Average Error: 15.5 → 0.9
Time: 33.8s
Precision: 64
Internal Precision: 576
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\left(\left(\sqrt[3]{g} \cdot \left(\sqrt[3]{\sqrt[3]{\frac{-1}{2}}} \cdot \sqrt[3]{\sqrt[3]{\frac{-1}{2}}}\right)\right) \cdot \sqrt[3]{\sqrt[3]{\frac{-1}{2}}}\right) \cdot \sqrt[3]{\frac{-1}{a}}\]

Error

Bits error versus g

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.5

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

  3. Applied cbrt-div0.9

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

  4. Taylor expanded around -inf 62.8

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

  5. Applied simplify0.9

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

  7. Applied add-cube-cbrt0.9

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

  8. Applied associate-*r*0.9

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

Runtime

Time bar (total: 33.8s)Debug logProfile

herbie shell --seed 2018167 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))