Average Error: 15.2 → 0.9
Time: 16.2s
Precision: 64
Internal Precision: 128
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\frac{1}{\sqrt{\frac{\sqrt[3]{2 \cdot a}}{\sqrt[3]{g}}}}}{\sqrt{\frac{\sqrt[3]{2 \cdot a}}{\sqrt[3]{g}}}}\]

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. Initial simplification15.2

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

  4. Applied cbrt-div0.8

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

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

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

  7. Applied associate-/l*0.8

    \[\leadsto \color{blue}{\frac{1}{\frac{\sqrt[3]{a \cdot 2}}{\sqrt[3]{g}}}}\]
  8. Using strategy rm

  9. Applied add-sqr-sqrt0.9

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

  10. Applied associate-/r*0.9

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

  11. Final simplification0.9

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

Runtime

Time bar (total: 16.2s)Debug logProfile

herbie shell --seed 2018274 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))