Average Error: 15.4 → 0.8
Time: 4.2s
Precision: binary64
\[\sqrt[3]{\frac{g}{2 \cdot a}} \]
↓
\[\sqrt[3]{g} \cdot \sqrt[3]{\frac{0.5}{a}} \]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{g} \cdot \sqrt[3]{\frac{0.5}{a}}

(FPCore (g a) :precision binary64 (cbrt (/ g (* 2.0 a))))
↓
(FPCore (g a) :precision binary64 (* (cbrt g) (cbrt (/ 0.5 a))))
double code(double g, double a) {
	return cbrt((g / (2.0 * a)));
}
↓
double code(double g, double a) {
	return cbrt(g) * 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 15.4

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

  2. Applied div-inv_binary6415.4

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

  3. Applied cbrt-prod_binary640.8

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

  4. Simplified0.8

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

  5. Applied *-un-lft-identity_binary640.8

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

  6. Applied *-un-lft-identity_binary640.8

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

  7. Applied times-frac_binary640.8

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

  8. Applied cbrt-prod_binary640.8

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

  9. Final simplification0.8

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

Reproduce

herbie shell --seed 2022160 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))