Average Error: 0.0 → 0.0
Time: 3.2s
Precision: binary64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\log \left(e^{\sqrt[3]{{\left(\frac{-\left(f + n\right)}{f - n}\right)}^{3}}}\right)\]

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-cbrt-cube41.2

    \[\leadsto \log \left(e^{\frac{-\left(f + n\right)}{\color{blue}{\sqrt[3]{\left(\left(f - n\right) \cdot \left(f - n\right)\right) \cdot \left(f - n\right)}}}}\right)\]

  6. Applied add-cbrt-cube42.0

    \[\leadsto \log \left(e^{\frac{\color{blue}{\sqrt[3]{\left(\left(-\left(f + n\right)\right) \cdot \left(-\left(f + n\right)\right)\right) \cdot \left(-\left(f + n\right)\right)}}}{\sqrt[3]{\left(\left(f - n\right) \cdot \left(f - n\right)\right) \cdot \left(f - n\right)}}}\right)\]

  7. Applied cbrt-undiv42.0

    \[\leadsto \log \left(e^{\color{blue}{\sqrt[3]{\frac{\left(\left(-\left(f + n\right)\right) \cdot \left(-\left(f + n\right)\right)\right) \cdot \left(-\left(f + n\right)\right)}{\left(\left(f - n\right) \cdot \left(f - n\right)\right) \cdot \left(f - n\right)}}}}\right)\]

  8. Simplified0.0

    \[\leadsto \log \left(e^{\sqrt[3]{\color{blue}{{\left(\frac{-\left(f + n\right)}{f - n}\right)}^{3}}}}\right)\]

  9. Final simplification0.0

    \[\leadsto \log \left(e^{\sqrt[3]{{\left(\frac{-\left(f + n\right)}{f - n}\right)}^{3}}}\right)\]

Reproduce

herbie shell --seed 2020171 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (neg (+ f n)) (- f n)))