Average Error: 15.9 → 0.9
Time: 15.5s
Precision: 64
Internal Precision: 576
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\left(\sqrt[3]{\frac{-1}{2}} \cdot \sqrt[3]{g}\right) \cdot \sqrt[3]{\frac{-1}{a}}\]

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 15.9

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

  3. Applied div-inv15.9

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

  4. Applied cbrt-prod0.9

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

  5. Taylor expanded around -inf 34.0

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

  6. Simplified0.8

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

  8. Applied associate-*r*0.9

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

  9. Final simplification0.9

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

Runtime

Time bar (total: 15.5s)Debug logProfile

herbie shell --seed 2018256 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))