Average Error: 15.2 → 0.9
Time: 38.4s
Precision: 64
Internal Precision: 576
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{-1}{a}} \cdot \left(\left(\sqrt[3]{\sqrt[3]{\frac{-1}{2}}} \cdot \sqrt[3]{\sqrt[3]{\frac{-1}{2}}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{\frac{-1}{2}}} \cdot \sqrt[3]{g}\right)\right)\]

Error

Bits error versus g

Bits error versus a

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.2

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

  3. Applied div-inv15.2

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

  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

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

  6. Applied simplify0.9

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

  8. Applied add-cube-cbrt0.9

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

  9. Applied associate-*l*0.9

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

Runtime

Time bar (total: 38.4s)Debug logProfile

herbie shell --seed 2018296 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))