Average Error: 16.0 → 0.9
Time: 2.6s
Precision: binary64
\[\sqrt[3]{\frac{g}{2 \cdot a}} \]
↓
\[\sqrt[3]{0.5} \cdot \left(\sqrt[3]{\frac{-1}{a}} \cdot \sqrt[3]{-g}\right) \]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{0.5} \cdot \left(\sqrt[3]{\frac{-1}{a}} \cdot \sqrt[3]{-g}\right)

(FPCore (g a) :precision binary64 (cbrt (/ g (* 2.0 a))))
↓
(FPCore (g a)
 :precision binary64
 (* (cbrt 0.5) (* (cbrt (/ -1.0 a)) (cbrt (- g)))))
double code(double g, double a) {
	return cbrt(g / (2.0 * a));
}
↓
double code(double g, double a) {
	return cbrt(0.5) * (cbrt(-1.0 / a) * cbrt(-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 16.0

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

  3. Applied div-inv_binary6416.1

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

  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 div-inv_binary640.9

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

  8. Applied cbrt-prod_binary640.9

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

  9. Applied associate-*r*_binary640.9

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

  10. Simplified0.9

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

  12. Applied add-cbrt-cube_binary641.0

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

  13. Simplified0.9

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

  14. Taylor expanded around -inf 49.3

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

  15. Simplified0.9

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

  16. Final simplification0.9

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

Reproduce

herbie shell --seed 2021205 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))