\[0.5 \cdot \sqrt{2 \cdot \left(\sqrt{re \cdot re + im \cdot im} + re\right)} \]
0.5 \cdot \sqrt{2 \cdot \left(\sqrt{re \cdot re + im \cdot im} + re\right)}
(FPCore (re im)
 :precision binary64
 (* 0.5 (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))))
double code(double re, double im) {
	return 0.5 * sqrt(2.0 * (sqrt((re * re) + (im * im)) + re));
}

Reproduce

Please include this information when filing a bug report:

herbie shell --seed 2022118 
(FPCore (re im)
  :name "math.sqrt on complex, real part"
  :precision binary64

  :herbie-target
  (if (< re 0.0) (* 0.5 (* (sqrt 2.0) (sqrt (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))) (* 0.5 (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))))

  (* 0.5 (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))))

Backtrace

mpfr->C: argument is not non-null `mpfr' pointer argument: 0.0LC
bfzero?/opt/racket-8.1/share/pkgs/math-lib/math/private/bigfloat/mpfr.rkt7974
bigfloat->normal-string/data/pavpan/nightlies/herbie/shortest-number/src/pretty-print.rkt60
bigfloat-interval-shortest/data/pavpan/nightlies/herbie/shortest-number/src/pretty-print.rkt1000
regimes-sidx->spoint/data/pavpan/nightlies/herbie/shortest-number/src/core/regimes.rkt2572
sindices->spoints/data/pavpan/nightlies/herbie/shortest-number/src/core/regimes.rkt2160
f54.../match/compiler.rkt54040
extract!/data/pavpan/nightlies/herbie/shortest-number/src/mainloop.rkt3940
run-improve!/data/pavpan/nightlies/herbie/shortest-number/src/mainloop.rkt3260
(unnamed)/data/pavpan/nightlies/herbie/shortest-number/src/sandbox.rkt666
(unnamed)/opt/racket-8.1/share/pkgs/profile-lib/main.rkt4010
profile-thunk/opt/racket-8.1/share/pkgs/profile-lib/main.rkt90
(unnamed)/opt/racket-8.1/collects/racket/engine.rkt4224