Average Error: 0.0 → 0.0
Time: 57.5s
Precision: 64
Internal Precision: 320
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\sqrt{(-3 \cdot \left(v \cdot v\right) + 1)_*} \cdot \left(\left(1 - v \cdot v\right) \cdot \frac{\sqrt{2}}{4}\right)\]

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. Applied simplify0.0

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

Runtime

Time bar (total: 57.5s)Debug logProfile

herbie shell --seed '#(1071373924 2949776965 1885069702 3247780810 90874544 2263903749)' +o rules:numerics
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))