\[\frac{-\left(f + n\right)}{f - n}\]
Test:
subtraction fraction
Bits:
128 bits
Bits error versus f
Bits error versus n
Time: 7.1 s
Input Error: 0.1
Output Error: 0.1
Log: ⚲
Profile: 🕒
\(\log \left({e}^{\left(\frac{-\left(f + n\right)}{f - n}\right)}\right)\)
  1. Started with
    \[\frac{-\left(f + n\right)}{f - n}\]
    0.1
  2. Using strategy rm
    0.1
  3. Applied add-log-exp to get
    \[\color{red}{\frac{-\left(f + n\right)}{f - n}} \leadsto \color{blue}{\log \left(e^{\frac{-\left(f + n\right)}{f - n}}\right)}\]
    0.1
  4. Using strategy rm
    0.1
  5. Applied *-un-lft-identity to get
    \[\log \left(e^{\frac{-\left(f + n\right)}{\color{red}{f - n}}}\right) \leadsto \log \left(e^{\frac{-\left(f + n\right)}{\color{blue}{1 \cdot \left(f - n\right)}}}\right)\]
    0.1
  6. Applied *-un-lft-identity to get
    \[\log \left(e^{\frac{\color{red}{-\left(f + n\right)}}{1 \cdot \left(f - n\right)}}\right) \leadsto \log \left(e^{\frac{\color{blue}{1 \cdot \left(-\left(f + n\right)\right)}}{1 \cdot \left(f - n\right)}}\right)\]
    0.1
  7. Applied times-frac to get
    \[\log \left(e^{\color{red}{\frac{1 \cdot \left(-\left(f + n\right)\right)}{1 \cdot \left(f - n\right)}}}\right) \leadsto \log \left(e^{\color{blue}{\frac{1}{1} \cdot \frac{-\left(f + n\right)}{f - n}}}\right)\]
    0.1
  8. Applied exp-prod to get
    \[\log \color{red}{\left(e^{\frac{1}{1} \cdot \frac{-\left(f + n\right)}{f - n}}\right)} \leadsto \log \color{blue}{\left({\left(e^{\frac{1}{1}}\right)}^{\left(\frac{-\left(f + n\right)}{f - n}\right)}\right)}\]
    0.1
  9. Applied simplify to get
    \[\log \left({\color{red}{\left(e^{\frac{1}{1}}\right)}}^{\left(\frac{-\left(f + n\right)}{f - n}\right)}\right) \leadsto \log \left({\color{blue}{e}}^{\left(\frac{-\left(f + n\right)}{f - n}\right)}\right)\]
    0.1

Original test:


(lambda ((f default) (n default))
  #:name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))