subtraction fraction

Average Error: 0.0 → 0.0

Time: 6.7min

Precision: binary64

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

Math

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

↓

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

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 neg-mul-1 0.0

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

4. Applied associate-/l* 0.0

   \[\leadsto \color{blue}{\frac{-1}{\frac{f - n}{f + n}}}\]
5. Using strategy rm

6. Applied add-log-exp 0.0

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

7. Final simplification 0.0

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

Reproduce

herbie shell --seed 2020181 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (neg (+ f n)) (- f n)))