Average Error: 0.1 → 0.2
Time: 23.3s
Precision: 64
Internal Precision: 384
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{\frac{e \cdot \sin v}{\sqrt[3]{1 + e \cdot \cos v} \cdot \sqrt[3]{1 + e \cdot \cos v}}}{\sqrt[3]{1 + e \cdot \cos v}}\]

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 add-cube-cbrt0.2

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

  4. Applied associate-/r*0.2

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

Runtime

Time bar (total: 23.3s)Debug logProfile

herbie shell --seed '#(1070833653 108281690 3330367898 3632331308 3494323072 43156186)' 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))