Average Error: 0.0 → 0.0
Time: 2.5m
Precision: 64
Internal Precision: 384
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\sqrt[3]{\frac{\sqrt{2}}{4} \cdot \left(\left(\left(1 - v \cdot \left(v \cdot 3\right)\right) \cdot \frac{\frac{2}{4}}{4}\right) \cdot \sqrt{1 - v \cdot \left(v \cdot 3\right)}\right)} \cdot \left(1 - v \cdot v\right)\]

Error

Bits error versus v

Derivation

  1. Initial program 0.0

    \[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
  2. Using strategy rm

  3. Applied add-cbrt-cube0.0

    \[\leadsto \color{blue}{\sqrt[3]{\left(\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right)\right) \cdot \left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right)}} \cdot \left(1 - v \cdot v\right)\]

  4. Applied simplify0.0

    \[\leadsto \sqrt[3]{\color{blue}{\frac{\sqrt{2}}{4} \cdot \left(\left(\left(1 - v \cdot \left(v \cdot 3\right)\right) \cdot \frac{\frac{2}{4}}{4}\right) \cdot \sqrt{1 - v \cdot \left(v \cdot 3\right)}\right)}} \cdot \left(1 - v \cdot v\right)\]
  5. Removed slow pow expressions.

Runtime

Time bar (total: 2.5m)Debug logProfile

herbie shell --seed '#(1063282112 2455465480 4141627379 3773598652 1647277307 776739644)' 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))