Average Error: 26.0 → 25.1
Time: 3.7s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double a, double b, double c, double d) {
	return ((double) (((double) (((double) (a * c)) + ((double) (b * d)))) / ((double) (((double) (c * c)) + ((double) (d * d))))));
}

↓
double code(double a, double b, double c, double d) {
	double VAR;
	if ((((double) (((double) (((double) (a * c)) + ((double) (b * d)))) / ((double) (((double) (c * c)) + ((double) (d * d)))))) <= 2.4827453124024694e+305)) {
		VAR = ((double) (((double) (((double) (((double) (a * c)) + ((double) (b * d)))) / ((double) sqrt(((double) (((double) (c * c)) + ((double) (d * d)))))))) / ((double) sqrt(((double) (((double) (c * c)) + ((double) (d * d))))))));
	} else {
		VAR = ((double) (b * ((double) (1.0 / ((double) sqrt(((double) (((double) (c * c)) + ((double) (d * d))))))))));
	}
	return VAR;
}

Error
Bits error versus a
Bits error versus b
Bits error versus c
Bits error versus d
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original26.0
Target0.4
Herbie25.1
\[\]
Derivation
  1. Split input into 2 regimes
  2. if  (/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))  < 2.4827453124024694e305
    1. Initial program 13.7
      \[\]
    2. Using strategy rm
    3. Applied add-sqr-sqrt13.7
      \[\leadsto \]
    4. Applied associate-/r*13.6
      \[\leadsto \]
    if 2.4827453124024694e305 <  (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) 
    1. Initial program 63.9
      \[\]
    2. Using strategy rm
    3. Applied add-sqr-sqrt63.9
      \[\leadsto \]
    4. Applied *-un-lft-identity63.9
      \[\leadsto \]
    5. Applied times-frac63.9
      \[\leadsto \]
    6. Taylor expanded around 0 60.3
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification25.1
    \[\leadsto \]
Reproduce
herbie shell --seed 2020190 
(FPCore (a b c d)
  :name "Complex division, real part"
  :precision binary64

  :herbie-target
  (if (< (fabs d) (fabs c)) (/ (+ a (* b (/ d c))) (+ c (* d (/ d c)))) (/ (+ b (* a (/ c d))) (+ d (* c (/ c d)))))

  (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))))