Average Error: 38.9 → 18.1
Time: 4.5s
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 ((((double) sqrt(((double) (2.0 * ((double) (((double) sqrt(((double) (((double) (re * re)) + ((double) (im * im)))))) - re)))))) <= 0.0)) {
		VAR = ((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))))))))))))));
	} else {
		double VAR_1;
		if ((((double) sqrt(((double) (2.0 * ((double) (((double) sqrt(((double) (((double) (re * re)) + ((double) (im * im)))))) - re)))))) <= 8.147744050765327e-81)) {
			VAR_1 = ((double) (0.5 * ((double) sqrt(((double) (2.0 * ((double) (im - re))))))));
		} else {
			double VAR_2;
			if ((((double) sqrt(((double) (2.0 * ((double) (((double) sqrt(((double) (((double) (re * re)) + ((double) (im * im)))))) - re)))))) <= 1.1177314541969561e+74)) {
				VAR_2 = ((double) (((double) sqrt(((double) (2.0 * ((double) (((double) sqrt(((double) (((double) (re * re)) + ((double) (im * im)))))) - re)))))) * 0.5));
			} else {
				VAR_2 = ((double) (0.5 * ((double) (((double) sqrt(2.0)) * ((double) sqrt(((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
Derivation
  1. Split input into 4 regimes
  2. if  (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))  < 0.0
    1. Initial program 57.4
      \[\]
    2. Using strategy rm
    3. Applied flip--57.4
      \[\leadsto \]
    4. Applied associate-*r/57.4
      \[\leadsto \]
    5. Applied sqrt-div57.4
      \[\leadsto \]
    6. Simplified26.0
      \[\leadsto \]
    7. Simplified26.0
      \[\leadsto \]
    if 0.0 <  (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))  < 8.147744050765327e-81
    1. Initial program 54.0
      \[\]
    2. Taylor expanded around 0 28.1
      \[\leadsto \]
    if 8.147744050765327e-81 <  (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))  < 1.11773145419695607e74
    1. Initial program 0.4
      \[\]
    if 1.11773145419695607e74 <  (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))) 
    1. Initial program 62.5
      \[\]
    2. Taylor expanded around 0 28.7
      \[\leadsto \]
    3. Using strategy rm
    4. Applied sqrt-prod28.9
      \[\leadsto \]
  3. Recombined 4 regimes into one program.
  4. Final simplification18.1
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(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)))))