Average Error: 17.4 → 1.2
Time: 4.9s
Precision: binary64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{\sqrt[3]{g} \cdot \left(\sqrt[3]{\sqrt[3]{g} \cdot \sqrt[3]{g}} \cdot \sqrt[3]{\sqrt[3]{g}}\right)}{2}} \cdot \frac{\sqrt[3]{\sqrt[3]{g}}}{\sqrt[3]{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\frac{\sqrt[3]{g} \cdot \left(\sqrt[3]{\sqrt[3]{g} \cdot \sqrt[3]{g}} \cdot \sqrt[3]{\sqrt[3]{g}}\right)}{2}} \cdot \frac{\sqrt[3]{\sqrt[3]{g}}}{\sqrt[3]{a}}
double code(double g, double a) {
	return ((double) cbrt(((double) (g / ((double) (2.0 * a))))));
}
↓
double code(double g, double a) {
	return ((double) (((double) cbrt(((double) (((double) (((double) cbrt(g)) * ((double) (((double) cbrt(((double) (((double) cbrt(g)) * ((double) cbrt(g)))))) * ((double) cbrt(((double) cbrt(g)))))))) / 2.0)))) * ((double) (((double) cbrt(((double) cbrt(g)))) / ((double) cbrt(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 17.4

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

  3. Applied add-cube-cbrt17.6

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

  4. Applied times-frac17.6

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

  5. Applied cbrt-prod6.3

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

  7. Applied cbrt-div1.1

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

  9. Applied add-cube-cbrt1.2

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

  10. Applied cbrt-prod1.2

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

  11. Final simplification1.2

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

Reproduce

herbie shell --seed 2020157 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))