Average Error: 15.9 → 0.9
Time: 4.1s
Precision: binary64
\[\sqrt[3]{\frac{g}{2 \cdot a}} \]
↓
\[\sqrt[3]{g} \cdot \left(\sqrt[3]{\frac{-1}{a}} \cdot \sqrt[3]{-0.5}\right) \]
(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));
}

public static double code(double g, double a) {
	return Math.cbrt((g / (2.0 * a)));
}
↓
public static double code(double g, double a) {
	return Math.cbrt(g) * (Math.cbrt((-1.0 / a)) * Math.cbrt(-0.5));
}

function code(g, a)
	return cbrt(Float64(g / Float64(2.0 * a)))
end
↓
function code(g, a)
	return Float64(cbrt(g) * Float64(cbrt(Float64(-1.0 / a)) * cbrt(-0.5)))
end

code[g_, a_] := N[Power[N[(g / N[(2.0 * a), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]
↓
code[g_, a_] := N[(N[Power[g, 1/3], $MachinePrecision] * N[(N[Power[N[(-1.0 / a), $MachinePrecision], 1/3], $MachinePrecision] * N[Power[-0.5, 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{g} \cdot \left(\sqrt[3]{\frac{-1}{a}} \cdot \sqrt[3]{-0.5}\right)

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 15.9

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

  2. Applied egg-rr0.8

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

  3. Taylor expanded in a around -inf 34.5

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

  4. Simplified0.9

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

  5. Final simplification0.9

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

Reproduce

herbie shell --seed 2022151 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))