Average Error: 60.2 → 49.6
Time: 13.5s
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) {
	return ((double) (((double) (1.0 / ((double) (a + ((double) (((double) log(1.0)) + ((double) (eps * ((double) (0.5 * ((double) pow(((double) log(1.0)), 2.0)))))))))))) * ((double) (((double) (((double) pow(((double) exp(((double) (a + b)))), eps)) - 1.0)) / ((double) (((double) pow(((double) exp(b)), eps)) - 1.0))))));
}

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
Target15.0
Herbie49.6
\[\]
Derivation
  1. Initial program 60.2
    \[\]
  2. Simplified60.4
    \[\leadsto \]
  3. Taylor expanded around 0 54.5
    \[\leadsto \]
  4. Simplified54.5
    \[\leadsto \]
  5. Using strategy rm
  6. Applied *-un-lft-identity54.5
    \[\leadsto \]
  7. Applied times-frac54.5
    \[\leadsto \]
  8. Applied associate-*r*54.5
    \[\leadsto \]
  9. Simplified49.6
    \[\leadsto \]
  10. Final simplification49.6
    \[\leadsto \]
Reproduce
herbie shell --seed 2020181 
(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))))