Average Error: 15.3 → 0.9
Time: 3.6s
Precision: binary64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\sqrt[3]{g \cdot {\left(\sqrt[3]{0.5}\right)}^{3}}}{\sqrt[3]{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\frac{\sqrt[3]{g \cdot {\left(\sqrt[3]{0.5}\right)}^{3}}}{\sqrt[3]{a}}
(FPCore (g a) :precision binary64 (cbrt (/ g (* 2.0 a))))
↓
(FPCore (g a)
 :precision binary64
 (/ (cbrt (* g (pow (cbrt 0.5) 3.0))) (cbrt a)))
double code(double g, double a) {
	return cbrt(g / (2.0 * a));
}
↓
double code(double g, double a) {
	return cbrt(g * pow(cbrt(0.5), 3.0)) / cbrt(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 cbrt-div_binary640.9

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

  8. Applied associate-*r/_binary640.9

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

  9. Simplified0.9

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

  11. Applied add-cbrt-cube_binary641.0

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

  12. Simplified0.9

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

  13. Final simplification0.9

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

Alternatives

Reproduce

herbie shell --seed 2021118 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))