Average Error: 15.5 → 0.9
Time: 3.1s
Precision: binary64
\[\sqrt[3]{\frac{g}{2 \cdot a}} \]
↓
\[\left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{-1}{a}}\right) \cdot \sqrt[3]{-0.5} \]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{-1}{a}}\right) \cdot \sqrt[3]{-0.5}

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

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 15.5

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

  3. Applied div-inv_binary6415.6

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

  4. Applied cbrt-prod_binary640.9

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

  5. Simplified0.9

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

  6. Taylor expanded around -inf 34.8

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

  7. Simplified0.9

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

  9. Applied associate-*r*_binary640.9

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

  10. Final simplification0.9

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

Reproduce

herbie shell --seed 2021207 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))