2-ancestry mixing, zero discriminant

Average Error: 24.65% → 1.32%

Time: 5.9s

Precision: binary64

Cost: 13248

Math

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

↓

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

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(1.0 / Float64(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[(1.0 / N[(N[Power[a, 1/3], $MachinePrecision] / N[Power[N[(g * 0.5), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 24.65

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

2. Applied egg-rr 24.58

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

3. Applied egg-rr 1.35

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

4. Simplified 1.32

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

   [Start] 1.35	\[ \frac{1}{\sqrt[3]{a} \cdot \frac{1}{\sqrt[3]{g \cdot 0.5}}} \]
   associate-*r/ [=>] 1.32	\[ \frac{1}{\color{blue}{\frac{\sqrt[3]{a} \cdot 1}{\sqrt[3]{g \cdot 0.5}}}} \]
   associate-*l/ [<=] 1.32	\[ \frac{1}{\color{blue}{\frac{\sqrt[3]{a}}{\sqrt[3]{g \cdot 0.5}} \cdot 1}} \]
   *-rgt-identity [=>] 1.32	\[ \frac{1}{\color{blue}{\frac{\sqrt[3]{a}}{\sqrt[3]{g \cdot 0.5}}}} \]

5. Final simplification 1.32

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

Alternatives

Alternative 1
Error	1.31%
Cost	13120

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

Alternative 2
Error	1.3%
Cost	13120

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

Alternative 3
Error	24.59%
Cost	6848

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

Alternative 4
Error	24.58%
Cost	6848

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

Alternative 5
Error	24.65%
Cost	6720

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

Reproduce

herbie shell --seed 2023101 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))