According to the formula writer this formula is a newton mandelbrot mash-up.
Regular bailouts, inverse bailouts it can be so confusing at times.
Pre-rendered at the usual http://maxitersfractalfollies.blogspot.com
And finally welcome back Paul, keeper of the FOTD!

Newtonish Mandelbrot      { ;fract515.gif a minibrot
                     ; blank
                     ; calctime   0:34:08.17
                     ; created Nov 13, 2010
                     ;  Fractint Version 2004 Patchlevel 10
  reset=2004 type=formula formulafile=_m.frm formulaname=man-newt-man
  center-mag=-0.78353162878688400/+0.06835193132850351/2185.907/1/44.99999\
  99999986215/-4.14705769724577067e-012 params=0/0 float=y
  maxiter=1500 inside=0 logmap=42
  colors=0Sm000000000000000000000000000000100100200400500700900B00D00G00I0\
  0L00O10Q10T10W10Z10a10e10h20k20o20r20v20y20z30z50z60z80z90zB0zC0zE0zF0zH\
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  0zq0zs0zt0zv0zw0zy0zz1zz3zz4zz6zz7zz7zy7zx7zx7zw7zv7zv7zu7yt7ys7ys7yr7yq\
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  3sK3sJ2sJ2sI2sH2sH2sG2sF2rE2rE2rD2rC2rC2rB1rA1rA1r91q81q71q71q61q51q51q4\
  1q31p20p20o20n20m20m20l20k20j20j20i20h20g20g20f20e20d20d20c20b20a20a20`2\
  0_20Z20Z20Y20X20W20W20V20U20T20T20S20R20Q20Q20P20O20N20N20M20L20K20K20J2\
  0I20H20H20G20F20E20E20E20D20D20C20C20C20B20B20A20A20A2092092092082082072\
  0720720620620520520520420420420320320220220220120120010
  }
frm:man-newt-man {; Sylvie Gallet [101324,3444], 1995 +R.B.
              ; tiny mod on original Mandel-Newton by Sylvie
              ; tweaked brainlessly by Robin Bussell
              ; to give a hybrid mandel-newton fractal
  z = pixel, c = z, iter = 1, test1 = 1
  rad = 3.1, center = (1.0,0.1)
  pix = (10*pixel+(5.0,-3.4))*(-0.1,-0.95)
  zn = center+rad/(pix-center)
  limit = real(p1), b1 = 16, b2 = 0.0001 :
  test1 = (1-test1), test2=(iter!=limit)
  z = (z-zn)*test2 + zn
  z2 = z*z, z4 = z2*z2, z1 = (z4*z-1)/(4*z4)
  z = (z2+c)*test1 + (z-z1)*(1-test1)
  iter = iter+1
  ((|z| <= b1) * test1) || ((|z1| >= b2) * (1-test1))
  ;SOURCE: forummsg.frm
}
Roger Alexander