Average Error: 15.7 → 0.8
Time: 7.8s
Precision: binary64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{g} \cdot \sqrt[3]{\frac{{\left(\sqrt[3]{0.5}\right)}^{3}}{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{g} \cdot \sqrt[3]{\frac{{\left(\sqrt[3]{0.5}\right)}^{3}}{a}}
(FPCore (g a) :precision binary64 (cbrt (/ g (* 2.0 a))))
↓
(FPCore (g a)
 :precision binary64
 (* (cbrt g) (cbrt (/ (pow (cbrt 0.5) 3.0) a))))
double code(double g, double a) {
	return cbrt(g / (2.0 * a));
}
↓
double code(double g, double a) {
	return cbrt(g) * cbrt(pow(cbrt(0.5), 3.0) / 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 15.7

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

  3. Applied div-inv_binary64_212115.7

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

  4. Applied cbrt-prod_binary64_21550.9

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

  5. Simplified0.8

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

  6. Taylor expanded around 0 35.2

    \[\leadsto \sqrt[3]{g} \cdot \color{blue}{\left({\left(\frac{1}{a}\right)}^{0.3333333333333333} \cdot \sqrt[3]{0.5}\right)}\]

  7. Simplified0.9

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

  9. Applied add-cbrt-cube_binary64_21601.0

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

  10. Simplified0.8

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

  11. Final simplification0.8

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

Reproduce

herbie shell --seed 2021028 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))