Average Error: 60.2 → 0.8
Time: 15.4s
Precision: binary64
\[\]
\[\]
↓
\[\]
↓
double code(double a, double b, double eps) {
	return ((double) (((double) (eps * ((double) (((double) exp(((double) (((double) (a + b)) * eps)))) - 1.0)))) / ((double) (((double) (((double) exp(((double) (a * eps)))) - 1.0)) * ((double) (((double) exp(((double) (b * eps)))) - 1.0))))));
}

↓
double code(double a, double b, double eps) {
	double VAR;
	if (((((double) (((double) (eps * ((double) (((double) exp(((double) (eps * ((double) (a + b)))))) - 1.0)))) / ((double) (((double) (((double) exp(((double) (eps * a)))) - 1.0)) * ((double) (((double) exp(((double) (eps * b)))) - 1.0)))))) <= -3.0606955957916557e-99) || !(((double) (((double) (eps * ((double) (((double) exp(((double) (eps * ((double) (a + b)))))) - 1.0)))) / ((double) (((double) (((double) exp(((double) (eps * a)))) - 1.0)) * ((double) (((double) exp(((double) (eps * b)))) - 1.0)))))) <= 0.009927997727509082))) {
		VAR = ((double) (((double) (1.0 / b)) + ((double) (1.0 / a))));
	} else {
		VAR = ((double) (((double) (eps * ((double) (((double) exp(((double) (eps * ((double) (a + b)))))) - 1.0)))) / ((double) (((double) (((double) exp(((double) (eps * a)))) - 1.0)) * ((double) (((double) exp(((double) (eps * b)))) - 1.0))))));
	}
	return VAR;
}

Error
Bits error versus a
Bits error versus b
Bits error versus eps
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original60.2
Target15.1
Herbie0.8
\[\]
Derivation
  1. Split input into 2 regimes
  2. if  (/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))  < -3.06069559579165575e-99 or 0.0099279977275090817 <  (/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))) 
    1. Initial program 63.3
      \[\]
    2. Taylor expanded around 0 0.7
      \[\leadsto \]
    if -3.06069559579165575e-99 <  (/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))  < 0.0099279977275090817
    1. Initial program 3.0
      \[\]
  3. Recombined 2 regimes into one program.
  4. Final simplification0.8
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (a b eps)
  :name "expq3 (problem 3.4.2)"
  :precision binary64
  :pre (and (< -1.0 eps) (< eps 1.0))

  :herbie-target
  (/ (+ a b) (* a b))

  (/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))))