Average Error: 0.0 → 0.0
Time: 2.7m
Precision: 64
Internal Precision: 576
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\sqrt{(\left(v \cdot v\right) \cdot \left(-3\right) + 1)_*} \cdot \left(\frac{\sqrt{2}}{4} \cdot \left(1 - v \cdot v\right)\right)\]

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. Initial simplification0.0

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

  3. Final simplification0.0

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

Runtime

Time bar (total: 2.7m)Debug logProfile

herbie shell --seed 2018221 +o rules:numerics
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))