Average Error: 15.6 → 0.9
Time: 3.4s
Precision: binary64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\sqrt[3]{\frac{0.5}{a}}}{\frac{1}{\sqrt[3]{g}}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\frac{\sqrt[3]{\frac{0.5}{a}}}{\frac{1}{\sqrt[3]{g}}}
(FPCore (g a) :precision binary64 (cbrt (/ g (* 2.0 a))))
↓
(FPCore (g a) :precision binary64 (/ (cbrt (/ 0.5 a)) (/ 1.0 (cbrt g))))
double code(double g, double a) {
	return ((double) cbrt((g / ((double) (2.0 * a)))));
}
↓
double code(double g, double a) {
	return (((double) cbrt((0.5 / a))) / (1.0 / ((double) cbrt(g))));
}

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 15.6

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

  3. Applied cbrt-div_binary640.8

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

  5. Applied clear-num_binary640.8

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

  7. Applied div-inv_binary640.9

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

  8. Applied associate-/r*_binary640.9

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

  10. Applied add-cbrt-cube_binary640.9

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

  11. Applied cbrt-undiv_binary640.9

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

  12. Simplified0.9

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

  13. Final simplification0.9

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

Reproduce

herbie shell --seed 2020210 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))