Average Error: 15.7 → 0.9
Time: 3.9s
Precision: binary64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{g} \cdot \left(\sqrt[3]{\sqrt{0.5}} \cdot \sqrt[3]{\frac{\sqrt{0.5}}{a}}\right)\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{g} \cdot \left(\sqrt[3]{\sqrt{0.5}} \cdot \sqrt[3]{\frac{\sqrt{0.5}}{a}}\right)
(FPCore (g a) :precision binary64 (cbrt (/ g (* 2.0 a))))
↓
(FPCore (g a)
 :precision binary64
 (* (cbrt g) (* (cbrt (sqrt 0.5)) (cbrt (/ (sqrt 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(sqrt(0.5)) * cbrt(sqrt(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 15.7

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

  3. Applied div-inv_binary64_553115.7

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

  4. Applied cbrt-prod_binary64_55650.9

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

  5. Simplified0.8

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

  7. Applied *-un-lft-identity_binary64_55340.8

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

  8. Applied add-sqr-sqrt_binary64_55560.8

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

  9. Applied times-frac_binary64_55400.8

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

  10. Applied cbrt-prod_binary64_55650.9

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

  11. Simplified0.9

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

  12. Final simplification0.9

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

Reproduce

herbie shell --seed 2020353 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))