Average Error: 26.6 → 26.4
Time: 4.5s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	return ((double) (((double) (((double) (x_46_re * y_46_re)) + ((double) (x_46_im * y_46_im)))) / ((double) (((double) (y_46_re * y_46_re)) + ((double) (y_46_im * y_46_im))))));
}

↓
double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double VAR;
	if ((((double) (((double) (((double) (x_46_re * y_46_re)) + ((double) (x_46_im * y_46_im)))) / ((double) (((double) (y_46_re * y_46_re)) + ((double) (y_46_im * y_46_im)))))) <= 1.6816948944806213e+249)) {
		VAR = ((double) (((double) (((double) (((double) (x_46_re * y_46_re)) + ((double) (x_46_im * y_46_im)))) / ((double) sqrt(((double) (((double) (y_46_re * y_46_re)) + ((double) (y_46_im * y_46_im)))))))) / ((double) sqrt(((double) (((double) (y_46_re * y_46_re)) + ((double) (y_46_im * y_46_im))))))));
	} else {
		VAR = ((double) (x_46_re / ((double) sqrt(((double) (((double) (y_46_re * y_46_re)) + ((double) (y_46_im * y_46_im))))))));
	}
	return VAR;
}

Error
Bits error versus x.re
Bits error versus x.im
Bits error versus y.re
Bits error versus y.im
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Split input into 2 regimes
  2. if  (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))  < 1.6816948944806213e249
    1. Initial program 14.9
      \[\]
    2. Using strategy rm
    3. Applied add-sqr-sqrt14.9
      \[\leadsto \]
    4. Applied associate-/r*14.8
      \[\leadsto \]
    if 1.6816948944806213e249 <  (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im))) 
    1. Initial program 60.8
      \[\]
    2. Using strategy rm
    3. Applied add-sqr-sqrt60.8
      \[\leadsto \]
    4. Applied associate-/r*60.7
      \[\leadsto \]
    5. Taylor expanded around inf 60.2
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification26.4
    \[\leadsto \]
Reproduce
herbie shell --seed 2020181 
(FPCore (x.re x.im y.re y.im)
  :name "_divideComplex, real part"
  :precision binary64
  (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im))))