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\[\left(0.5\right) \cdot \left(\sqrt{\left(\left(2.0\right) \cdot \left(\frac{\left(\sqrt{\left(\frac{\left(re \cdot re\right)}{\left(im \cdot im\right)}\right)}\right)}{re}\right)\right)}\right)\]
\left(0.5\right) \cdot \left(\sqrt{\left(\left(2.0\right) \cdot \left(\frac{\left(\sqrt{\left(\frac{\left(re \cdot re\right)}{\left(im \cdot im\right)}\right)}\right)}{re}\right)\right)}\right)
double f(double re, double im) {
        double r11933 = 0.5;
        double r11934 = /* ERROR: no posit support in C */;
        double r11935 = 2.0;
        double r11936 = /* ERROR: no posit support in C */;
        double r11937 = re;
        double r11938 = r11937 * r11937;
        double r11939 = im;
        double r11940 = r11939 * r11939;
        double r11941 = r11938 + r11940;
        double r11942 = sqrt(r11941);
        double r11943 = r11942 + r11937;
        double r11944 = r11936 * r11943;
        double r11945 = sqrt(r11944);
        double r11946 = r11934 * r11945;
        return r11946;
}

Reproduce

herbie shell --seed 2019138 
(FPCore (re im)
  :name "math.sqrt on complex, real part"
  (*.p16 (real->posit16 0.5) (sqrt.p16 (*.p16 (real->posit16 2.0) (+.p16 (sqrt.p16 (+.p16 (*.p16 re re) (*.p16 im im))) re)))))