Average Error: 15.1 → 0.9
Time: 4.4s
Precision: binary64
\[\sqrt[3]{\frac{g}{2 \cdot a}} \]
↓
\[\sqrt[3]{g} \cdot \left(\sqrt[3]{\sqrt[3]{0.5} \cdot \sqrt[3]{0.5}} \cdot \sqrt[3]{\frac{\sqrt[3]{0.5}}{a}}\right) \]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{g} \cdot \left(\sqrt[3]{\sqrt[3]{0.5} \cdot \sqrt[3]{0.5}} \cdot \sqrt[3]{\frac{\sqrt[3]{0.5}}{a}}\right)

(FPCore (g a) :precision binary64 (cbrt (/ g (* 2.0 a))))
↓
(FPCore (g a)
 :precision binary64
 (* (cbrt g) (* (cbrt (* (cbrt 0.5) (cbrt 0.5))) (cbrt (/ (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(cbrt(0.5) * cbrt(0.5)) * cbrt(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 15.1

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

  2. Applied div-inv_binary6415.1

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

  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 *-un-lft-identity_binary640.8

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

  6. Applied add-cube-cbrt_binary640.8

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

  7. Applied times-frac_binary640.9

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

  8. Applied cbrt-prod_binary640.9

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

  9. Simplified0.9

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

  10. Applied *-un-lft-identity_binary640.9

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

  11. Final simplification0.9

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

Reproduce

herbie shell --seed 2021329 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))