Average Error: 31.4 → 13.4
Time: 1.8s
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 ((((double) (x * x)) <= 4.8858151717241e-320)) {
		VAR = -1.0;
	} else {
		double VAR_1;
		if ((((double) (x * x)) <= 4.1505650008460107e-224)) {
			VAR_1 = ((double) log(((double) exp(((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 ((((double) (x * x)) <= 3.689995523729111e-16)) {
				VAR_2 = -1.0;
			} else {
				double VAR_3;
				if ((((double) (x * x)) <= 3.099850220915352e+269)) {
					VAR_3 = ((double) log(((double) exp(((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
Original31.4
Target31.1
Herbie13.4
\[\]
Derivation
  1. Split input into 3 regimes
  2. if  (* x x)  < 4.88582e-320 or 4.15056500084601071e-224 <  (* x x)  < 3.6899955237291112e-16
    1. Initial program 25.3
      \[\]
    2. Taylor expanded around 0 14.6
      \[\leadsto \]
    if 4.88582e-320 <  (* x x)  < 4.15056500084601071e-224 or 3.6899955237291112e-16 <  (* x x)  < 3.0998502209153518e269
    1. Initial program 15.5
      \[\]
    2. Using strategy rm
    3. Applied add-log-exp15.5
      \[\leadsto \]
    4. Simplified15.5
      \[\leadsto \]
    if 3.0998502209153518e269 <  (* x x) 
    1. Initial program 57.9
      \[\]
    2. Taylor expanded around inf 9.2
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification13.4
    \[\leadsto \]
Reproduce
herbie shell --seed 2020180 
(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))))