Average Error: 14.8 → 0.8
Time: 16.0s
Precision: 64
Internal Precision: 128
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\left(\sqrt[3]{\frac{-1}{2}} \cdot \sqrt[3]{\frac{-1}{a}}\right) \cdot \sqrt[3]{g}\]

Error

Bits error versus g

Bits error versus a

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Your Program's Arguments

Results

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Derivation

  1. Initial program 14.8

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

  2. Initial simplification14.8

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

  4. Applied div-inv14.8

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

  5. Applied cbrt-prod0.9

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

  6. Taylor expanded around -inf 33.7

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

  7. Simplified0.8

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

  8. Final simplification0.8

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

Runtime

Time bar (total: 16.0s)Debug logProfile

herbie shell --seed 2018278 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))