Average Error: 0.1 → 0.1
Time: 21.6s
Precision: 64
Internal Precision: 576
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{\frac{e \cdot \sin v}{\sqrt{\log \left(e^{\cos v \cdot e}\right) + 1}}}{\sqrt{\cos v \cdot e + 1}}\]

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. Initial simplification0.1

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

  4. Applied add-log-exp0.1

    \[\leadsto \frac{e \cdot \sin v}{\color{blue}{\log \left(e^{\cos v \cdot e}\right)} + 1}\]
  5. Using strategy rm

  6. Applied add-sqr-sqrt0.1

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

  7. Applied associate-/r*0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Runtime

Time bar (total: 21.6s)Debug logProfile

herbie shell --seed 2018242 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))