Average Error: 15.5 → 0.8
Time: 3.1s
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 15.5

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

  3. Applied div-inv_binary6415.5

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

  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 pow1_binary640.8

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

  8. Applied pow1_binary640.8

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

  9. Applied pow-prod-down_binary640.8

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

  10. Final simplification0.8

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

Reproduce

herbie shell --seed 2021190 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))