Average Error: 15.3 → 0.8
Time: 19.2s
Precision: 64
Internal Precision: 576
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}\]

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 15.3

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

  2. Initial simplification15.3

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

  4. Applied cbrt-div0.8

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

  5. Taylor expanded around -inf 62.8

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

  6. Simplified0.8

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

  7. Taylor expanded around 0 0.8

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

  8. Final simplification0.8

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

Runtime

Time bar (total: 19.2s)Debug logProfile

herbie shell --seed 2018234 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))