<?
function theta($n) {
    return $n >= 1 ? 1 : 0;
}

function sgn($n) {
    switch (true) {
        case $n > 0: return 1;
        case $n < 0: return -1;
        default: return 0;
    }
}

function x($t) {
    return ((-25/37*sin(58/37-4*$t)+809/54*sin($t+11/7)+9/19*sin(2*$t+108/23)+17/23*sin(3*$t+49/31)+11/12*sin(5*$t+107/68)-17/27)*
    theta(71*M_PI-$t)*theta($t-67*M_PI)+(-6/49*sin(39/25-8*$t)-3/32*sin(39/25-7*$t)-2/11*
    sin(64/41-6*$t)-107/68*sin(36/23-2*$t)-228/31*sin(69/44-$t)+17/36*sin(3*$t+11/7)+11/49*sin(4*$t+113/24)+1/63*
    sin(5*$t+29/19)+1091/31)*theta(67*M_PI-$t)*theta($t-63*M_PI)+(35/8*sin($t+11/7)+15/23*sin(2*$t+52/33)+11/30*
    sin(3*$t+11/7)+1/18*sin(4*$t+63/40)-556/17)*theta(63*M_PI-$t)*theta($t-59*M_PI)+(-104/31*sin(27/41-2*$t)+523/45*
    sin($t+29/25)+40/37*sin(3*$t+25/41)+21/17*sin(4*$t+121/26)+148/27)*theta(59*M_PI-$t)*theta($t-55*M_PI)+(-9/20*sin(13/11-18*
    $t)-9/26*sin(88/63-17*$t)-15/41*sin(81/161-15*$t)-7/15*sin(25/18-14*$t)-59/89*sin(13/34-12*$t)-87/38*sin(9/10-6*$t)-117/22*
    sin(23/42-5*$t)+582/13*sin($t+64/37)+88/25*sin(2*$t+229/49)+1458/47*sin(3*$t+48/23)+167/50*sin(4*$t+151/50)+135/22*
    sin(7*$t+93/32)+143/102*sin(8*$t+100/33)+2/21*sin(9*$t+169/47)+41/124*sin(10*$t+84/19)+7/39*sin(11*$t+147/73)+15/17*
    sin(13*$t+69/17)+6/29*sin(16*$t+2/25)+7/43*sin(19*$t+57/16)+5/36*sin(20*$t+20/53)+225/41)*theta(55*M_PI-$t)*
    theta($t-51*M_PI)+(-22/27*sin(21/19-33*$t)-23/28*sin(56/75-32*$t)-9/14*sin(18/29-31*$t)-32/33*sin(145/109-29*$t)-11/23*
    sin(27/38-28*$t)-91/114*sin(26/31-26*$t)-47/40*sin(73/55-24*$t)-54/53*sin(8/21-21*$t)-38/25*sin(65/43-19*$t)-108/65*
    sin(11/17-14*$t)-11/27*sin(289/193-9*$t)+3415/31*sin($t+65/34)+916/35*sin(2*$t+168/41)+85/16*sin(3*$t+37/41)+92/35*
    sin(4*$t+107/32)+107/27*sin(5*$t+14/31)+47/25*sin(6*$t+7/11)+35/12*sin(7*$t+49/26)+26/23*sin(8*$t+82/21)+48/25*
    sin(10*$t+26/103)+35/38*sin(11*$t+23/32)+15/22*sin(12*$t+160/41)+285/286*sin(13*$t+3/38)+8/19*sin(15*$t+336/79)+48/31*
    sin(16*$t+10/3)+122/87*sin(17*$t+37/23)+68/31*sin(18*$t+1/27)+11/9*sin(20*$t+58/21)+49/44*sin(22*$t+4)+22/29*
    sin(23*$t+68/53)+1/2*sin(25*$t+86/23)+17/37*sin(27*$t+148/33)+21/29*sin(30*$t+137/30)+12/29*sin(34*$t+202/47)+15/34*
    sin(35*$t+10/29)+861/37)*theta(51*M_PI-$t)*theta($t-47*M_PI)+(-5/13*sin(9/14-8*$t)-33/25*sin(105/106-6*$t)-12/61*
    sin(47/46-5*$t)-17/35*sin(6/11-4*$t)-617/35*sin(58/41-2*$t)+97/24*sin($t+49/11)+93/43*sin(3*$t+53/24)+52/69*
    sin(7*$t+19/8)+16/31)*theta(47*M_PI-$t)*theta($t-43*M_PI)+(-10/31*sin(55/39-6*$t)+708/23*sin($t+53/28)+10/17*
    sin(2*$t+303/70)+201/200*sin(3*$t+275/92)+8/15*sin(4*$t+129/29)+2/23*sin(5*$t+110/41)+18/89*sin(7*$t+73/30)+949/15)*
    theta(43*M_PI-$t)*theta($t-39*M_PI)+(-22/41*sin(42/41-5*$t)-9/19*sin(11/31-3*$t)+1168/41*sin($t+59/37)+13/21*
    sin(2*$t+382/83)+15/29*sin(4*$t+105/29)+7/17*sin(6*$t+67/19)-2875/47)*theta(39*M_PI-$t)*theta($t-35*M_PI)+(-15/19*sin(1/26-
    14*$t)-111/31*sin(7/31-4*$t)+3698/39*sin($t+31/20)+135/22*sin(2*$t+1/35)+136/11*sin(3*$t+71/46)+57/13*sin(5*$t+29/19)+22/25*
    sin(6*$t+80/31)+29/40*sin(7*$t+212/47)+31/26*sin(8*$t+1/31)+55/27*sin(9*$t+51/29)+46/31*sin(10*$t+3/23)+27/29*
    sin(11*$t+48/47)+5/21*sin(12*$t+49/24)+23/40*sin(13*$t+11/9)+13/59*sin(15*$t+26/37)-15/16)*theta(35*M_PI-$t)*theta($t-31*M_PI)+
    (53/32*sin($t+54/37)+267/26*sin(2*$t+239/92)+35/33*sin(3*$t+13/34)+8/9*sin(4*$t+19/25)+7/15*sin(5*$t+17/16)+3/5*
    sin(6*$t+57/22)+15/52*sin(7*$t+27/22)+15/49*sin(8*$t+28/23)+2/17*sin(9*$t+180/77)+3/38*sin(10*$t+64/35)+5/34*
    sin(11*$t+35/24)+3/31*sin(12*$t+21/22)-5662/43)*theta(31*M_PI-$t)*theta($t-27*M_PI)+(-6/25*sin(12/47-9*$t)+77/36*
    sin($t+159/35)+114/11*sin(2*$t+37/8)+13/19*sin(3*$t+77/41)+11/27*sin(4*$t+128/71)+6/11*sin(5*$t+191/52)+96/193*
    sin(6*$t+19/11)+3/17*sin(7*$t+7/4)+3/17*sin(8*$t+6/7)+3/20*sin(10*$t+31/43)+4078/31)*theta(27*M_PI-$t)*theta($t-23*M_PI)+
    (-21/64*sin(2/21-7*$t)-35/58*sin(29/33-6*$t)-5/26*sin(13/19-5*$t)+3153/26*sin($t+29/19)+35/27*sin(2*$t+67/23)+19/9*
    sin(3*$t+32/7)+3/14*sin(4*$t+19/18)-12/7)*theta(23*M_PI-$t)*theta($t-19*M_PI)+(-19/30*sin(19/24-16*$t)-10/23*sin(41/27-15*$t)-
    66/67*sin(17/21-14*$t)-43/42*sin(1/64-13*$t)-41/19*sin(16/33-8*$t)+28281/404*sin($t+114/31)+756/43*sin(2*$t+904/201)+817/41*
    sin(3*$t+25/32)+371/43*sin(4*$t+208/45)+80/21*sin(5*$t+68/37)+139/52*sin(6*$t+31/7)+160/61*sin(7*$t+69/43)+37/31*sin(9*$t+
    128/43)+33/67*sin(10*$t+14/17)+11/12*sin(11*$t+9/4)+13/33*sin(12*$t+69/59)+9/44*sin(17*$t+96/61)+17/36*sin(18*$t+1/40)+5/17*
    sin(19*$t+83/104)+5/18*sin(20*$t+7/10)+23/57*sin(21*$t+91/29)+5/37*sin(22*$t+5/3)+11/30*sin(23*$t+177/62)+2/21*sin(24*$t+
    63/17)+9/41*sin(25*$t+111/28)+4/33*sin(26*$t+159/44)+7/29*sin(27*$t+75/28)+2/9*sin(28*$t+134/89)+3/20*sin(29*$t+80/43)+1/20*
    sin(30*$t+71/30)+4/29*sin(31*$t+137/76)+1/53*sin(32*$t+34/29)+5/33*sin(33*$t+12/5)+4/27*sin(34*$t+7/23)+2/29*sin(35*$t+28/13)+
    2302/41)*theta(19*M_PI-$t)*theta($t-15*M_PI)+(-20/29*sin(3/25-11*$t)-53/25*sin(17/16-7*$t)-293/21*sin(17/37-5*$t)-853/43*
    sin(107/71-3*$t)+2467/29*sin($t+13/10)+307/9*sin(2*$t+85/41)+443/28*sin(4*$t+41/24)+127/27*sin(6*$t+181/41)+79/33*
    sin(8*$t+74/19)+173/69*sin(9*$t+341/146)+17/21*sin(10*$t+152/45)+41/31*sin(12*$t+110/29)+36/107*sin(13*$t+55/14)+27/34*
    sin(14*$t+41/12)+49/30*sin(15*$t+26/15)+5/4*sin(16*$t+8/15)+13/20*sin(17*$t+67/46)+11/12*sin(18*$t+31/37)+47/53*
    sin(19*$t+30/19)+35/36*sin(20*$t+21/19)+29/37*sin(21*$t+47/39)+23/30*sin(22*$t+32/23)+29/38*sin(23*$t+66/31)+7/11*
    sin(24*$t+42/37)+5/27*sin(25*$t+211/49)+5/23*sin(26*$t+141/49)+1/6*sin(27*$t+113/25)+11/37*sin(28*$t+152/83)+10/29*sin(29*
    $t+22/39)+14/69*sin(30*$t+17/22)+3/41*sin(31*$t+51/31)+7/23*sin(32*$t+61/28)+7/39*sin(33*$t+38/15)+5/19*sin(34*$t+47/18)+
    1/10*sin(35*$t+26/37)+5/24*sin(36*$t+171/41)-2471/81)*theta(15*M_PI-$t)*theta($t-11*M_PI)+(-9/41*sin(27/25-14*$t)-9/16*
    sin(67/46-12*$t)-63/125*sin(26/21-10*$t)-4/23*sin(16/43-9*$t)-5/13*sin(11/34-8*$t)+319/6*sin($t+26/21)+51/28*sin(2*$t+58/21)+
    353/39*sin(3*$t+17/20)+23/16*sin(4*$t+9/35)+7/2*sin(5*$t+101/67)+31/29*sin(6*$t+19/33)+2/23*sin(7*$t+92/33)+7/23*sin(11*$t+
    31/52)+4/37*sin(13*$t+135/47)+2/29*sin(15*$t+206/55)+2534/25)*theta(11*M_PI-$t)*theta($t-7*M_PI)+(-125/29*sin(53/36-4*$t)-
    845/12*sin(5/29-$t)+127/18*sin(2*$t+87/44)+334/35*sin(3*$t+61/31)+3/8*sin(5*$t+95/22)+27/14*sin(6*$t+39/32)+8/9*sin(7*$t+27/11)+
    14/9*sin(8*$t+131/36)-4169/40)*theta(7*M_PI-$t)*theta($t-3*M_PI)+(-17/31*sin(3/16-42*$t)-7/20*sin(19/22-39*$t)-12/31*sin(48/37-
    38*$t)-17/38*sin(38/61-26*$t)-50/29*sin(203/204-25*$t)-125/42*sin(1/21-20*$t)-34/31*sin(28/33-19*$t)-317/32*sin(4/11-10*$t)-
    277/33*sin(53/40-9*$t)+2468/19*sin($t+12/25)+1180/21*sin(2*$t+142/33)+1501/28*sin(3*$t+41/27)+281/39*sin(4*$t+41/29)+452/37*
    sin(5*$t+115/57)+725/49*sin(6*$t+184/67)+591/52*sin(7*$t+52/29)+289/25*sin(8*$t+141/53)+107/27*sin(11*$t+3/10)+281/46*sin(12*$t+
    104/33)+27/8*sin(13*$t+108/35)+15/23*sin(14*$t+43/18)+27/25*sin(15*$t+10/21)+73/34*sin(16*$t+99/35)+349/350*sin(17*$t+48/23)+18/
    19*sin(18*$t+137/68)+11/16*sin(21*$t+14/41)+28/17*sin(22*$t+85/22)+33/53*sin(23*$t+4/3)+21/32*sin(24*$t+7/3)+91/40*sin(27*$t+
    103/27)+10/7*sin(28*$t+58/13)+62/35*sin(29*$t+49/25)+41/29*sin(30*$t+87/35)+27/29*sin(31*$t+13/37)+8/17*sin(32*$t+49/48)+14/
    23*sin(33*$t+101/31)+2/25*sin(34*$t+26/33)+17/30*sin(35*$t+101/41)+11/38*sin(36*$t+2/33)+73/97*sin(37*$t+28/31)+11/27*sin(40*$t+
    167/111)+11/43*sin(41*$t+69/19)+1/37*sin(43*$t+43/38)+19/43*sin(44*$t+71/17)+10/23*sin(45*$t+38/9)-371/61)*theta(3*M_PI-$t)*
    theta($t+M_PI))*theta(sqrt(sgn(sin($t/2))));
}

function y($t) {
    return ((16/35*sin($t+11/7)+56/27*sin(2*$t+96/61)+22/27*sin(3*$t+52/33)+74/47*sin(4*$t+52/33)+13/32*sin(5*$t+67/42)+4093/22)*
    theta(71*M_PI-$t)*theta($t-67*M_PI)+(-3/32*sin(61/39-8*$t)+341/32*sin($t+11/7)+11/14*sin(2*$t+47/10)+23/12*sin(3*$t+52/33)+
    3/20*sin(4*$t+53/33)+58/117*sin(5*$t+52/33)+3/38*sin(6*$t+61/13)+8/41*sin(7*$t+58/37)+3055/19)*theta(67*M_PI-$t)*theta($t-63*M_PI)+
    (111/10*sin($t+11/7)+10/29*sin(2*$t+202/43)+67/50*sin(3*$t+11/7)+1/32*sin(4*$t+639/137)+5035/31)*theta(63*M_PI-$t)*theta($t-59*M_PI)+
    (-35/71*sin(4/17-4*$t)-35/34*sin(53/52-3*$t)+175/36*sin($t+123/44)+83/27*sin(2*$t+133/32)+13847/111)*theta(59*M_PI-$t)*theta($t-55*
    M_PI)+(-38/39*sin(19/14-17*$t)-13/27*sin(31/22-16*$t)-49/39*sin(31/33-13*$t)-55/56*sin(4/3-11*$t)-76/51*sin(6/29-8*$t)+127/35*
    sin($t+190/67)+1061/78*sin(2*$t+61/33)+953/143*sin(3*$t+53/16)+48/29*sin(4*$t+33/20)+127/26*sin(5*$t+317/72)+281/36*sin(6*$t+107/
    39)+48/35*sin(7*$t+41/12)+1/8*sin(9*$t+3/34)+380/381*sin(10*$t+47/26)+27/31*sin(12*$t+86/35)+11/32*sin(14*$t+10/19)+15/22*sin(15*$t+
    11/27)+2/3*sin(18*$t+17/8)+2/29*sin(19*$t+181/40)+5/27*sin(20*$t+20/13)-14371/74)*theta(55*M_PI-$t)*theta($t-51*M_PI)+(-14/27*
    sin(31/23-35*$t)-9/17*sin(23/28-34*$t)-5/14*sin(18/13-28*$t)-9/23*sin(11/20-27*$t)-14/29*sin(33/46-26*$t)-59/24*sin(44/31-17*$t)-
    137/73*sin(15/22-16*$t)-7/23*sin(7/5-12*$t)-137/73*sin(11/19-10*$t)-44/31*sin(2/33-9*$t)-2708/65*sin(16/21-2*$t)-818/31*sin(29/33-
    $t)+435/22*sin(3*$t+21/20)+113/24*sin(4*$t+124/27)+641/95*sin(5*$t+51/31)+61/15*sin(6*$t+39/11)+303/76*sin(7*$t+275/118)+140/29*
    sin(8*$t+127/29)+51/28*sin(11*$t+50/29)+43/40*sin(13*$t+67/43)+59/46*sin(14*$t+173/99)+67/35*sin(15*$t+31/24)+45/22*sin(18*$t+67/
    16)+24/19*sin(19*$t+20/9)+3/17*sin(20*$t+44/27)+18/31*sin(21*$t+49/34)+37/62*sin(22*$t+11/15)+13/31*sin(23*$t+115/67)+16/37*sin(24*
    $t+22/7)+4/35*sin(25*$t+26/33)+4/43*sin(29*$t+79/17)+11/37*sin(30*$t+383/85)+8/35*sin(31*$t+259/97)+9/20*sin(32*$t+27/10)+22/37*
    sin(33*$t+26/15)+5589/19)*theta(51*M_PI-$t)*theta($t-47*M_PI)+(-101/30*sin(23/15-3*$t)+177/19*sin($t+63/38)+73/19*sin(2*$t+58/15)+
    50/33*sin(4*$t+51/14)+5/17*sin(5*$t+541/135)+29/35*sin(6*$t+125/29)+31/52*sin(7*$t+181/41)+7/12*sin(8*$t+122/35)+3986/25)*theta(47*
    M_PI-$t)*theta($t-43*M_PI)+(-2/25*sin(13/34-7*$t)-3/26*sin(9/8-4*$t)+430/17*sin($t+6/31)+24/37*sin(2*$t+137/35)+50/37*sin(3*$t+
    26/23)+4/45*sin(5*$t+268/161)+7/20*sin(6*$t+19/6)+8835/43)*theta(43*M_PI-$t)*theta($t-39*M_PI)+(-11/50*sin(46/55-5*$t)+345/13*
    sin($t+1/10)+67/41*sin(2*$t+90/29)+5/2*sin(3*$t+2/19)+39/79*sin(4*$t+565/141)+23/42*sin(6*$t+67/22)+6008/29)*theta(39*M_PI-$t)*
    theta($t-35*M_PI)+(-21/53*sin(74/73-15*$t)-15/22*sin(78/67-14*$t)-291/104*sin(1/14-7*$t)-4561/456*sin(2/17-$t)+107/44*sin(2*$t+
    46/29)+45/22*sin(3*$t+128/51)+553/32*sin(4*$t+144/31)+25/16*sin(5*$t+127/37)+53/30*sin(6*$t+129/29)+1/11*sin(8*$t+60/31)+36/23*
    sin(9*$t+107/42)+61/37*sin(10*$t+141/32)+26/25*sin(11*$t+13/45)+7/23*sin(12*$t+64/51)+6/23*sin(13*$t+113/45)+7673/35)*theta(35*
    M_PI-$t)*theta($t-31*M_PI)+(-4/27*sin(12/17-12*$t)-4/15*sin(35/44-10*$t)-5/31*sin(4/37-8*$t)-10/39*sin(43/65-6*$t)+493/19*sin($t+
    239/54)+7/13*sin(2*$t+125/48)+65/16*sin(3*$t+95/23)+16/39*sin(4*$t+15/41)+5/14*sin(5*$t+77/31)+54/163*sin(7*$t+181/45)+9/55*sin(9*
    $t+47/19)+4/47*sin(11*$t+126/29)+7332/43)*theta(31*M_PI-$t)*theta($t-27*M_PI)+(-30/91*sin(3/16-7*$t)-20/79*sin(37/28-5*$t)+247/11*
    sin($t+88/23)+23/17*sin(2*$t+140/37)+461/123*sin(3*$t+55/26)+16/31*sin(4*$t+36/11)+50/149*sin(6*$t+55/54)+3/34*sin(8*$t+212/77)+
    9/43*sin(9*$t+1/25)+5/33*sin(10*$t+107/35)+1817/11)*theta(27*M_PI-$t)*theta($t-23*M_PI)+(-14/29*sin(99/85-6*$t)-1/20*sin(14/15-3*
    $t)-4823/38*sin(1/17-$t)+37/31*sin(2*$t+101/27)+212/213*sin(4*$t+25/17)+14/37*sin(5*$t+119/53)+15/44*sin(7*$t+13/51)+6158/33)*
    theta(23*M_PI-$t)*theta($t-19*M_PI)+(-5/31*sin(83/82-35*$t)-3/26*sin(51/35-33*$t)-4/33*sin(22/51-31*$t)-5/22*sin(10/23-29*$t)-31/
    61*sin(4/21-17*$t)-222/35*sin(21/19-5*$t)+2486/43*sin($t+78/17)+684/31*sin(2*$t+17/20)+411/32*sin(3*$t+49/17)+5/41*sin(4*$t+4/27)+
    61/13*sin(6*$t+113/25)+48/25*sin(7*$t+39/35)+206/61*sin(8*$t+5/23)+11/24*sin(9*$t+23/36)+107/106*sin(10*$t+5/3)+67/33*sin(11*$t+51/
    23)+41/17*sin(12*$t+53/25)+117/34*sin(13*$t+50/29)+81/28*sin(14*$t+29/28)+43/27*sin(15*$t+25/56)+32/37*sin(16*$t+5/26)+10/27*
    sin(18*$t+158/43)+34/61*sin(19*$t+37/21)+24/49*sin(20*$t+31/27)+1/4*sin(21*$t+132/79)+11/38*sin(22*$t+37/30)+8/31*sin(23*$t+
    119/26)+5/18*sin(24*$t+109/34)+4/19*sin(25*$t+8/25)+3/23*sin(26*$t+25/21)+7/27*sin(27*$t+2/19)+4/23*sin(28*$t+43/25)+19/75*
    sin(30*$t+43/14)+8/63*sin(32*$t+109/24)+1/60*sin(34*$t+23/42)-615/34)*theta(19*M_PI-$t)*theta($t-15*M_PI)+(-1/23*sin(8/13-33*
    $t)-6/19*sin(337/336-28*$t)-1/34*sin(13/34-27*$t)-11/16*sin(9/11-24*$t)-49/74*sin(34/29-23*$t)-41/36*sin(77/78-22*$t)-35/27*
    sin(91/92-21*$t)-40/27*sin(57/43-19*$t)-1/2*sin(6/49-14*$t)-31/34*sin(39/29-11*$t)-27/14*sin(53/37-5*$t)-79/7*sin(9/29-4*$t)-
    597/20*sin(11/21-$t)+823/33*sin(2*$t+35/29)+281/17*sin(3*$t+170/43)+1805/258*sin(6*$t+65/21)+293/55*sin(7*$t+102/47)+323/108*
    sin(8*$t+5/6)+20/11*sin(9*$t+196/43)+27/29*sin(10*$t+89/21)+21/8*sin(12*$t+29/22)+103/49*sin(13*$t+32/53)+27/25*sin(15*$t+83/34)+
    18/25*sin(16*$t+91/31)+55/39*sin(17*$t+167/40)+233/232*sin(18*$t+99/23)+29/24*sin(20*$t+51/11)+9/20*sin(25*$t+142/31)+2/29*
    sin(26*$t+85/28)+9/40*sin(29*$t+73/18)+5/27*sin(30*$t+47/13)+2/7*sin(31*$t+31/11)+7/26*sin(32*$t+53/32)+22/87*sin(34*$t+93/26)+
    5/46*sin(35*$t+233/70)+3/22*sin(36*$t+87/19)+346/27)*theta(15*M_PI-$t)*theta($t-11*M_PI)+(-3/35*sin(41/28-14*$t)-14/33*sin(40/
    53-9*$t)-38/51*sin(41/47-7*$t)-91/11*sin(8/13-3*$t)-2058/25*sin(44/35-$t)+26/29*sin(2*$t+23/9)+41/31*sin(4*$t+41/62)+5/4*
    sin(5*$t+1/18)+87/88*sin(6*$t+69/53)+17/39*sin(8*$t+74/35)+33/98*sin(10*$t+113/31)+8/29*sin(11*$t+1/176)+17/47*sin(12*$t+64/15)+
    2/15*sin(13*$t+208/83)+3/26*sin(15*$t+48/17)-3394/23)*theta(11*M_PI-$t)*theta($t-7*M_PI)+(-27/37*sin(37/34-7*$t)-29/8*sin(3/16-
    4*$t)-77/13*sin(3/31-3*$t)-3113/38*sin(44/45-$t)+96/11*sin(2*$t+159/38)+49/82*sin(5*$t+21/8)+73/37*sin(6*$t+25/27)+31/33*
    sin(8*$t+59/26)-3567/28)*theta(7*M_PI-$t)*theta($t-3*M_PI)+(-11/36*sin(40/27-45*$t)-9/19*sin(14/31-41*$t)-10/27*sin(31/26-33*$t)-
    8/11*sin(31/24-31*$t)-13/10*sin(13/48-29*$t)-66/25*sin(48/43-23*$t)-29/14*sin(53/66-19*$t)-129/34*sin(2/31-14*$t)-77/46*
    sin(15/22-13*$t)-47/41*sin(4/15-12*$t)-393/38*sin(24/31-7*$t)+3862/51*sin($t+146/31)+1101/8*sin(2*$t+78/29)+329/22*sin(3*$t+67/26)
    +246/25*sin(4*$t+32/13)+596/49*sin(5*$t+101/32)+41/10*sin(6*$t+31/18)+287/45*sin(8*$t+27/35)+172/29*sin(9*$t+66/19)+311/40*
    sin(10*$t+143/37)+97/20*sin(11*$t+56/29)+160/39*sin(15*$t+377/94)+77/25*sin(16*$t+31/30)+74/25*sin(17*$t+47/17)+15/14*
    sin(18*$t+113/35)+37/20*sin(20*$t+23/29)+24/47*sin(21*$t+74/27)+28/41*sin(22*$t+135/32)+19/20*sin(24*$t+199/149)+33/67*
    sin(25*$t+148/43)+47/36*sin(26*$t+55/28)+13/10*sin(27*$t+71/33)+19/17*sin(28*$t+47/11)+25/27*sin(30*$t+35/39)+5/18*sin(32*$t+6/23)+
    11/29*sin(34*$t+59/19)+23/33*sin(35*$t+173/72)+16/31*sin(36*$t+67/19)+9/31*sin(37*$t+6/29)+7/25*sin(38*$t+25/12)+19/31*sin(39*
    $t+135/29)+21/53*sin(40*$t+21/34)+1/14*sin(42*$t+24/13)+17/32*sin(43*$t+35/34)+27/43*sin(44*$t+107/31)-9223/25)*theta(3*M_PI-$t)*
    theta($t+M_PI))*theta(sqrt(sgn(sin($t/2))));
}

$limit     = M_PI*72;
$padding   = 10;
$zoom      = .5;
$step      = 0.005;

$im    = imagecreate($padding + 420 * $zoom, $padding + 940 * $zoom);
$black = imagecolorallocate($im, 0, 0, 0);
$white = imagecolorallocate($im, 255, 255, 255);

imagefill($im, 0, 0, $black);

for ($t = 0; $t<$limit; $t+=$step) {
    $x = (x($t) + 206) * $zoom + $padding;
    $y = (344 - y($t)) * $zoom + $padding;
    imagesetpixel($im, $x, $y, $white);
}

imagepng($im, 'out.png', 9);