Average Error: 1.0 → 0.0
Time: 3.4m
Precision: 64
Internal Precision: 384
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{4}{e^{\left(\log \left(3 \cdot \pi\right) + \log \left(1 - v \cdot v\right)\right) + \log \left(\sqrt{2 - 6 \cdot \left(v \cdot v\right)}\right)}}\]

Error

Bits error versus v

Derivation

  1. Initial program 1.0

    \[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
  2. Using strategy rm

  3. Applied add-exp-log1.0

    \[\leadsto \frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \color{blue}{e^{\log \left(\sqrt{2 - 6 \cdot \left(v \cdot v\right)}\right)}}}\]

  4. Applied add-exp-log1.0

    \[\leadsto \frac{4}{\left(\left(3 \cdot \pi\right) \cdot \color{blue}{e^{\log \left(1 - v \cdot v\right)}}\right) \cdot e^{\log \left(\sqrt{2 - 6 \cdot \left(v \cdot v\right)}\right)}}\]

  5. Applied add-exp-log1.0

    \[\leadsto \frac{4}{\left(\color{blue}{e^{\log \left(3 \cdot \pi\right)}} \cdot e^{\log \left(1 - v \cdot v\right)}\right) \cdot e^{\log \left(\sqrt{2 - 6 \cdot \left(v \cdot v\right)}\right)}}\]

  6. Applied prod-exp1.0

    \[\leadsto \frac{4}{\color{blue}{e^{\log \left(3 \cdot \pi\right) + \log \left(1 - v \cdot v\right)}} \cdot e^{\log \left(\sqrt{2 - 6 \cdot \left(v \cdot v\right)}\right)}}\]

  7. Applied prod-exp0.0

    \[\leadsto \frac{4}{\color{blue}{e^{\left(\log \left(3 \cdot \pi\right) + \log \left(1 - v \cdot v\right)\right) + \log \left(\sqrt{2 - 6 \cdot \left(v \cdot v\right)}\right)}}}\]

Runtime

Time bar (total: 3.4m)Debug logProfile

herbie shell --seed '#(1064397287 3527694221 3797617954 1138343853 2854031332 1153838279)' 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))