Average Error: 15.5 → 0.9
Time: 3.7s
Precision: binary64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\left(\sqrt[3]{\sqrt[3]{0.25}} \cdot \sqrt[3]{g}\right) \cdot \sqrt[3]{\frac{\sqrt[3]{0.5}}{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\left(\sqrt[3]{\sqrt[3]{0.25}} \cdot \sqrt[3]{g}\right) \cdot \sqrt[3]{\frac{\sqrt[3]{0.5}}{a}}
(FPCore (g a) :precision binary64 (cbrt (/ g (* 2.0 a))))
↓
(FPCore (g a)
 :precision binary64
 (* (* (cbrt (cbrt 0.25)) (cbrt g)) (cbrt (/ (cbrt 0.5) a))))
double code(double g, double a) {
	return cbrt(g / (2.0 * a));
}
↓
double code(double g, double a) {
	return (cbrt(cbrt(0.25)) * cbrt(g)) * cbrt(cbrt(0.5) / 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 15.5

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

  3. Applied div-inv_binary64_314415.5

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

  4. Applied cbrt-prod_binary64_31780.9

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

  5. Simplified0.8

    \[\leadsto \sqrt[3]{g} \cdot \color{blue}{\sqrt[3]{\frac{0.5}{a}}}\]
  6. Using strategy rm

  7. Applied *-un-lft-identity_binary64_31470.8

    \[\leadsto \sqrt[3]{g} \cdot \sqrt[3]{\frac{0.5}{\color{blue}{1 \cdot a}}}\]

  8. Applied add-cube-cbrt_binary64_31820.8

    \[\leadsto \sqrt[3]{g} \cdot \sqrt[3]{\frac{\color{blue}{\left(\sqrt[3]{0.5} \cdot \sqrt[3]{0.5}\right) \cdot \sqrt[3]{0.5}}}{1 \cdot a}}\]

  9. Applied times-frac_binary64_31530.8

    \[\leadsto \sqrt[3]{g} \cdot \sqrt[3]{\color{blue}{\frac{\sqrt[3]{0.5} \cdot \sqrt[3]{0.5}}{1} \cdot \frac{\sqrt[3]{0.5}}{a}}}\]

  10. Applied cbrt-prod_binary64_31780.9

    \[\leadsto \sqrt[3]{g} \cdot \color{blue}{\left(\sqrt[3]{\frac{\sqrt[3]{0.5} \cdot \sqrt[3]{0.5}}{1}} \cdot \sqrt[3]{\frac{\sqrt[3]{0.5}}{a}}\right)}\]

  11. Applied associate-*r*_binary64_30870.9

    \[\leadsto \color{blue}{\left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{\sqrt[3]{0.5} \cdot \sqrt[3]{0.5}}{1}}\right) \cdot \sqrt[3]{\frac{\sqrt[3]{0.5}}{a}}}\]

  12. Simplified0.9

    \[\leadsto \color{blue}{\left(\sqrt[3]{\sqrt[3]{0.5} \cdot \sqrt[3]{0.5}} \cdot \sqrt[3]{g}\right)} \cdot \sqrt[3]{\frac{\sqrt[3]{0.5}}{a}}\]
  13. Using strategy rm

  14. Applied add-cbrt-cube_binary64_31830.9

    \[\leadsto \left(\sqrt[3]{\color{blue}{\sqrt[3]{\left(\left(\sqrt[3]{0.5} \cdot \sqrt[3]{0.5}\right) \cdot \left(\sqrt[3]{0.5} \cdot \sqrt[3]{0.5}\right)\right) \cdot \left(\sqrt[3]{0.5} \cdot \sqrt[3]{0.5}\right)}}} \cdot \sqrt[3]{g}\right) \cdot \sqrt[3]{\frac{\sqrt[3]{0.5}}{a}}\]

  15. Simplified0.9

    \[\leadsto \left(\sqrt[3]{\sqrt[3]{\color{blue}{0.25}}} \cdot \sqrt[3]{g}\right) \cdot \sqrt[3]{\frac{\sqrt[3]{0.5}}{a}}\]

  16. Final simplification0.9

    \[\leadsto \left(\sqrt[3]{\sqrt[3]{0.25}} \cdot \sqrt[3]{g}\right) \cdot \sqrt[3]{\frac{\sqrt[3]{0.5}}{a}}\]

Reproduce

herbie shell --seed 2020358 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))