Average Error: 0.1 → 0.1
Time: 25.8s
Precision: 64
Internal Precision: 576
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\left(e \cdot \sin v\right) \cdot \frac{1}{(\left(\cos v\right) \cdot e + 1)_*}\]

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. Using strategy rm

  3. Applied div-inv0.1

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

  4. Applied simplify0.1

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

Runtime

Time bar (total: 25.8s)Debug logProfile

herbie shell --seed 2018207 +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))