Average Error: 30.8 → 13.4
Time: 2.9s
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 ((y <= -2.0283904122069306e+54)) {
		VAR = -1.0;
	} else {
		double VAR_1;
		if ((y <= -4.943141398320038e+33)) {
			VAR_1 = 1.0;
		} else {
			double VAR_2;
			if ((y <= -2.0470558918808e-12)) {
				VAR_2 = ((double) (((double) (((double) (x * x)) - ((double) (y * ((double) (y * 4.0)))))) / ((double) (((double) (x * x)) + ((double) (y * ((double) (y * 4.0))))))));
			} else {
				double VAR_3;
				if ((y <= -2.989023498775882e-21)) {
					VAR_3 = 1.0;
				} else {
					double VAR_4;
					if ((y <= -7.889044677899444e-163)) {
						VAR_4 = ((double) (((double) (((double) (((double) (x * x)) - ((double) (y * ((double) (y * 4.0)))))) / ((double) sqrt(((double) (((double) (x * x)) + ((double) (y * ((double) (y * 4.0)))))))))) / ((double) sqrt(((double) (((double) (x * x)) + ((double) (y * ((double) (y * 4.0))))))))));
					} else {
						double VAR_5;
						if ((y <= 2.3617540025890117e-149)) {
							VAR_5 = 1.0;
						} else {
							double VAR_6;
							if ((y <= 341.54445514348123)) {
								VAR_6 = ((double) (((double) (((double) (x * x)) - ((double) (y * ((double) (y * 4.0)))))) / ((double) (((double) (x * x)) + ((double) (y * ((double) (y * 4.0))))))));
							} else {
								VAR_6 = -1.0;
							}
							VAR_5 = VAR_6;
						}
						VAR_4 = VAR_5;
					}
					VAR_3 = VAR_4;
				}
				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
Original30.8
Target30.5
Herbie13.4
\[\]
Derivation
  1. Split input into 4 regimes
  2. if  y  < -2.02839041220693056e54 or 341.54445514348123 <  y 
    1. Initial program 42.0
      \[\]
    2. Taylor expanded around 0 14.1
      \[\leadsto \]
    if -2.02839041220693056e54 <  y  < -4.94314139832003796e33 or -2.04705589188079983e-12 <  y  < -2.98902349877588194e-21 or -7.88904467789944394e-163 <  y  < 2.361754002589012e-149
    1. Initial program 27.4
      \[\]
    2. Taylor expanded around inf 10.4
      \[\leadsto \]
    if -4.94314139832003796e33 <  y  < -2.04705589188079983e-12 or 2.361754002589012e-149 <  y  < 341.54445514348123
    1. Initial program 15.3
      \[\]
    if -2.98902349877588194e-21 <  y  < -7.88904467789944394e-163
    1. Initial program 14.5
      \[\]
    2. Using strategy rm
    3. Applied add-sqr-sqrt14.5
      \[\leadsto \]
    4. Applied associate-/r*14.5
      \[\leadsto \]
    5. Simplified14.5
      \[\leadsto \]
  3. Recombined 4 regimes into one program.
  4. Final simplification13.4
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(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))))