Average Error: 0.0 → 0.0
Time: 25.8s
Precision: 64
Internal Precision: 320
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\sqrt{-3 \cdot \left(v \cdot v\right) + 1} \cdot \log \left(e^{\frac{1 - v \cdot v}{\frac{4}{\sqrt{2}}}}\right)\]

Error

Bits error versus v

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Results

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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

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

  4. Applied add-log-exp0.0

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

  5. Final simplification0.0

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

Runtime

Time bar (total: 25.8s)Debug logProfile

herbie shell --seed 2018255 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))