Average Error: 0.1 → 0.1
Time: 25.5s
Precision: 64
Internal Precision: 576
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
\[\sin v \cdot \left(\frac{1}{(\left(\cos v\right) \cdot e + 1)_*} \cdot e\right)\]

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. Initial simplification0.1

    \[\leadsto \frac{\sin v}{(\left(\cos v\right) \cdot e + 1)_*} \cdot e\]
  3. Using strategy rm
  4. Applied div-inv0.1

    \[\leadsto \color{blue}{\left(\sin v \cdot \frac{1}{(\left(\cos v\right) \cdot e + 1)_*}\right)} \cdot e\]
  5. Applied associate-*l*0.1

    \[\leadsto \color{blue}{\sin v \cdot \left(\frac{1}{(\left(\cos v\right) \cdot e + 1)_*} \cdot e\right)}\]
  6. Final simplification0.1

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

Runtime

Time bar (total: 25.5s)Debug logProfile

herbie shell --seed 2018234 +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))