Average Error: 38.2 → 19.9
Time: 4.9s
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 <= -2.2927799014051263e+89)) {
		VAR = ((double) (0.5 * ((double) sqrt(((double) (2.0 * ((double) (re * -2.0))))))));
	} else {
		double VAR_1;
		if ((re <= -3.046798939941476e-126)) {
			VAR_1 = ((double) (0.5 * ((double) sqrt(((double) (2.0 * ((double) (((double) (((double) cbrt(((double) sqrt(((double) (((double) (re * re)) + ((double) (im * im)))))))) * ((double) (((double) cbrt(((double) sqrt(((double) (((double) (re * re)) + ((double) (im * im)))))))) * ((double) cbrt(((double) sqrt(((double) (((double) (re * re)) + ((double) (im * im)))))))))))) - re))))))));
		} else {
			double VAR_2;
			if (((re <= 1.9400859152886943e-72) || !(re <= 5.828409004054647e+165))) {
				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  < -2.29277990140512628e89
    1. Initial program 49.8
      \[\]
    2. Taylor expanded around -inf 10.2
      \[\leadsto \]
    3. Simplified10.2
      \[\leadsto \]
    if -2.29277990140512628e89 <  re  < -3.04679893994147599e-126
    1. Initial program 14.7
      \[\]
    2. Using strategy rm
    3. Applied add-cube-cbrt15.2
      \[\leadsto \]
    if -3.04679893994147599e-126 <  re  < 1.94008591528869432e-72 or 5.8284090040546467e165 <  re 
    1. Initial program 38.1
      \[\]
    2. Taylor expanded around 0 21.1
      \[\leadsto \]
    if 1.94008591528869432e-72 <  re  < 5.8284090040546467e165
    1. Initial program 48.6
      \[\]
    2. Using strategy rm
    3. Applied flip--48.6
      \[\leadsto \]
    4. Applied associate-*r/48.7
      \[\leadsto \]
    5. Applied sqrt-div48.8
      \[\leadsto \]
    6. Simplified30.2
      \[\leadsto \]
    7. Simplified30.2
      \[\leadsto \]
  3. Recombined 4 regimes into one program.
  4. Final simplification19.9
    \[\leadsto \]
Reproduce
herbie shell --seed 2020181 
(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)))))