Average Error: 15.3 → 0.8
Time: 21.7s
Precision: 64
Internal Precision: 576
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}\]

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 15.3

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

  3. Applied cbrt-div0.8

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

  4. Taylor expanded around -inf 62.8

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

  5. Simplified0.8

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

  6. Taylor expanded around inf 0.8

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

  7. Final simplification0.8

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

Runtime

Time bar (total: 21.7s)Debug logProfile

herbie shell --seed 2018234 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))