Average Error: 15.9 → 0.9
Time: 1.6s
Precision: binary64
\[\sqrt[3]{\frac{g}{2 \cdot a}} \]
↓
\[\frac{1}{\sqrt[3]{a}} \cdot {\left(\frac{1}{\sqrt[3]{g \cdot 0.5}}\right)}^{-1} \]
(FPCore (g a) :precision binary64 (cbrt (/ g (* 2.0 a))))
↓
(FPCore (g a)
 :precision binary64
 (* (/ 1.0 (cbrt a)) (pow (/ 1.0 (cbrt (* g 0.5))) -1.0)))
double code(double g, double a) {
	return cbrt((g / (2.0 * a)));
}
↓
double code(double g, double a) {
	return (1.0 / cbrt(a)) * pow((1.0 / cbrt((g * 0.5))), -1.0);
}

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

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

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

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

Error

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Your Program's Arguments

Results

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Derivation

  1. Initial program 15.9

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

  2. Applied egg-rr0.8

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

  3. Applied egg-rr0.8

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

  4. Applied egg-rr0.8

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

  5. Applied egg-rr0.9

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

  6. Final simplification0.9

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

Reproduce

herbie shell --seed 2022211 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))