)+3*atan(1/239)+4*atan(3/1042))=1);
is(tan(22*atan(1/28)+2*atan(1/443)-5*atan(1/1393)-10*atan(1/11018))=1);
is(tan(22*atan(1/38)+17*atan(7/601)+10*atan(7/8149))=1);
is(tan(44*atan(1/57)+7*atan(1/239)-12*atan(1/682)+24*atan(1/12943))=1);
is(tan(88*atan(1/172)+51*atan(1/239)+32*atan(1/682)+44*atan(1/5357)+68*atan(1/12943))=1);
is(tan(88*atan(1/172)+51*atan(1/239)+32*atan(1/682)+44*atan(1/5357)+68*atan(1/12944))=1);</lang>
{{out}}
<pre>(%i2)
(%o2) true
(%i3)
(%o3) true
(%i4)
(%o4) true
(%i5)
(%o5) true
(%i6)
(%o6) true
(%i7)
(%o7) true
(%i8)
(%o8) true
(%i9)
(%o9) true
(%i10)
(%o10) true
(%i11)
(%o11) true
(%i12)
(%o12) true
(%i13)
(%o13) true
(%i14)
(%o14) true
(%i15)
(%o15) true
(%i16)
(%o16) true
(%i17)
(%o17) true
(%i18)
(%o18) false</pre>
=={{header|OCaml}}==
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