Average Error: 15.3 → 0.8
Time: 3.9s
Precision: binary64
\[\sqrt[3]{\frac{g}{2 \cdot a}} \]
↓
\[\sqrt[3]{0.5} \cdot \left(\sqrt[3]{-g} \cdot \sqrt[3]{\frac{-1}{a}}\right) \]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{0.5} \cdot \left(\sqrt[3]{-g} \cdot \sqrt[3]{\frac{-1}{a}}\right)

(FPCore (g a) :precision binary64 (cbrt (/ g (* 2.0 a))))
↓
(FPCore (g a)
 :precision binary64
 (* (cbrt 0.5) (* (cbrt (- g)) (cbrt (/ -1.0 a)))))
double code(double g, double a) {
	return cbrt((g / (2.0 * a)));
}
↓
double code(double g, double a) {
	return cbrt(0.5) * (cbrt(-g) * cbrt((-1.0 / 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 15.3

    \[\sqrt[3]{\frac{g}{2 \cdot a}} \]

  2. Applied egg-rr0.8

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

  3. Taylor expanded in a around -inf 49.1

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

  4. Simplified0.8

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

  5. Final simplification0.8

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

Reproduce

herbie shell --seed 2022125 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))