Average Error: 15.1 → 0.9
Time: 17.2s
Precision: 64
Internal Precision: 128
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{1}{2}} \cdot \frac{\sqrt[3]{g}}{\sqrt[3]{a}}\]

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 15.1

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

  3. Applied div-inv15.1

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

  4. Applied cbrt-prod0.9

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

  5. Taylor expanded around 0 33.4

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

  6. Simplified0.8

    \[\leadsto \sqrt[3]{g} \cdot \color{blue}{\left(\sqrt[3]{\frac{1}{a}} \cdot \sqrt[3]{\frac{1}{2}}\right)}\]
  7. Using strategy rm

  8. Applied associate-*r*0.8

    \[\leadsto \color{blue}{\left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{a}}\right) \cdot \sqrt[3]{\frac{1}{2}}}\]
  9. Using strategy rm

  10. Applied cbrt-div0.9

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

  11. Applied associate-*r/0.9

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

  12. Final simplification0.9

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

Runtime

Time bar (total: 17.2s)Debug logProfile

herbie shell --seed 2018349 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))