subtraction fraction

Average Error: 0.0 → 0.0

Time: 2.6s

Precision: binary64

Math

\[\frac{-\left(f + n\right)}{f - n}\]

↓

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

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-exp 0.0

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

5. Applied *-un-lft-identity 0.0

   \[\leadsto \log \left(e^{\frac{-\left(f + n\right)}{\color{blue}{1 \cdot \left(f - n\right)}}}\right)\]

6. Applied *-un-lft-identity 0.0

   \[\leadsto \log \left(e^{\frac{\color{blue}{1 \cdot \left(-\left(f + n\right)\right)}}{1 \cdot \left(f - n\right)}}\right)\]

7. Applied times-frac 0.0

   \[\leadsto \log \left(e^{\color{blue}{\frac{1}{1} \cdot \frac{-\left(f + n\right)}{f - n}}}\right)\]

8. Applied exp-prod 0.0

   \[\leadsto \log \color{blue}{\left({\left(e^{\frac{1}{1}}\right)}^{\left(\frac{-\left(f + n\right)}{f - n}\right)}\right)}\]

9. Simplified 0.0

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

10. Final simplification 0.0

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

Reproduce

herbie shell --seed 2020157 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (neg (+ f n)) (- f n)))