Average Error: 31.5 → 12.8
Time: 2.4s
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 <= -3.752645835216144e+68)) {
		VAR = 1.0;
	} else {
		double VAR_1;
		if ((x <= -2.8358808443238253e+54)) {
			VAR_1 = -1.0;
		} else {
			double VAR_2;
			if ((x <= -128170599.86509866)) {
				VAR_2 = ((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_3;
				if ((x <= -2.583596787935841e-15)) {
					VAR_3 = -1.0;
				} else {
					double VAR_4;
					if ((x <= -2.0380687870564522e-162)) {
						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 ((x <= 1.3475495652570812e-153)) {
							VAR_5 = -1.0;
						} else {
							double VAR_6;
							if ((x <= 7.362224235363507e+87)) {
								VAR_6 = ((double) (((double) (x * ((double) (x / ((double) (((double) (x * x)) + ((double) (y * ((double) (y * 4.0)))))))))) - ((double) (y * ((double) (y / ((double) (((double) (((double) (x * x)) + ((double) (y * ((double) (y * 4.0)))))) / 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
Original31.5
Target31.3
Herbie12.8
\[\]
Derivation
  1. Split input into 4 regimes
  2. if  x  < -3.75264583521614402e68 or 7.36222423536350657e87 <  x 
    1. Initial program 47.8
      \[\]
    2. Taylor expanded around inf 11.8
      \[\leadsto \]
    if -3.75264583521614402e68 <  x  < -2.8358808443238253e54 or -128170599.86509866 <  x  < -2.58359678793584112e-15 or -2.03806878705645224e-162 <  x  < 1.3475495652570812e-153
    1. Initial program 30.1
      \[\]
    2. Taylor expanded around 0 10.3
      \[\leadsto \]
    if -2.8358808443238253e54 <  x  < -128170599.86509866 or -2.58359678793584112e-15 <  x  < -2.03806878705645224e-162
    1. Initial program 15.6
      \[\]
    2. Using strategy rm
    3. Applied add-sqr-sqrt15.6
      \[\leadsto \]
    4. Applied associate-/r*15.6
      \[\leadsto \]
    5. Simplified15.6
      \[\leadsto \]
    if 1.3475495652570812e-153 <  x  < 7.36222423536350657e87
    1. Initial program 16.1
      \[\]
    2. Using strategy rm
    3. Applied div-sub16.1
      \[\leadsto \]
    4. Simplified16.3
      \[\leadsto \]
    5. Simplified15.8
      \[\leadsto \]
  3. Recombined 4 regimes into one program.
  4. Final simplification12.8
    \[\leadsto \]
Reproduce
herbie shell --seed 2020190 
(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))))