Average Error: 0.0 → 0.0
Time: 3.1s
Precision: binary64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\sqrt[3]{{\left(\frac{-1}{\frac{f - n}{f + n}}\right)}^{3}}\]

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 neg-mul-10.0

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

  4. Applied associate-/l*0.0

    \[\leadsto \color{blue}{\frac{-1}{\frac{f - n}{f + n}}}\]
  5. Using strategy rm

  6. Applied add-cbrt-cube41.9

    \[\leadsto \frac{-1}{\frac{f - n}{\color{blue}{\sqrt[3]{\left(\left(f + n\right) \cdot \left(f + n\right)\right) \cdot \left(f + n\right)}}}}\]

  7. Applied add-cbrt-cube41.8

    \[\leadsto \frac{-1}{\frac{\color{blue}{\sqrt[3]{\left(\left(f - n\right) \cdot \left(f - n\right)\right) \cdot \left(f - n\right)}}}{\sqrt[3]{\left(\left(f + n\right) \cdot \left(f + n\right)\right) \cdot \left(f + n\right)}}}\]

  8. Applied cbrt-undiv41.8

    \[\leadsto \frac{-1}{\color{blue}{\sqrt[3]{\frac{\left(\left(f - n\right) \cdot \left(f - n\right)\right) \cdot \left(f - n\right)}{\left(\left(f + n\right) \cdot \left(f + n\right)\right) \cdot \left(f + n\right)}}}}\]

  9. Applied add-cbrt-cube41.8

    \[\leadsto \frac{\color{blue}{\sqrt[3]{\left(-1 \cdot -1\right) \cdot -1}}}{\sqrt[3]{\frac{\left(\left(f - n\right) \cdot \left(f - n\right)\right) \cdot \left(f - n\right)}{\left(\left(f + n\right) \cdot \left(f + n\right)\right) \cdot \left(f + n\right)}}}\]

  10. Applied cbrt-undiv41.8

    \[\leadsto \color{blue}{\sqrt[3]{\frac{\left(-1 \cdot -1\right) \cdot -1}{\frac{\left(\left(f - n\right) \cdot \left(f - n\right)\right) \cdot \left(f - n\right)}{\left(\left(f + n\right) \cdot \left(f + n\right)\right) \cdot \left(f + n\right)}}}}\]

  11. Simplified0.0

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\frac{-1}{\frac{f - n}{f + n}}\right)}^{3}}}\]

  12. Final simplification0.0

    \[\leadsto \sqrt[3]{{\left(\frac{-1}{\frac{f - n}{f + n}}\right)}^{3}}\]

Reproduce

herbie shell --seed 2020162 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (neg (+ f n)) (- f n)))