Average Error: 15.0 → 0.9
Time: 12.0s
Precision: 64
Internal Precision: 576
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\sqrt[3]{g}}{\sqrt[3]{a \cdot 2}}\]

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 15.0

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

  2. Initial simplification15.0

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

  4. Applied div-inv15.0

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

  5. Applied cbrt-prod0.9

    \[\leadsto \color{blue}{\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{a \cdot 2}}}\]
  6. Using strategy rm

  7. Applied cbrt-div0.9

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

  8. Applied associate-*r/0.9

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

  9. Final simplification0.9

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

Runtime

Time bar (total: 12.0s)Debug logProfile

herbie shell --seed 2018273 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))