Average Error: 0.0 → 0.0
Time: 1.2m
Precision: 64
Internal Precision: 384
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\sqrt[3]{\frac{\frac{-\left(n + f\right)}{f - n}}{\frac{f - n}{n + f} \cdot \frac{f - n}{n + f}}}\]

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-cube41.1

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

  4. Applied add-cbrt-cube41.3

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

  5. Applied cbrt-undiv41.3

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

  6. Applied simplify0.0

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

Runtime

Time bar (total: 1.2m)Debug logProfile

herbie shell --seed '#(1070355188 2193211668 3977393919 3454156579 3755371326 1656365382)' 
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))