Average Error: 38.1 → 30.7
Time: 5.6s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double re, double im) {
	return ((double) (0.5 * ((double) sqrt(((double) (2.0 * ((double) (((double) sqrt(((double) (((double) (re * re)) + ((double) (im * im)))))) + re))))))));
}

↓
double code(double re, double im) {
	double VAR;
	if ((im <= -4.7178184386274894e+157)) {
		VAR = ((double) (0.5 * ((double) sqrt(((double) (2.0 * ((double) (re + re))))))));
	} else {
		double VAR_1;
		if ((im <= -8.818158973525325e-65)) {
			VAR_1 = ((double) (0.5 * ((double) sqrt(((double) (2.0 * ((double) (((double) (im * im)) / ((double) (((double) sqrt(((double) (((double) (im * im)) + ((double) (re * re)))))) - re))))))))));
		} else {
			double VAR_2;
			if ((im <= 7.4408620014427016e-118)) {
				VAR_2 = ((double) (0.5 * ((double) sqrt(((double) (2.0 * ((double) (re + re))))))));
			} else {
				VAR_2 = ((double) (0.5 * ((double) sqrt(((double) (2.0 * ((double) (im + re))))))));
			}
			VAR_1 = VAR_2;
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error
Bits error versus re
Bits error versus im
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original38.1
Target33.4
Herbie30.7
\[\]
Derivation
  1. Split input into 3 regimes
  2. if  im  < -4.7178184386274894e157 or -8.81815897352532454e-65 <  im  < 7.44086200144270156e-118
    1. Initial program 44.9
      \[\]
    2. Taylor expanded around inf 42.7
      \[\leadsto \]
    if -4.7178184386274894e157 <  im  < -8.81815897352532454e-65
    1. Initial program 22.4
      \[\]
    2. Using strategy rm
    3. Applied flip-+27.7
      \[\leadsto \]
    4. Simplified21.9
      \[\leadsto \]
    if 7.44086200144270156e-118 <  im 
    1. Initial program 37.0
      \[\]
    2. Taylor expanded around 0 19.1
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification30.7
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(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)))))