Average Error: 0.0 → 0.0
Time: 32.6s
Precision: 64
Internal Precision: 320
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\frac{\left(\sqrt{2} - \sqrt{2} \cdot {v}^{4}\right) \cdot \sqrt{1 + \left(v \cdot v\right) \cdot -3}}{\left(1 + v \cdot v\right) \cdot 4}\]

Error

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Using strategy rm

  3. Applied flip--0.0

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

  4. Applied associate-*l/0.0

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

  5. Applied frac-times0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Runtime

Time bar (total: 32.6s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes0.00.00.00.00%
herbie shell --seed 2018274 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))