Average Error: 0.0 → 0.0
Time: 2.9s
Precision: binary64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\sqrt[3]{{\left(\frac{f + n}{n - f}\right)}^{3}}\]

Error

Bits error versus f

Bits error versus n

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  4. Applied add-cbrt-cube41.4

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

  5. Applied add-cbrt-cube42.2

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

  6. Applied cbrt-undiv42.2

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020185 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (neg (+ f n)) (- f n)))