2-ancestry mixing, zero discriminant

Average Error: 24.54% → 1.31%

Time: 5.7s

Precision: binary64

Cost: 13120

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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((a * 2.0));
}

Julia

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

↓

function code(g, a)
	return Float64(cbrt(g) / cbrt(Float64(a * 2.0)))
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[Power[N[(a * 2.0), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 24.54

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

2. Applied egg-rr 1.35

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

3. Simplified 1.31

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

   [Start] 1.35	\[ \sqrt[3]{g} \cdot \frac{1}{\sqrt[3]{2 \cdot a}} \]
   associate-*r/ [=>] 1.31	\[ \color{blue}{\frac{\sqrt[3]{g} \cdot 1}{\sqrt[3]{2 \cdot a}}} \]
   *-rgt-identity [=>] 1.31	\[ \frac{\color{blue}{\sqrt[3]{g}}}{\sqrt[3]{2 \cdot a}} \]
   *-commutative [=>] 1.31	\[ \frac{\sqrt[3]{g}}{\sqrt[3]{\color{blue}{a \cdot 2}}} \]

4. Final simplification 1.31

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

Alternatives

Alternative 1
Error	1.31%
Cost	13120

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

Alternative 2
Error	24.53%
Cost	6720

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

Alternative 3
Error	24.54%
Cost	6720

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

Reproduce

herbie shell --seed 2023093 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))