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    double cr = begin.real();
    double ci = begin.imag();
    double ci2 = ci*ci;

    //Quick rejection check if c is in 2nd order period bulb
     if( (cr+1.0) * (cr+1.0) + ci2 < 0.0625) return -1;

     //Quick rejection check if c is in main cardioid
     double q = (cr-0.25)*(cr-0.25) + ci2;
     if( q*(q+(cr-0.25)) < 0.25*ci2) return -1;


     // test for the smaller bulb left of the period-2 bulb
     if (( ((cr+1.309)*(cr+1.309)) + ci*ci) < 0.00345) return -1;

     // check for the smaller bulbs on top and bottom of the cardioid
     if ((((cr+0.125)*(cr+0.125)) + (ci-0.744)*(ci-0.744)) < 0.0088) return -1;
     if ((((cr+0.125)*(cr+0.125)) + (ci+0.744)*(ci+0.744)) < 0.0088) return -1;

IF(((ABS(c - CMPLX(-1,0) )) < 0.25) .OR. ((ABS( 1.0 - SQRT(1-(4*c)) ))  < 1.0 ) ) THEN