Average Error: 15.3 → 0.8
Time: 5.9s
Precision: binary64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{1}{\frac{\sqrt[3]{a}}{\sqrt[3]{0.5 \cdot g}}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\frac{1}{\frac{\sqrt[3]{a}}{\sqrt[3]{0.5 \cdot g}}}
(FPCore (g a) :precision binary64 (cbrt (/ g (* 2.0 a))))
↓
(FPCore (g a) :precision binary64 (/ 1.0 (/ (cbrt a) (cbrt (* 0.5 g)))))
double code(double g, double a) {
	return cbrt(g / (2.0 * a));
}
↓
double code(double g, double a) {
	return 1.0 / (cbrt(a) / cbrt(0.5 * g));
}

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_binary64_143915.3

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

  4. Applied cbrt-prod_binary64_14730.9

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

  5. Simplified0.8

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

  7. Applied cbrt-div_binary64_14740.9

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

  8. Applied associate-*r/_binary64_13840.9

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

  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_binary64_14781.0

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

  12. Simplified0.9

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

  14. Applied clear-num_binary64_14410.9

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

  15. Simplified0.8

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

  16. Final simplification0.8

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

Reproduce

herbie shell --seed 2021064 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))