Average Error: 0.0 → 0.0
Time: 3.7s
Precision: binary64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\sqrt[3]{\log \left(e^{{\left(\frac{-\left(f + n\right)}{f - n}\right)}^{3}}\right)}\]

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-cbrt-cube43.3

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

  4. Applied add-cbrt-cube44.3

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

  5. Applied cbrt-undiv44.3

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

  6. Simplified0.0

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\frac{-\left(f + n\right)}{f - n}\right)}^{3}}}\]
  7. Using strategy rm

  8. Applied add-log-exp0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020156 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (neg (+ f n)) (- f n)))