Average Error: 0.1 → 0.3
Time: 35.4s
Precision: 64
Internal Precision: 384
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e}{\frac{(\left(\cos v\right) \cdot e + 1)_*}{\sin v}}\]

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 associate-/l*0.3

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

  4. Applied simplify0.3

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

Runtime

Time bar (total: 35.4s)Debug logProfile

herbie shell --seed '#(1070355188 2193211668 3977393919 3454156579 3755371326 1656365382)' +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))