Average Error: 15.8 → 0.8
Time: 4.3s
Precision: binary64
\[\sqrt[3]{\frac{g}{2 \cdot a}} \]
↓
\[\left(\sqrt[3]{g} \cdot \sqrt[3]{0.5}\right) \cdot \sqrt[3]{\frac{1}{a}} \]
(FPCore (g a) :precision binary64 (cbrt (/ g (* 2.0 a))))
↓
(FPCore (g a) :precision binary64 (* (* (cbrt g) (cbrt 0.5)) (cbrt (/ 1.0 a))))
double code(double g, double a) {
	return cbrt((g / (2.0 * a)));
}
↓
double code(double g, double a) {
	return (cbrt(g) * cbrt(0.5)) * cbrt((1.0 / a));
}

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(0.5)) * Math.cbrt((1.0 / a));
}

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

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

\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\left(\sqrt[3]{g} \cdot \sqrt[3]{0.5}\right) \cdot \sqrt[3]{\frac{1}{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 15.8

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

  2. Applied div-inv_binary6415.8

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

  3. Applied cbrt-prod_binary640.9

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

  4. Simplified0.8

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

  5. Applied div-inv_binary640.8

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

  6. Applied cbrt-prod_binary640.9

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

  7. Applied associate-*r*_binary640.8

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

  8. Final simplification0.8

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

Reproduce

herbie shell --seed 2022129 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))