Average Error: 15.1 → 0.9
Time: 16.6s
Precision: 64
Internal Precision: 128
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{1}{\frac{\sqrt[3]{2 \cdot a}}{\sqrt[3]{g}}}\]

Error

Bits error versus g

Bits error versus a

Try it out

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. Initial simplification15.1

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

  4. Applied cbrt-div0.9

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

  6. Applied clear-num0.9

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

  7. Taylor expanded around 0 33.4

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

  8. Simplified0.9

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

  9. Final simplification0.9

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

Runtime

Time bar (total: 16.6s)Debug logProfile

herbie shell --seed 2018346 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))