Average Error: 15.6 → 0.8
Time: 14.8s
Precision: 64
Internal Precision: 384
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{\frac{1}{2}}{a}} \cdot \sqrt[3]{g}\]

Error

Bits error versus g

Bits error versus a

Derivation

  1. Initial program 15.6

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

  3. Applied div-inv15.7

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

  4. Applied cbrt-prod0.9

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

  5. Taylor expanded around inf 33.9

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

  6. Applied simplify0.8

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

Runtime

Time bar (total: 14.8s)Debug logProfile

herbie shell --seed '#(1070227846 1561819246 480764335 4016816270 2602869839 2117310382)' +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))