Average Error: 0.1 → 0.1
Time: 22.6s
Precision: 64
Internal Precision: 320
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{(e \cdot \left(\cos v\right) + 1)_*}\]

Error

Bits error versus e

Bits error versus v

Derivation

  1. Initial program 0.1

    \[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]

  2. Applied simplify0.1

    \[\leadsto \color{blue}{\frac{e \cdot \sin v}{(e \cdot \left(\cos v\right) + 1)_*}}\]

Runtime

Time bar (total: 22.6s)Debug logProfile

herbie shell --seed '#(1072330854 3074818769 591214268 3603999196 3863745332 3332387116)' +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))