Average Error: 26.7 → 23.5
Time: 4.9s
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_im * y_46_re)) - ((double) (x_46_re * 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 (((y_46_im <= -2.7466643681102755e-252) || !(y_46_im <= 2.2944353920244916e-209))) {
		VAR = ((double) (((double) (((double) (y_46_re * ((double) (x_46_im / ((double) sqrt(((double) (((double) (y_46_re * y_46_re)) + ((double) (y_46_im * y_46_im)))))))))) - ((double) (y_46_im * ((double) (x_46_re / ((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) (((double) (((double) (1.0 / ((double) fabs(((double) cbrt(((double) (((double) (y_46_re * y_46_re)) + ((double) (y_46_im * y_46_im)))))))))) * ((double) (((double) (((double) (y_46_re * x_46_im)) - ((double) (y_46_im * x_46_re)))) / ((double) sqrt(((double) cbrt(((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))))))));
	}
	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  y.im  < -2.74666436811027551e-252 or 2.29443539202449163e-209 <  y.im 
    1. Initial program 27.1
      \[\]
    2. Using strategy rm
    3. Applied add-sqr-sqrt27.1
      \[\leadsto \]
    4. Applied associate-/r*27.0
      \[\leadsto \]
    5. Using strategy rm
    6. Applied div-sub27.0
      \[\leadsto \]
    7. Simplified25.6
      \[\leadsto \]
    8. Simplified23.4
      \[\leadsto \]
    if -2.74666436811027551e-252 <  y.im  < 2.29443539202449163e-209
    1. Initial program 24.0
      \[\]
    2. Using strategy rm
    3. Applied add-sqr-sqrt24.0
      \[\leadsto \]
    4. Applied associate-/r*23.9
      \[\leadsto \]
    5. Using strategy rm
    6. Applied add-cube-cbrt24.3
      \[\leadsto \]
    7. Applied sqrt-prod24.3
      \[\leadsto \]
    8. Applied *-un-lft-identity24.3
      \[\leadsto \]
    9. Applied times-frac24.3
      \[\leadsto \]
    10. Simplified24.3
      \[\leadsto \]
    11. Simplified24.3
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification23.5
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (x.re x.im y.re y.im)
  :name "_divideComplex, imaginary part"
  :precision binary64
  (/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im))))