Average Error: 15.3 → 0.8
Time: 26.0s
Precision: 64
Internal Precision: 384
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{g \cdot \frac{-1}{2}} \cdot \sqrt[3]{\frac{-1}{a}}\]

Error

Bits error versus g

Bits error versus a

Derivation

  1. Initial program 15.3

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

  3. Applied div-inv15.3

    \[\leadsto \sqrt[3]{\color{blue}{g \cdot \frac{1}{2 \cdot a}}}\]

  4. Applied cbrt-prod0.8

    \[\leadsto \color{blue}{\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}}\]

  5. Taylor expanded around -inf 62.8

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

  6. Applied simplify0.8

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

  8. Applied cbrt-unprod0.8

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

Runtime

Time bar (total: 26.0s)Debug logProfile

herbie shell --seed '#(1070131407 1246090267 3027482374 2150728003 2026520792 2347815650)' 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))