Average Error: 15.6 → 0.8
Time: 1.6s
Precision: binary64
\[\sqrt[3]{\frac{g}{2 \cdot a}} \]
↓
\[\frac{\sqrt[3]{g \cdot 0.5}}{\sqrt[3]{a}} \]
(FPCore (g a) :precision binary64 (cbrt (/ g (* 2.0 a))))
↓
(FPCore (g a) :precision binary64 (/ (cbrt (* g 0.5)) (cbrt a)))
double code(double g, double a) {
	return cbrt((g / (2.0 * a)));
}
↓
double code(double g, double a) {
	return cbrt((g * 0.5)) / cbrt(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 * 0.5)) / Math.cbrt(a);
}

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

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

\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\frac{\sqrt[3]{g \cdot 0.5}}{\sqrt[3]{a}}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.6

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

  2. Applied egg-rr0.8

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

  3. Final simplification0.8

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

Reproduce

herbie shell --seed 2022197 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))