Average Error: 0.0 → 0.0
Time: 5.8m
Precision: 64
Internal Precision: 128
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\sqrt[3]{\left(-\frac{f + n}{f - n}\right) \cdot \left(\frac{f + n}{f - n} \cdot \frac{f + n}{f - n}\right)}\]

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-cube0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019088 
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))