Average Error: 15.3 → 0.9
Time: 30.6s
Precision: 64
Internal Precision: 576
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\frac{1}{\sqrt[3]{\frac{1}{g}}}}{\sqrt[3]{2 \cdot a}}\]

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. 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. Taylor expanded around inf 48.7

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

  7. Applied simplify0.9

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

Runtime

Time bar (total: 30.6s)Debug logProfile

herbie shell --seed 2018206 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))