Average Error: 39.2 → 39.2
Time: 2.0s
Precision: binary64
\[\log \left(1 - \frac{\ell - r}{\ell}\right)\]
↓
\[\log \left(1 - \frac{\ell - r}{\ell}\right)\]
\log \left(1 - \frac{\ell - r}{\ell}\right)
↓
\log \left(1 - \frac{\ell - r}{\ell}\right)
double code(double l, double r) {
	return ((double) log(((double) (1.0 - ((double) (((double) (l - r)) / l))))));
}
↓
double code(double l, double r) {
	return ((double) log(((double) (1.0 - ((double) (((double) (l - r)) / l))))));
}

Error

Bits error versus l

Bits error versus r

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 39.2

    \[\log \left(1 - \frac{\ell - r}{\ell}\right)\]

  2. Final simplification39.2

    \[\leadsto \log \left(1 - \frac{\ell - r}{\ell}\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (l r)
  :name "(log (- 1 (/ (- l r) l)))"
  :precision binary64
  (log (- 1.0 (/ (- l r) l))))