Average Error: 37.5 → 0.4
Time: 5.6s
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 <= -1.4223670267152646e-08) || !(eps <= 2.0374182041794392e-10))) {
		VAR = ((double) (((double) (((double) (((double) sin(x)) * ((double) cos(eps)))) + ((double) (((double) cos(x)) * ((double) sin(eps)))))) - ((double) sin(x))));
	} else {
		VAR = ((double) (((double) (2.0 * ((double) sin(((double) (eps / 2.0)))))) * ((double) cos(((double) (((double) (x + ((double) (eps + x)))) / 2.0))))));
	}
	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
Original37.5
Target15.3
Herbie0.4
\[\]
Derivation
  1. Split input into 2 regimes
  2. if  eps  < -1.4223670267152646e-8 or 2.0374182041794392e-10 <  eps 
    1. Initial program 30.3
      \[\]
    2. Using strategy rm
    3. Applied sin-sum0.6
      \[\leadsto \]
    if -1.4223670267152646e-8 <  eps  < 2.0374182041794392e-10
    1. Initial program 45.0
      \[\]
    2. Using strategy rm
    3. Applied diff-sin45.0
      \[\leadsto \]
    4. Simplified0.3
      \[\leadsto \]
    5. Using strategy rm
    6. Applied associate-*r*0.3
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification0.4
    \[\leadsto \]
Reproduce
herbie shell --seed 2020192 
(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)))