Error

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 add-log-exp0.0

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

5. Applied add-cube-cbrt0.0

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

6. Applied log-prod0.0

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

7. Simplified0.0

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

8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019053 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))