Average Error: 14.8 → 0.9
Time: 33.7s
Precision: 64
Internal Precision: 384
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\sqrt[3]{g}}{\sqrt[3]{a}} \cdot {\left(\frac{2}{1}\right)}^{\left(-\frac{1}{3}\right)}\]

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. Using strategy rm

  5. Applied clear-num0.8

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

  6. Taylor expanded around inf 34.0

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

  7. Applied simplify0.9

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

Runtime

Time bar (total: 33.7s)Debug logProfile

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