Average Error: 0.0 → 0.0
Time: 21.7s
Precision: 64
Internal precision: 128
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot {v}^2}\right) \cdot \left(1 - {v}^2\right)\]
⬇
\[e^{\log \left(\frac{\sqrt{2}}{4}\right) + \log \left(\sqrt{1 - 3 \cdot {v}^2}\right)} \cdot \left(1 - {v}^2\right)\]

Error

Bits error versus v

Derivation

  1. Initial program 0.0

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

  3. Applied add-exp-log 0.0

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

  4. Applied add-exp-log 0.0

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

  5. Applied prod-exp 0.0

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

Runtime

Time bar (total: 21.7s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(445090408 2096966519 1102989176 1729990921 3285957378 3536114456)'
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (sqr v))))) (- 1 (sqr v))))