Average Error: 0.1 → 0.1
Time: 22.8s
Precision: 64
Internal Precision: 128
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{\sqrt[3]{\left(\cos v \cdot e\right) \cdot \left(\left(\cos v \cdot e\right) \cdot \left(\cos v \cdot e\right)\right)} + 1}\]

Error

Bits error versus e

Bits error versus v

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  2. Initial simplification0.1

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

  3. Taylor expanded around -inf 0.1

    \[\leadsto \frac{e \cdot \sin v}{\color{blue}{e \cdot \cos v} + 1}\]
  4. Using strategy rm

  5. Applied add-cbrt-cube0.1

    \[\leadsto \frac{e \cdot \sin v}{\color{blue}{\sqrt[3]{\left(\left(e \cdot \cos v\right) \cdot \left(e \cdot \cos v\right)\right) \cdot \left(e \cdot \cos v\right)}} + 1}\]

  6. Final simplification0.1

    \[\leadsto \frac{e \cdot \sin v}{\sqrt[3]{\left(\cos v \cdot e\right) \cdot \left(\left(\cos v \cdot e\right) \cdot \left(\cos v \cdot e\right)\right)} + 1}\]

Runtime

Time bar (total: 22.8s)Debug logProfile

herbie shell --seed 2018346 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))