Average Error: 16.0 → 0.8
Time: 3.3s
Precision: binary64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{g} \cdot \left(\sqrt[3]{-0.5} \cdot \sqrt[3]{\frac{-1}{a}}\right)\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{g} \cdot \left(\sqrt[3]{-0.5} \cdot \sqrt[3]{\frac{-1}{a}}\right)
double code(double g, double a) {
	return ((double) cbrt(((double) (g / ((double) (2.0 * a))))));
}
↓
double code(double g, double a) {
	return ((double) (((double) cbrt(g)) * ((double) (((double) cbrt(-0.5)) * ((double) cbrt(((double) (-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 16.0

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

  3. Applied div-inv16.0

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

  4. Applied cbrt-prod0.9

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

  5. Taylor expanded around -inf 34.3

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

  6. Simplified0.8

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

  7. Final simplification0.8

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

Reproduce

herbie shell --seed 2020185 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))