Average Error: 26.4 → 18.2
Time: 6.0s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	return ((x_46_re * y_46_re) + (x_46_im * y_46_im)) / ((y_46_re * y_46_re) + (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 tmp;
	if ((y_46_im <= -3.6058658773741186e+115) || !(y_46_im <= 2.2524233065491668e+111)) {
		tmp = x_46_im / y_46_im;
	} else {
		tmp = (((x_46_re * y_46_re) + (y_46_im * x_46_im)) * (1.0 / sqrt(pow(y_46_re, 2.0) + pow(y_46_im, 2.0)))) / sqrt((y_46_re * y_46_re) + (y_46_im * y_46_im));
	}
	return tmp;
}

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  y.im  < -3.60586587737411862e115 or 2.25242330654916681e111 <  y.im 
    1. Initial program 41.1
      \[\]
    2. Using strategy rm
    3. Applied add-sqr-sqrt41.1
      \[\leadsto \]
    4. Applied associate-/r*41.1
      \[\leadsto \]
    5. Simplified41.1
      \[\leadsto \]
    6. Taylor expanded around 0 42.6
      \[\leadsto \]
    7. Taylor expanded around 0 16.4
      \[\leadsto \]
    if -3.60586587737411862e115 <  y.im  < 2.25242330654916681e111
    1. Initial program 19.0
      \[\]
    2. Using strategy rm
    3. Applied add-sqr-sqrt19.1
      \[\leadsto \]
    4. Applied associate-/r*19.0
      \[\leadsto \]
    5. Simplified19.0
      \[\leadsto \]
    6. Using strategy rm
    7. Applied div-inv19.0
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification18.2
    \[\leadsto \]
Reproduce
herbie shell --seed 2020338 
(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))))