Average Error: 38.2 → 27.1
Time: 4.7s
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 <= -2.5723644386022114e-302)) {
		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 <= 2.7348232889716076e-169)) {
			VAR_1 = ((double) (0.5 * ((double) sqrt(((double) (2.0 * ((double) (re + im))))))));
		} else {
			double VAR_2;
			if ((re <= 5.1160026767062117e-144)) {
				VAR_2 = ((double) (0.5 * ((double) sqrt(((double) (2.0 * ((double) (((double) sqrt(((double) (re + ((double) sqrt(((double) (((double) (im * im)) + ((double) (re * re)))))))))) * ((double) sqrt(((double) (re + ((double) sqrt(((double) (((double) (im * im)) + ((double) (re * re))))))))))))))))));
			} else {
				double VAR_3;
				if ((re <= 4.7357972410850955e-105)) {
					VAR_3 = ((double) (0.5 * ((double) sqrt(((double) (2.0 * ((double) (re + im))))))));
				} else {
					double VAR_4;
					if ((re <= 9.207225632419575e+119)) {
						VAR_4 = ((double) (0.5 * ((double) sqrt(((double) (2.0 * ((double) (re + ((double) sqrt(((double) (((double) (im * im)) + ((double) (re * re))))))))))))));
					} else {
						VAR_4 = ((double) (0.5 * ((double) sqrt(((double) (2.0 * ((double) (re + re))))))));
					}
					VAR_3 = VAR_4;
				}
				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
Original38.2
Target33.3
Herbie27.1
\[\]
Derivation
  1. Split input into 5 regimes
  2. if  re  < -2.5723644386022114e-302
    1. Initial program 45.3
      \[\]
    2. Using strategy rm
    3. Applied flip-+45.2
      \[\leadsto \]
    4. Applied associate-*r/45.2
      \[\leadsto \]
    5. Applied sqrt-div45.3
      \[\leadsto \]
    6. Simplified34.5
      \[\leadsto \]
    if -2.5723644386022114e-302 <  re  < 2.73482328897160755e-169 or 5.11600267670621171e-144 <  re  < 4.73579724108509554e-105
    1. Initial program 26.1
      \[\]
    2. Taylor expanded around 0 35.2
      \[\leadsto \]
    if 2.73482328897160755e-169 <  re  < 5.11600267670621171e-144
    1. Initial program 20.3
      \[\]
    2. Using strategy rm
    3. Applied add-sqr-sqrt20.5
      \[\leadsto \]
    4. Simplified20.5
      \[\leadsto \]
    5. Simplified20.5
      \[\leadsto \]
    if 4.73579724108509554e-105 <  re  < 9.20722563241957548e119
    1. Initial program 15.6
      \[\]
    if 9.20722563241957548e119 <  re 
    1. Initial program 55.2
      \[\]
    2. Taylor expanded around inf 10.2
      \[\leadsto \]
  3. Recombined 5 regimes into one program.
  4. Final simplification27.1
    \[\leadsto \]
Reproduce
herbie shell --seed 2020181 
(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)))))