Average Error: 38.1 → 8.7
Time: 15.0s
Precision: 64
Internal Precision: 2368
$\log \left(1 - \frac{\ell - r}{\ell}\right)$
$\begin{array}{l} \mathbf{if}\;r \le 3.6202312021135434 \cdot 10^{-294}:\\ \;\;\;\;\log \left(\frac{r}{\ell}\right)\\ \mathbf{else}:\\ \;\;\;\;\log r - \log \ell\\ \end{array}$

# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Split input into 2 regimes
2. ## if r < 3.6202312021135434e-294

1. Initial program 39.0

$\log \left(1 - \frac{\ell - r}{\ell}\right)$
2. Initial simplification16.2

$\leadsto \log \left(\frac{r}{\ell}\right)$

## if 3.6202312021135434e-294 < r

1. Initial program 37.1

$\log \left(1 - \frac{\ell - r}{\ell}\right)$
2. Initial simplification15.2

$\leadsto \log \left(\frac{r}{\ell}\right)$
3. Using strategy rm
4. Applied log-div0.6

$\leadsto \color{blue}{\log r - \log \ell}$
3. Recombined 2 regimes into one program.
4. Final simplification8.7

$\leadsto \begin{array}{l} \mathbf{if}\;r \le 3.6202312021135434 \cdot 10^{-294}:\\ \;\;\;\;\log \left(\frac{r}{\ell}\right)\\ \mathbf{else}:\\ \;\;\;\;\log r - \log \ell\\ \end{array}$

# Runtime

Time bar (total: 15.0s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)'
(FPCore (l r)
:name "log(1 - (l - r) / l)"
(log (- 1 (/ (- l r) l))))