2-ancestry mixing, zero discriminant

Average Error: 16.0 → 0.8

Time: 5.1s

Precision: binary64

Cost: 13248

Math

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

↓

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

FPCore

(FPCore (g a) :precision binary64 (cbrt (/ g (* 2.0 a))))

↓

(FPCore (g a) :precision binary64 (* (/ 1.0 (cbrt a)) (cbrt (* g 0.5))))

C

double code(double g, double a) {
	return cbrt((g / (2.0 * a)));
}

↓

double code(double g, double a) {
	return (1.0 / cbrt(a)) * cbrt((g * 0.5));
}

Java

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.cbrt((g * 0.5));
}

Julia

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

↓

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

Wolfram

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[(g * 0.5), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 16.0

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

2. Applied egg-rr 0.8

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

3. Applied egg-rr 0.8

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

4. Final simplification 0.8

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

Alternatives

Alternative 1
Error	0.8
Cost	13120

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

Alternative 2
Error	0.8
Cost	13120

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

Alternative 3
Error	0.9
Cost	13120

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

Alternative 4
Error	16.0
Cost	6848

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

Alternative 5
Error	16.4
Cost	6720

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

Alternative 6
Error	16.0
Cost	6720

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

Reproduce

herbie shell --seed 2022297 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))