Average Error: 60.4 → 31.7
Time: 14.0s
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 ((b <= -8.908678098616857e+104)) {
		VAR = ((double) (((double) (eps * ((double) (((double) exp(((double) (eps * ((double) (b + a)))))) - 1.0)))) / ((double) (((double) (((double) (eps * a)) + ((double) (((double) (eps * eps)) * ((double) (((double) (a * ((double) (a * 0.5)))) + ((double) (eps * ((double) (0.16666666666666666 * ((double) pow(a, 3.0)))))))))))) * ((double) (((double) exp(((double) (b * eps)))) - 1.0))))));
	} else {
		VAR = ((double) (1.0 / b));
	}
	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
Original60.4
Target14.9
Herbie31.7
\[\]
Derivation
  1. Split input into 2 regimes
  2. if  b  < -8.9086780986168568e104
    1. Initial program 53.0
      \[\]
    2. Taylor expanded around 0 45.3
      \[\leadsto \]
    3. Simplified45.0
      \[\leadsto \]
    if -8.9086780986168568e104 <  b 
    1. Initial program 61.7
      \[\]
    2. Taylor expanded around 0 56.9
      \[\leadsto \]
    3. Simplified56.4
      \[\leadsto \]
    4. Using strategy rm
    5. Applied associate-*l*56.2
      \[\leadsto \]
    6. Simplified56.2
      \[\leadsto \]
    7. Taylor expanded around inf 56.2
      \[\leadsto \]
    8. Simplified56.9
      \[\leadsto \]
    9. Taylor expanded around 0 29.4
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification31.7
    \[\leadsto \]
Reproduce
herbie shell --seed 2020179 
(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))))