Average Error: 37.8 → 20.7
Time: 3.9s
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 ((re <= -1.3272029508543682e-33)) {
		VAR = ((double) (0.5 * ((double) sqrt(((double) (re * -4.0))))));
	} else {
		double VAR_1;
		if ((re <= 2.7223419195749627e+50)) {
			VAR_1 = ((double) (0.5 * ((double) sqrt(((double) (2.0 * ((double) (im - re))))))));
		} else {
			VAR_1 = ((double) (0.5 * ((double) (((double) sqrt(((double) (2.0 * ((double) (im * im)))))) / ((double) sqrt(((double) (re + ((double) sqrt(((double) (((double) (im * im)) + ((double) (re * re))))))))))))));
		}
		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
Derivation
  1. Split input into 3 regimes
  2. if  re  < -1.3272029508543682e-33
    1. Initial program 36.3
      \[\]
    2. Taylor expanded around -inf 15.8
      \[\leadsto \]
    3. Simplified15.8
      \[\leadsto \]
    if -1.3272029508543682e-33 <  re  < 2.72234191957496269e50
    1. Initial program 30.2
      \[\]
    2. Taylor expanded around 0 15.0
      \[\leadsto \]
    if 2.72234191957496269e50 <  re 
    1. Initial program 58.2
      \[\]
    2. Using strategy rm
    3. Applied flip--58.2
      \[\leadsto \]
    4. Applied associate-*r/58.3
      \[\leadsto \]
    5. Applied sqrt-div58.3
      \[\leadsto \]
    6. Simplified41.1
      \[\leadsto \]
    7. Simplified41.1
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification20.7
    \[\leadsto \]
Reproduce
herbie shell --seed 2020180 
(FPCore (re im)
  :name "math.sqrt on complex, imaginary part, im greater than 0 branch"
  :precision binary64
  :pre (> im 0.0)
  (* 0.5 (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))))