Average Error: 0.1 → 0.1
Time: 23.8s
Precision: 64
Internal Precision: 128
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\left(\frac{1}{1 - \left(e \cdot \cos v\right) \cdot \left(e \cdot \cos v\right)} \cdot \left(1 - e \cdot \cos v\right)\right) \cdot \left(e \cdot \sin v\right)\]

Error

Bits error versus e

Bits error versus v

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Your Program's Arguments

Results

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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. Using strategy rm

  5. Applied flip-+0.1

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

  6. Applied associate-/r/0.1

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

  7. Final simplification0.1

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

Runtime

Time bar (total: 23.8s)Debug logProfile

herbie shell --seed 2018285 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))