Average Error: 14.8 → 0.8
Time: 19.0s
Precision: 64
Internal Precision: 384
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{-1}{2}}\right) \cdot \sqrt[3]{\frac{-1}{a}}\]

Error

Bits error versus g

Bits error versus a

Derivation

  1. Initial program 14.8

    \[\sqrt[3]{\frac{g}{2 \cdot a}}\]
  2. Using strategy rm

  3. Applied cbrt-div0.8

    \[\leadsto \color{blue}{\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}}\]

  4. Taylor expanded around -inf 62.8

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

  5. Applied simplify0.8

    \[\leadsto \color{blue}{\left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{-1}{2}}\right) \cdot \sqrt[3]{\frac{-1}{a}}}\]

Runtime

Time bar (total: 19.0s)Debug logProfile

herbie shell --seed '#(1070355188 2193211668 3977393919 3454156579 3755371326 1656365382)' 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))