Average Error: 14.9 → 0.9
Time: 16.5s
Precision: 64
Internal Precision: 576
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{1}{\sqrt[3]{\frac{1}{g}} \cdot \sqrt[3]{\frac{-2}{\frac{-1}{a}}}}\]

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 14.9

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

  3. Applied cbrt-div0.8

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

  5. Applied *-un-lft-identity0.8

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

  6. Applied associate-/l*0.9

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

  7. Taylor expanded around inf 48.3

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

  8. Simplified0.9

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

  9. Taylor expanded around -inf 62.7

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

  10. Simplified0.9

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

  11. Final simplification0.9

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

Runtime

Time bar (total: 16.5s)Debug logProfile

herbie shell --seed 2018254 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))