Average Error: 15.8 → 0.8
Time: 3.9s
Precision: binary64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\sqrt[3]{g \cdot 0.5}}{\sqrt[3]{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\frac{\sqrt[3]{g \cdot 0.5}}{\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) (g * 0.5)))) / ((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 15.8

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

  3. Applied div-inv15.8

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

  4. Applied cbrt-prod0.9

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

  5. Taylor expanded around 0 33.9

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

  6. Simplified0.9

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

  8. Applied associate-*r/0.9

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

  10. Applied cbrt-unprod0.8

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

  11. Final simplification0.8

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

Reproduce

herbie shell --seed 2020184 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))