Average Error: 38.9 → 26.5
Time: 5.0s
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 <= -3.4246941374715e-310)) {
		VAR = ((double) (0.5 * ((double) (((double) sqrt(((double) (((double) (im * im)) * 2.0)))) / ((double) sqrt(((double) (((double) sqrt(((double) (((double) (im * im)) + ((double) (re * re)))))) - re))))))));
	} else {
		double VAR_1;
		if ((re <= 1.1095515437686829e+75)) {
			VAR_1 = ((double) (0.5 * ((double) sqrt(((double) (2.0 * ((double) (re + ((double) sqrt(((double) (((double) (im * im)) + ((double) (re * re))))))))))))));
		} else {
			VAR_1 = ((double) (0.5 * ((double) sqrt(((double) (2.0 * ((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
Target
Original38.9
Target34.0
Herbie26.5
\[\]
Derivation
  1. Split input into 3 regimes
  2. if  re  < -3.424694137471509e-310
    1. Initial program 45.9
      \[\]
    2. Using strategy rm
    3. Applied flip-+45.7
      \[\leadsto \]
    4. Applied associate-*r/45.7
      \[\leadsto \]
    5. Applied sqrt-div45.8
      \[\leadsto \]
    6. Simplified35.2
      \[\leadsto \]
    if -3.424694137471509e-310 <  re  < 1.10955154376868287e75
    1. Initial program 22.4
      \[\]
    if 1.10955154376868287e75 <  re 
    1. Initial program 46.5
      \[\]
    2. Taylor expanded around inf 10.7
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification26.5
    \[\leadsto \]
Reproduce
herbie shell --seed 2020180 
(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)))))