Average Error: 38.7 → 31.0
Time: 3.6s
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 <= -2.4849948128403756e-150)) {
		VAR = ((double) (0.5 * ((double) sqrt(((double) (2.0 * ((double) (im * ((double) (im / ((double) (((double) sqrt(((double) (((double) (re * re)) + ((double) (im * im)))))) - re))))))))))));
	} else {
		double VAR_1;
		if ((im <= 9.700144651592025e-181)) {
			VAR_1 = ((double) (0.5 * ((double) sqrt(((double) (2.0 * ((double) (re + re))))))));
		} else {
			double VAR_2;
			if ((im <= 1.4225952660417887e-100)) {
				VAR_2 = ((double) (0.5 * ((double) sqrt(((double) (2.0 * ((double) (im * ((double) (im / ((double) (((double) sqrt(((double) (((double) (re * re)) + ((double) (im * im)))))) - re))))))))))));
			} else {
				double VAR_3;
				if ((im <= 1.049793563727917e-26)) {
					VAR_3 = ((double) (0.5 * ((double) sqrt(((double) (2.0 * ((double) (re + re))))))));
				} else {
					VAR_3 = ((double) (0.5 * ((double) sqrt(((double) (2.0 * ((double) (im + re))))))));
				}
				VAR_2 = VAR_3;
			}
			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
Original38.7
Target33.7
Herbie31.0
\[\]
Derivation
  1. Split input into 3 regimes
  2. if  im  < -2.4849948128403756e-150 or 9.7001446515920246e-181 <  im  < 1.42259526604178867e-100
    1. Initial program 36.5
      \[\]
    2. Using strategy rm
    3. Applied flip-+42.8
      \[\leadsto \]
    4. Simplified37.6
      \[\leadsto \]
    5. Using strategy rm
    6. Applied *-un-lft-identity37.6
      \[\leadsto \]
    7. Applied times-frac36.8
      \[\leadsto \]
    8. Simplified36.8
      \[\leadsto \]
    if -2.4849948128403756e-150 <  im  < 9.7001446515920246e-181 or 1.42259526604178867e-100 <  im  < 1.049793563727917e-26
    1. Initial program 40.6
      \[\]
    2. Taylor expanded around inf 37.1
      \[\leadsto \]
    if 1.049793563727917e-26 <  im 
    1. Initial program 40.1
      \[\]
    2. Taylor expanded around 0 15.8
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification31.0
    \[\leadsto \]
Reproduce
herbie shell --seed 2020192 
(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)))))