Average Error: 20.3 → 5.8
Time: 1.7s
Precision: binary64
\[\]
\[\]
↓
\[\]
↓
double code(double x, double y) {
	return ((double) (((double) (((double) (x - y)) * ((double) (x + y)))) / ((double) (((double) (x * x)) + ((double) (y * y))))));
}

↓
double code(double x, double y) {
	double VAR;
	if ((y <= -1.3227300723852667e+154)) {
		VAR = -1.0;
	} else {
		double VAR_1;
		if ((y <= -8.153797794968458e-160)) {
			VAR_1 = ((double) (((double) (((double) (x - y)) / ((double) sqrt(((double) (((double) (x * x)) + ((double) (y * y)))))))) * ((double) (((double) (y + x)) / ((double) sqrt(((double) (((double) (x * x)) + ((double) (y * y))))))))));
		} else {
			double VAR_2;
			if ((y <= 7.434273359978173e-214)) {
				VAR_2 = 1.0;
			} else {
				double VAR_3;
				if ((y <= 1.6793339788522405e-181)) {
					VAR_3 = -1.0;
				} else {
					VAR_3 = ((double) (((double) (((double) (x - y)) / ((double) sqrt(((double) (((double) (x * x)) + ((double) (y * y)))))))) * ((double) (((double) (y + x)) / ((double) sqrt(((double) (((double) (x * x)) + ((double) (y * y))))))))));
				}
				VAR_2 = VAR_3;
			}
			VAR_1 = VAR_2;
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error
Bits error versus x
Bits error versus y
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original20.3
Target0.1
Herbie5.8
\[\]
Derivation
  1. Split input into 3 regimes
  2. if  y  < -1.3227300723852667e154 or 7.434273359978173e-214 <  y  < 1.679333978852241e-181
    1. Initial program 57.9
      \[\]
    2. Taylor expanded around 0 7.2
      \[\leadsto \]
    if -1.3227300723852667e154 <  y  < -8.1537977949684577e-160 or 1.679333978852241e-181 <  y 
    1. Initial program 1.3
      \[\]
    2. Using strategy rm
    3. Applied add-sqr-sqrt1.3
      \[\leadsto \]
    4. Applied times-frac1.6
      \[\leadsto \]
    if -8.1537977949684577e-160 <  y  < 7.434273359978173e-214
    1. Initial program 30.9
      \[\]
    2. Taylor expanded around inf 13.7
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification5.8
    \[\leadsto \]
Reproduce
herbie shell --seed 2020192 
(FPCore (x y)
  :name "Kahan p9 Example"
  :precision binary64
  :pre (and (< 0.0 x 1.0) (< y 1.0))

  :herbie-target
  (if (< 0.5 (fabs (/ x y)) 2.0) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (- 1.0 (/ 2.0 (+ 1.0 (* (/ x y) (/ x y))))))

  (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))