Average Error: 15.3 → 0.8
Time: 2.3s
Precision: binary64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\left(\sqrt[3]{0.5} \cdot \sqrt[3]{g}\right) \cdot \sqrt[3]{\frac{1}{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\left(\sqrt[3]{0.5} \cdot \sqrt[3]{g}\right) \cdot \sqrt[3]{\frac{1}{a}}
(FPCore (g a) :precision binary64 (cbrt (/ g (* 2.0 a))))
↓
(FPCore (g a) :precision binary64 (* (* (cbrt 0.5) (cbrt g)) (cbrt (/ 1.0 a))))
double code(double g, double a) {
	return cbrt(g / (2.0 * a));
}
↓
double code(double g, double a) {
	return (cbrt(0.5) * cbrt(g)) * cbrt(1.0 / 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 15.3

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

  3. Applied div-inv_binary6415.3

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

  4. Applied cbrt-prod_binary640.9

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

  5. Simplified0.8

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

  7. Applied div-inv_binary640.8

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

  8. Applied cbrt-prod_binary640.8

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

  9. Applied associate-*r*_binary640.8

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

  10. Simplified0.8

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

  11. Final simplification0.8

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

Reproduce

herbie shell --seed 2020231 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))