Average Error: 0.0 → 0.0
Time: 26.2s
Precision: 64
Ground Truth: 128
\[\frac{-\left(f + n\right)}{f - n}\]
\[\sqrt[3]{\frac{-\left(n + f\right)}{f - n}} \cdot \sqrt[3]{{\left(\frac{f + n}{f - n}\right)}^2}\]

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-cube 41.1

    \[\leadsto \frac{-\left(f + n\right)}{\color{blue}{\sqrt[3]{{\left(f - n\right)}^3}}}\]
  4. Applied add-cbrt-cube 41.3

    \[\leadsto \frac{\color{blue}{\sqrt[3]{{\left(-\left(f + n\right)\right)}^3}}}{\sqrt[3]{{\left(f - n\right)}^3}}\]
  5. Applied cbrt-undiv 41.3

    \[\leadsto \color{blue}{\sqrt[3]{\frac{{\left(-\left(f + n\right)\right)}^3}{{\left(f - n\right)}^3}}}\]
  6. Applied simplify 0.0

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\frac{-\left(n + f\right)}{f - n}\right)}^3}}\]
  7. Using strategy rm
  8. Applied cube-mult 0.0

    \[\leadsto \sqrt[3]{\color{blue}{\frac{-\left(n + f\right)}{f - n} \cdot \left(\frac{-\left(n + f\right)}{f - n} \cdot \frac{-\left(n + f\right)}{f - n}\right)}}\]
  9. Applied cbrt-prod 0.0

    \[\leadsto \color{blue}{\sqrt[3]{\frac{-\left(n + f\right)}{f - n}} \cdot \sqrt[3]{\frac{-\left(n + f\right)}{f - n} \cdot \frac{-\left(n + f\right)}{f - n}}}\]
  10. Applied simplify 0.0

    \[\leadsto \sqrt[3]{\frac{-\left(n + f\right)}{f - n}} \cdot \color{blue}{\sqrt[3]{{\left(\frac{f + n}{f - n}\right)}^2}}\]
  11. Removed slow pow expressions

Runtime

Total time: 26.2s Debug log

Please include this information when filing a bug report:

herbie --seed '#(2329068606 3400991835 1858401710 3916298419 314755441 837447755)'
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))