Average Error: 0.0 → 0.0
Time: 28.3s
Precision: 64
Internal Precision: 128
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\log \left(\sqrt{e^{\frac{-\left(n + f\right)}{f - n}}}\right) + \log \left(\sqrt{e^{\frac{-\left(n + f\right)}{f - n}}}\right)\]

Error

Bits error versus f

Bits error versus n

Derivation

  1. Initial program 0.0

    \[\frac{-\left(f + n\right)}{f - n}\]
  2. Using strategy rm

  3. Applied add-log-exp0.0

    \[\leadsto \color{blue}{\log \left(e^{\frac{-\left(f + n\right)}{f - n}}\right)}\]
  4. Using strategy rm

  5. Applied add-sqr-sqrt0.0

    \[\leadsto \log \color{blue}{\left(\sqrt{e^{\frac{-\left(f + n\right)}{f - n}}} \cdot \sqrt{e^{\frac{-\left(f + n\right)}{f - n}}}\right)}\]

  6. Applied log-prod0.0

    \[\leadsto \color{blue}{\log \left(\sqrt{e^{\frac{-\left(f + n\right)}{f - n}}}\right) + \log \left(\sqrt{e^{\frac{-\left(f + n\right)}{f - n}}}\right)}\]

  7. Final simplification0.0

    \[\leadsto \log \left(\sqrt{e^{\frac{-\left(n + f\right)}{f - n}}}\right) + \log \left(\sqrt{e^{\frac{-\left(n + f\right)}{f - n}}}\right)\]

Reproduce

herbie shell --seed 2019051 
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))