Average Error: 15.5 → 0.9
Time: 22.0s
Precision: 64
Internal Precision: 384
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\sqrt[3]{\frac{\frac{1}{2}}{a}}}{\sqrt[3]{\frac{1}{g}}}\]

Error

Bits error versus g

Bits error versus a

Derivation

  1. Initial program 15.5

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

  3. Applied cbrt-div0.8

    \[\leadsto \color{blue}{\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}}\]
  4. 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 0 48.8

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

  7. Applied simplify0.9

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

Runtime

Time bar (total: 22.0s)Debug logProfile

herbie shell --seed '#(1070991898 1055468627 4280279443 640792587 928206309 3646738750)' 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))