Average Error: 15.1 → 0.8
Time: 29.9s
Precision: 64
Internal Precision: 576
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{g \cdot \frac{-1}{2}} \cdot \sqrt[3]{\frac{-1}{a}}\]

Error

Bits error versus g

Bits error versus a

Derivation

  1. Initial program 15.1

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

  3. Applied div-inv15.1

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

  4. Applied cbrt-prod0.9

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

  5. Taylor expanded around -inf 62.7

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

  6. Applied simplify0.9

    \[\leadsto \color{blue}{\left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{-1}{2}}\right) \cdot \sqrt[3]{\frac{-1}{a}}}\]
  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: 29.9s)Debug logProfile

herbie shell --seed '#(1071821486 549052472 3784827256 1559736200 3548510075 881134285)' +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))