2-ancestry mixing, zero discriminant

Average Error: 15.7 → 0.8

Time: 5.5s

Precision: binary64

Cost: 19648

Math

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

↓

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

FPCore

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

↓

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

C

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)));
}

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

Julia

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

↓

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

Wolfram

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[0.5, 1/3], $MachinePrecision] * N[Power[N[(1.0 / a), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 15.7

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

2. Applied egg-rr 0.8

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

3. Applied egg-rr 0.8

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

4. Final simplification 0.8

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

Alternatives

Alternative 1
Error	0.9
Cost	13248

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

Alternative 2
Error	0.8
Cost	13120

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

Alternative 3
Error	0.9
Cost	13120

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

Alternative 4
Error	15.7
Cost	6848

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

Alternative 5
Error	16.2
Cost	6720

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

Alternative 6
Error	15.7
Cost	6720

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

Reproduce

herbie shell --seed 2022313 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))