Average Error: 15.1 → 0.9
Time: 24.0s
Precision: 64
Internal Precision: 128
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\frac{\frac{1}{\sqrt[3]{\frac{\left|\sqrt[3]{2}\right|}{g}}}}{\sqrt[3]{\sqrt{\sqrt[3]{2}}}}}{\sqrt[3]{\sqrt{2} \cdot a}}\]

Error

Bits error versus g

Bits error versus a

Derivation

  1. Initial program 15.1

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

  3. Applied add-sqr-sqrt15.2

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

  4. Applied associate-*l*15.2

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

  5. Applied associate-/r*15.2

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

  6. Applied cbrt-div0.8

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

  8. Applied add-cube-cbrt0.9

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

  9. Applied sqrt-prod0.9

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

  10. Applied associate-/r*0.9

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

  11. Applied cbrt-div0.9

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

  12. Simplified0.9

    \[\leadsto \frac{\frac{\color{blue}{\sqrt[3]{\frac{g}{\left|\sqrt[3]{2}\right|}}}}{\sqrt[3]{\sqrt{\sqrt[3]{2}}}}}{\sqrt[3]{\sqrt{2} \cdot a}}\]
  13. Using strategy rm

  14. Applied *-un-lft-identity0.9

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

  15. Applied associate-/l*0.9

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

  16. Applied cbrt-div0.9

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

  17. Simplified0.9

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

  18. Final simplification0.9

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

Reproduce

herbie shell --seed 2019088 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))