Average Error: 0.1 → 0.1
Time: 17.1s
Precision: 64
Internal Precision: 128
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\sin v \cdot \frac{e}{1 + \cos v \cdot e}\]

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. Using strategy rm

  5. Applied associate-/r/0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019051 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))