Average Error: 36.8 → 0.4
Time: 5.1s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x, double eps) {
	return ((double) (((double) sin(((double) (x + eps)))) - ((double) sin(x))));
}

↓
double code(double x, double eps) {
	double VAR;
	if ((eps <= -9.845370976900334e-09)) {
		VAR = ((double) (((double) (((double) (((double) sin(x)) * ((double) cos(eps)))) + ((double) (((double) cos(x)) * ((double) sin(eps)))))) - ((double) sin(x))));
	} else {
		double VAR_1;
		if ((eps <= 6.897912047083434e-09)) {
			VAR_1 = ((double) (((double) (2.0 * ((double) sin(((double) (eps / 2.0)))))) * ((double) cos(((double) (((double) (x + ((double) (eps + x)))) / 2.0))))));
		} else {
			VAR_1 = ((double) (((double) (((double) sin(x)) * ((double) cos(eps)))) + ((double) (((double) (((double) cos(x)) * ((double) sin(eps)))) - ((double) sin(x))))));
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error
Bits error versus x
Bits error versus eps
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original36.8
Target14.6
Herbie0.4
\[\]
Derivation
  1. Split input into 3 regimes
  2. if  eps  < -9.8453709769003335e-9
    1. Initial program 28.1
      \[\]
    2. Using strategy rm
    3. Applied sin-sum0.5
      \[\leadsto \]
    if -9.8453709769003335e-9 <  eps  < 6.897912047083434e-9
    1. Initial program 45.4
      \[\]
    2. Using strategy rm
    3. Applied diff-sin45.4
      \[\leadsto \]
    4. Simplified0.3
      \[\leadsto \]
    5. Using strategy rm
    6. Applied associate-*r*0.3
      \[\leadsto \]
    if 6.897912047083434e-9 <  eps 
    1. Initial program 29.4
      \[\]
    2. Using strategy rm
    3. Applied sin-sum0.5
      \[\leadsto \]
    4. Applied associate--l+0.5
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification0.4
    \[\leadsto \]
Reproduce
herbie shell --seed 2020179 
(FPCore (x eps)
  :name "2sin (example 3.3)"
  :precision binary64

  :herbie-target
  (* 2.0 (* (cos (+ x (/ eps 2.0))) (sin (/ eps 2.0))))

  (- (sin (+ x eps)) (sin x)))