Average Error: 15.1 → 0.9
Time: 21.9s
Precision: 64
Internal Precision: 320
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\frac{1}{\sqrt[3]{a \cdot 2}}}{\sqrt[3]{\frac{1}{g}}}\]

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 15.1

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

  3. Applied cbrt-div0.9

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

  5. Applied clear-num0.9

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

  7. Applied div-inv0.9

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

  8. Applied associate-/r*0.9

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

  9. Taylor expanded around -inf 62.8

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

  10. Simplified0.9

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

  11. Final simplification0.9

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

Runtime

Time bar (total: 21.9s)Debug logProfile

herbie shell --seed 2018227 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))