Average Error: 26.1 → 25.3
Time: 3.6s
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)))))) <= 6.923981202126471e+297)) {
		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_im / ((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)))  < 6.92398120212647147e297
    1. Initial program 14.2
      \[\]
    2. Using strategy rm
    3. Applied add-sqr-sqrt14.2
      \[\leadsto \]
    4. Applied associate-/r*14.1
      \[\leadsto \]
    if 6.92398120212647147e297 <  (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im))) 
    1. Initial program 63.5
      \[\]
    2. Using strategy rm
    3. Applied add-sqr-sqrt63.5
      \[\leadsto \]
    4. Applied associate-/r*63.5
      \[\leadsto \]
    5. Taylor expanded around 0 60.4
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification25.3
    \[\leadsto \]
Reproduce
herbie shell --seed 2020192 
(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))))