Average Error: 15.6 → 0.8
Time: 4.8s
Precision: binary64
\[\sqrt[3]{\frac{g}{2 \cdot a}} \]
↓
\[\sqrt[3]{0.5} \cdot \left(\sqrt[3]{\frac{1}{a}} \cdot \sqrt[3]{g}\right) \]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{0.5} \cdot \left(\sqrt[3]{\frac{1}{a}} \cdot \sqrt[3]{g}\right)

(FPCore (g a) :precision binary64 (cbrt (/ g (* 2.0 a))))
↓
(FPCore (g a) :precision binary64 (* (cbrt 0.5) (* (cbrt (/ 1.0 a)) (cbrt g))))
double code(double g, double a) {
	return cbrt(g / (2.0 * a));
}
↓
double code(double g, double a) {
	return cbrt(0.5) * (cbrt(1.0 / a) * 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. Applied div-inv_binary6415.6

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

  3. Applied cbrt-prod_binary640.9

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

  4. Simplified0.8

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

  5. Applied *-commutative_binary640.8

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

  6. Applied div-inv_binary640.8

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

  7. Applied cbrt-prod_binary640.8

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

  8. Applied associate-*l*_binary640.8

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

  9. Final simplification0.8

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

Reproduce

herbie shell --seed 2021332 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))