Average Error: 58.6 → 0.6
Time: 4.3s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double eps) {
	return ((double) log(((double) (((double) (1.0 - eps)) / ((double) (1.0 + eps))))));
}

↓
double code(double eps) {
	return ((double) (((double) log(1.0)) + ((double) (2.0 * ((double) (((double) (eps * ((double) (eps - ((double) (eps / ((double) (1.0 * 1.0)))))))) - eps))))));
}

Error
Bits error versus eps
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original58.6
Target0.2
Herbie0.6
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Derivation
  1. Initial program 58.6
    \[\]
  2. Taylor expanded around 0 0.6
    \[\leadsto \]
  3. Simplified0.6
    \[\leadsto \]
  4. Final simplification0.6
    \[\leadsto \]
Reproduce
herbie shell --seed 2020180 
(FPCore (eps)
  :name "logq (problem 3.4.3)"
  :precision binary64

  :herbie-target
  (* -2.0 (+ (+ eps (/ (pow eps 3.0) 3.0)) (/ (pow eps 5.0) 5.0)))

  (log (/ (- 1.0 eps) (+ 1.0 eps))))