Average Error: 15.6 → 1.0
Time: 9.9s
Precision: 64
Internal Precision: 128
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
\[\frac{\sqrt[3]{g}}{\sqrt[3]{\sqrt[3]{2 \cdot a} \cdot \left(\sqrt[3]{2 \cdot a} \cdot \sqrt[3]{2 \cdot a}\right)}}\]

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 cbrt-div0.8

    \[\leadsto \color{blue}{\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}}\]
  4. Using strategy rm
  5. Applied add-cbrt-cube1.0

    \[\leadsto \frac{\sqrt[3]{g}}{\color{blue}{\sqrt[3]{\left(\sqrt[3]{2 \cdot a} \cdot \sqrt[3]{2 \cdot a}\right) \cdot \sqrt[3]{2 \cdot a}}}}\]
  6. Final simplification1.0

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

Reproduce

herbie shell --seed 2019050 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))