Average Error: 31.9 → 12.6
Time: 2.1s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x, double y) {
	return ((double) (((double) (((double) (x * x)) - ((double) (((double) (y * 4.0)) * y)))) / ((double) (((double) (x * x)) + ((double) (((double) (y * 4.0)) * y))))));
}

↓
double code(double x, double y) {
	double VAR;
	if ((x <= -1.8962936310719086e+79)) {
		VAR = 1.0;
	} else {
		double VAR_1;
		if ((x <= -6.449241694858416e-139)) {
			VAR_1 = ((double) (((double) (((double) (x * x)) - ((double) (y * ((double) (y * 4.0)))))) / ((double) (((double) (x * x)) + ((double) (y * ((double) (y * 4.0))))))));
		} else {
			double VAR_2;
			if ((x <= 9.049663672656093e-85)) {
				VAR_2 = -1.0;
			} else {
				double VAR_3;
				if ((x <= 1.4268480644529162e+90)) {
					VAR_3 = ((double) (((double) (((double) (x * x)) - ((double) (y * ((double) (y * 4.0)))))) / ((double) (((double) (x * x)) + ((double) (y * ((double) (y * 4.0))))))));
				} else {
					VAR_3 = 1.0;
				}
				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
Original31.9
Target31.6
Herbie12.6
\[\]
Derivation
  1. Split input into 3 regimes
  2. if  x  < -1.89629363107190863e79 or 1.42684806445291622e90 <  x 
    1. Initial program 49.3
      \[\]
    2. Taylor expanded around inf 11.0
      \[\leadsto \]
    if -1.89629363107190863e79 <  x  < -6.44924169485841637e-139 or 9.04966367265609278e-85 <  x  < 1.42684806445291622e90
    1. Initial program 16.1
      \[\]
    if -6.44924169485841637e-139 <  x  < 9.04966367265609278e-85
    1. Initial program 27.9
      \[\]
    2. Taylor expanded around 0 11.0
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification12.6
    \[\leadsto \]
Reproduce
herbie shell --seed 2020192 
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:arcBetween from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))) 0.9743233849626781) (- (/ (* x x) (+ (* x x) (* (* y y) 4.0))) (/ (* (* y y) 4.0) (+ (* x x) (* (* y y) 4.0)))) (- (pow (/ x (sqrt (+ (* x x) (* (* y y) 4.0)))) 2.0) (/ (* (* y y) 4.0) (+ (* x x) (* (* y y) 4.0)))))

  (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))))