Average Error: 20.5 → 5.2
Time: 1.4s
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 <= -3.093872020900152e+153)) {
		VAR = -1.0;
	} else {
		double VAR_1;
		if (((y <= -1.8407681256304194e-159) || !(y <= 6.147288565032054e-174))) {
			VAR_1 = ((double) (((double) (((double) (x - y)) * ((double) (y + x)))) / ((double) (((double) (x * x)) + ((double) (y * y))))));
		} else {
			VAR_1 = 1.0;
		}
		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
Original20.5
Target0.1
Herbie5.2
\[\]
Derivation
  1. Split input into 3 regimes
  2. if  y  < -3.0938720209001519e153
    1. Initial program 63.8
      \[\]
    2. Taylor expanded around 0 0
      \[\leadsto \]
    if -3.0938720209001519e153 <  y  < -1.8407681256304194e-159 or 6.1472885650320537e-174 <  y 
    1. Initial program 0.8
      \[\]
    if -1.8407681256304194e-159 <  y  < 6.1472885650320537e-174
    1. Initial program 30.1
      \[\]
    2. Taylor expanded around inf 15.4
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification5.2
    \[\leadsto \]
Reproduce
herbie shell --seed 2020181 
(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))))