\[0.5 \cdot \sqrt{2 \cdot \left(\sqrt{re \cdot re + im \cdot im} + re\right)}\]
0.5 \cdot \sqrt{2 \cdot \left(\sqrt{re \cdot re + im \cdot im} + re\right)}
double f(double re, double im) {
        double r8949 = 0.5;
        double r8950 = 2.0;
        double r8951 = re;
        double r8952 = r8951 * r8951;
        double r8953 = im;
        double r8954 = r8953 * r8953;
        double r8955 = r8952 + r8954;
        double r8956 = sqrt(r8955);
        double r8957 = r8956 + r8951;
        double r8958 = r8950 * r8957;
        double r8959 = sqrt(r8958);
        double r8960 = r8949 * r8959;
        return r8960;
}

Reproduce

Please include this information when filing a bug report:

herbie shell --seed 2019173 +o rules:numerics
(FPCore (re im)
  :name "math.sqrt on complex, real part"

  :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

atab-pick-alt: contract violation expected: alt? given: '(#<alt (λ (re im) (* 0.5 (sqrt (* (+ (hypot re im) re) 2.0))))>) in: the range of the #:picking-func argument of (-> alt-table? #:only-fresh boolean? #:picking-func (-> (listof alt?) alt?) (values alt? alt-table?)) contract from: /data/pavpan/nightlies/herbie/no-costs-2/src/core/alt-table.rkt blaming: /data/pavpan/nightlies/herbie/no-costs-2/src/mainloop.rkt (assuming the contract is correct) at: /data/pavpan/nightlies/herbie/no-costs-2/src/core/alt-table.rkt:13.3LC
raise-blame-error16/opt/racket-7.0/collects/racket/contract/private/blame.rkt3470
(unnamed)/data/pavpan/nightlies/herbie/no-costs-2/src/core/alt-table.rkt590
(unnamed)/opt/racket-7.0/collects/racket/contract/private/arrow-val-first.rkt38818
choose-best-alt!/data/pavpan/nightlies/herbie/no-costs-2/src/mainloop.rkt1100
run-iter!/data/pavpan/nightlies/herbie/no-costs-2/src/mainloop.rkt3190
for-loop/data/pavpan/nightlies/herbie/no-costs-2/src/mainloop.rkt3534
run-improve43/data/pavpan/nightlies/herbie/no-costs-2/src/mainloop.rkt3380
(unnamed)/opt/racket-7.0/collects/racket/private/more-scheme.rkt26128
run/opt/racket-7.0/share/pkgs/profile-lib/main.rkt392
profile-thunk16/opt/racket-7.0/share/pkgs/profile-lib/main.rkt90
(unnamed)/opt/racket-7.0/collects/racket/private/more-scheme.rkt26128