Average Error: 38.3 → 19.2
Time: 3.8s
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 <= -5.516385007189412e+131)) {
		VAR = ((double) (0.5 * ((double) sqrt(((double) (2.0 * ((double) (re * -2.0))))))));
	} else {
		double VAR_1;
		if ((re <= -3.3801084320698864e-75)) {
			VAR_1 = ((double) (0.5 * ((double) sqrt(((double) (2.0 * ((double) (((double) sqrt(((double) (((double) (re * re)) + ((double) (im * im)))))) - re))))))));
		} else {
			double VAR_2;
			if ((re <= 2.7892391254241995e+37)) {
				VAR_2 = ((double) (0.5 * ((double) sqrt(((double) (2.0 * ((double) (im - re))))))));
			} else {
				VAR_2 = ((double) (0.5 * ((double) (((double) sqrt(((double) (2.0 * ((double) (im * im)))))) / ((double) sqrt(((double) (re + ((double) sqrt(((double) (((double) (re * re)) + ((double) (im * im))))))))))))));
			}
			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
Derivation
  1. Split input into 4 regimes
  2. if  re  < -5.51638500718941234e131
    1. Initial program 57.9
      \[\]
    2. Taylor expanded around -inf 8.2
      \[\leadsto \]
    3. Simplified8.2
      \[\leadsto \]
    if -5.51638500718941234e131 <  re  < -3.3801084320698864e-75
    1. Initial program 16.1
      \[\]
    if -3.3801084320698864e-75 <  re  < 2.78923912542419952e37
    1. Initial program 31.1
      \[\]
    2. Taylor expanded around 0 14.9
      \[\leadsto \]
    if 2.78923912542419952e37 <  re 
    1. Initial program 58.0
      \[\]
    2. Using strategy rm
    3. Applied flip--58.0
      \[\leadsto \]
    4. Applied associate-*r/58.0
      \[\leadsto \]
    5. Applied sqrt-div58.0
      \[\leadsto \]
    6. Simplified38.0
      \[\leadsto \]
    7. Simplified38.0
      \[\leadsto \]
  3. Recombined 4 regimes into one program.
  4. Final simplification19.2
    \[\leadsto \]
Reproduce
herbie shell --seed 2020192 
(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)))))