subtraction fraction

Average Error: 0.0 → 0.0

Time: 10.6s

Precision: binary64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

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

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 add-cbrt-cube 41.7

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

4. Applied add-cbrt-cube 42.5

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

5. Applied cbrt-undiv 42.5

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

6. Simplified 0.0

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

8. Applied neg-mul-1 0.0

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

9. Applied associate-/l* 0.0

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

10. Final simplification 0.0

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

Reproduce

herbie shell --seed 2020182 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (neg (+ f n)) (- f n)))